Young's experiment [Archive]

nightlight

Sep27-04, 03:16 PM

ZapperZThe source you are citing has major confusion about the subtle part of the experiment. Please refer to this one below and see if it is any clearer.

http://www.optica.tn.tudelft.nl/education/photons.asp

Zz.
Detail from that page:

To generate the coherent light needed for this experiment a He-Ne laser was used, with an average wavelength of 632.8nm.

The problem is that even the most ideal laser light cannot show any non-classical effect here. Namely, if you were to place one detector behind each slit, the trigger by detector A does not exclude trigger by detector B since the laser light has Poisson distribution -- each detector triggers on its own whether or not the other one triggered (no collapse occurs). There is an old theorem of Sudarshan on this very question (the result also appears in a more elaborate paper from that same year by Roy Glauber, which is a foundations of Quantum Optics):

E.C.G. Sudarshan "The equivalence of semiclassical and quantum mechanical descriptions of statistical light beams" Phys. Rev. Lett., Vol 10(7), pp. 277-279, 1963.

Roy Glauber "The Quantum Theory of Optical Coherence" Phys. Rev., Vol 130(6), pp. 2529-2539, 1963.

Sudarshan shows that correlations among the trigger counts of any number of detectors are perfectly consistent with classical wave picture, i.e. you can think of a detector as simply thresholding the energy of the superposed incoming wave packet fragment (A or B) with the local field fluctuations, and triggering (or not triggering) based on these purely local causes, regardless of what the other detector did.

Thus there is nothing in these experiments that would surprise a 19th century physicist (other than technology itself). The students are usually confused by the lose claim that there is a "particle" which always goes one way or the other. If one thinks of two equal wave fragments and detector thresholding (after superposition with local field fluctuations), there is nothing in the experiment that is mysterious.

Even the much stricter non-classicality test, such as Bell's inequality experiments are still fully explicable with this kind of simple classical models (usually acknowledged via euphemisms: "detection loophole" or "fair sampling loophole"). You can check the earlier thread here (http://www.physicsforums.com/showthread.php?t=12311) where I posted more details and references, along with the discussions.

ZapperZ

Sep27-04, 04:19 PM

nightlight

Sep27-04, 05:05 PM

ZapperZ I'm not sure what your point here. Are you trying to say that there are no photons? Or are you trying to convey that the interference phenomena are purely due to classical waves?

I am saying that nothing in the experiment shows that one has to imagine a particle, thus the common "paradoxical" description is misleading. All their frame-by-frame pictures show is precisely the kind of discretization a 19th century physicist would expect to see if a detector thresholds the energy of incoming perfectly classical wave packet superposed with the local field fluctuations.

It does not show (and can't show since it isn't true) what is commonly claimed or hinted at in popular or "pedagogical" literature, which is that if you were to place two detectors, A and B, one behind each slit, that a trigger of A automatically excludes trigger of B (which would be a particle-like behavior, called "collapse" of wave function or a projection postulate in QM "measurement theory"). You get all 4 combinations of triggers (0,0), (0,1), (1,0) and (1,1) of (A,B). That is the prediction of Quantum Optics (see Sudarshan & Glauber papers) and also what the experiment shows. No wave collapse of B-wave fragment occurs when detector A triggers. The data and the Quntum Optics prediction here are perfectly classical.

What if I can show that ALL wave phenomena of light can also be described via the photon picuture? Then what? Is there an experiment that can clearly distinguish between the two? (This is not a trick question since I have already mentioned it a few times.)

The double-slit experiment doesn't show anything particle-like (the apparent discreteness is an artifact of detector trigger decision thresholding/discretization, which is the point of the Sudarshan's theorem).

Of course, you can simulate any wave field phenomena as a macroscopic/collective effect of many particles at a finer scale. Similarly, you can simulate particle behaviors with a microscopic wave fields in wave packets.

Whether fundamental entities are particles or waves has nothing to do with the double-slit experiment claims (in "pedagogical" and popular literature) -- no dual nature is shown by the experiment. All that is shown is consistent with a discretized detection of a wave phenomenon.

The detection loophole is well-known. If we have no such loophole, the EPR-type experiment would be a done deal. It is why we have to deal with the statistics of large number of data to be able to know how many standard deviation the results deviate from classical predictions. If we are not encumbered by such loophole, we could in principle just do one measurement and be done with.

That's incorrect characterization. The standard deviations have no relation with the detection or the fair sampling "loophole" -- they could have million times as many data points and thousand times as many standard deviation "accuracy" without touching the main problem (that the 90% of data isn't measured and that they assume ad hoc certain properties of the missing data). Check the earlier thread (http://www.physicsforums.com/showthread.php?t=12311) where this was discussed in detail and with references.

ZapperZ

Sep27-04, 05:19 PM

nightlight

Sep27-04, 06:19 PM

ZapperZ I didn't realize that this thread was about answering the validity of the photon picture.

It got there after some discussion of the Bell inequality experiments.

So you are asserting that if I stick to the photon picture, I cannot explain all the so-called wavelike observation as in the double slit expt.?

I am saying that if you put separate detectors A and B at each slit you will not obtain the usually claimed detection exclusivity that a single particle going through slit A or slit B would produce. The detector A trigger has no effect on the probability of trigger of B. The usual claim is that when the detector A triggers, the wave function in the region B somehow collapses, making detector B silent for that try. That is not what happens. The triggers of B are statistically independent from the triggers on A on each "try" (e.g. if you open & close the light shutter quickly enough for each "try" so that on average a single event is dected per try).

See T. Marcella, Eur. J. Phys., v.23, p.615 (2002).

He is using standard scattering amplitudes, i.e. analyzing the behavior of an extended object, wave, which spans both slits. Keep also in mind that you can affect the interference picture in a predictable manner by placing various optical phase delay devices on each path. That implies that a full phenomenon does involve two physical wave fragments propagating via separate paths, interacting with other objects along the way.

If you had a single particle going always via a single path, it would be insensitive to the relative phase delays of the two paths. The usual Quantum Optics solution is that the source produces Poisson distribution of the photons, with an average of 1 photon per try, although in each try there could be zero, one, two, three... etc photons. That kind of "particle" picture can account for these phase delay phenomena on two paths, but that is what makes it equivalent to classical picture as well.

So now we have, at best, the same set of experiments with two different explanations. Just because wavelike picture came first doesn't mean it is right, and just because photon picture came later, doesn't mean that is correct. Again, my question was, is there ANY other experiments that can clearly distinguish between the two and pick out where one deviates from the other? This, you did not answer.

You don't have a picture of a precisely 1 particle on each try producing the full set of double-slit phenomena (including replicating interference effects of the separate phase delays on each path). You can have a picture of "particles" provided you also assume that the particle number is not controllable, and that it is uncontrollable to exactly such degree that the detector triggers are precisely same as if a simple wave has split in two equal parts, each of which triggers its own detector independently of the other.

Thus the particle model with the uncontrollable particle number is more redundant explanation since you need a separate rule or a model to explain why is the particle number uncontrollable in exactly such way to mimick the wave behavior in detector trigger statistics.

The double-slit experiment is a weak criteria (from the early days of QM) to decide the question. The Bell's experiment was supposed to provide a sharper crietira, but so far it hasn't supported the "collapse" (of two particle state).

ZapperZ

Sep27-04, 06:50 PM

ZapperZ I didn't realize that this thread was about answering the validity of the photon picture.

It got there after some discussion of the Bell inequality experiments.

Sorry? I could have sworn the original question was on the double slit experiment, and that was what the webpage I replied with was also demonstrating. Where did Bell inequality came in?

So you are asserting that if I stick to the photon picture, I cannot explain all the so-called wavelike observation as in the double slit expt.?

I am saying that if you put separate detectors A and B at each slit you will not obtain the usually claimed detection exclusivity that a single particle going through slit A or slit B would produce. The detector A trigger has no effect on the probability of trigger of B. The usual claim is that when the detector A triggers, the wave function in the region B somehow collapses, making detector B silent for that try. That is not what happens. The triggers of B are statistically independent from the triggers on A on each "try" (e.g. if you open & close the light shutter quickly enough for each "try" so that on average a single event is dected per try).

See T. Marcella, Eur. J. Phys., v.23, p.615 (2002).

He is using standard scattering amplitudes, i.e. analyzing the behavior of an extended object, wave, which spans both slits. Keep also in mind that you can affect the interference picture in a predictable manner by placing various optical phase delay devices on each path. That implies that a full phenomenon does involve two physical wave fragments propagating via separate paths, interacting with other objects along the way.

If you had a single particle going always via a single path, it would be insensitive to the relative phase delays of the two paths. The usual Quantum Optics solution is that the source produces Poisson distribution of the photons, with an average of 1 photon per try, although in each try there could be zero, one, two, three... etc photons. That kind of "particle" picture can account for these phase delay phenomena on two paths, but that is what makes it equivalent to classical picture as well.

So now we have, at best, the same set of experiments with two different explanations. Just because wavelike picture came first doesn't mean it is right, and just because photon picture came later, doesn't mean that is correct. Again, my question was, is there ANY other experiments that can clearly distinguish between the two and pick out where one deviates from the other? This, you did not answer.

You don't have a picture of a precisely 1 particle on each try producing the full set of double-slit phenomena (including replicating interference effects of the separate phase delays on each path). You can have a picture of "particles" provided you also assume that the particle number is not controllable, and that it is uncontrollable to exactly such degree that the detector triggers are precisely same as if a simple wave has split in two equal parts, each of which triggers its own detector independently of the other.

Thus the particle model with the uncontrollable particle number is more redundant explanation since you need a separate rule or a model to explain why is the particle number uncontrollable in exactly such way to mimick the wave behavior in detector trigger statistics.

The double-slit experiment is a weak criteria (from the early days of QM) to decide the question. The Bell's experiment was supposed to provide a sharper crietira, but so far it hasn't supported the "collapse" (of two particle state).

You lost me in this one. What detectors? The interference phenomena as described with photons/electrons/neutrons/etc. are NOT about these "particles", but rather the superpostion of all the possible paths! It isn't the issue of one particle going through either slit, it's the issue of the possible path interfering, creating the often misleading impression that a single particle is interfereing with itself. A single-particle interference is NOT the same as a 2-particle interference.

Again, I have NO IDEA how this thread degenerated into a question of the validity of photons.

If you have a solid argument against it, then let me request that you read this paper:

J.J. Thorn et al., Am. J. Phys., v.72, p.1210 (2004).

The abstract is in one of my postings in my Journals section. If you believe the analysis and conclusion is faulty, please send either a rebuttal or a followup paper to AJP. This isn't a PRL or Science or Nature, so it shouldn't be as difficult to get published there. THEN we'll talk.

Zz.

Roberth

Sep27-04, 07:00 PM

nightlight

Sep27-04, 07:55 PM

If you have a solid argument against it, then let me request that you read this paper:

J.J. Thorn et al., Am. J. Phys., v.72, p.1210 (2004).

There is a semiclassical model of PDC sources (http://cul.arxiv.org/abs/quant-ph/0202097) (Stochastic Optics) which J.J. Thorn had used (just as there are for regular laser and thermal sources, as was known since Sudarshan-Glauber results from 1963).

Therefore the detection statistics and correlations for any number of detectors (and any number of optical elements) for the field from such source can always be replicated exactly by a semi-classical model. What euphemisms these latest folks have used for their particular form of ad-hockery for the missing data to make what's left look as absolutely non-classical is of as much importance as trying to take apart the latest claimed perpetuum mobile device or random data compressor.

That whole "Quantum Mystery Cult" is a dead horse of no importance to anybody or anything outside that particular tiny mutual back-patting society. That parasitic branch of pseudo-physics has never produced anything but 70+ years of (very) loud fast-talking to bedazzle the young and ignorant.

Nothing, no technology no phenomenon no day-to-day physics, was ever found to depend or require in any way their imaginary "collapse/projection postulate" (or its corollary, the Bell's theorem). The dynamical equations (of QM and QED/QFT) and Born postulate is what does the work. (See the thread mentioned earlier (http://www.physicsforums.com/showthread.php?t=12311) for the explanation of these statements.)

Cruithne

Sep28-04, 02:53 AM

The source you are citing has major confusion about the subtle part of the experiment. Please refer to this one below and see if it is any clearer.

http://www.optica.tn.tudelft.nl/education/photons.asp

Zz.

Cheers, that's a much clearer description of the experiment. I'll pass it on :smile:

ZapperZ

Sep28-04, 06:26 AM

vanesch

Sep28-04, 07:46 AM

[i]
Nothing, no technology no phenomenon no day-to-day physics, was ever found to depend or require in any way their imaginary "collapse/projection postulate" (or its corollary, the Bell's theorem). The dynamical equations (of QM and QED/QFT) and Born postulate is what does the work.

I wonder what difference you see between Born's postulate and the collapse postulate ? To me, they are one and the same thing: namely that, given a quantum state psi, and a measurement of a physical quantity which corresponds to a self-adjoint operator A, gives you the probability |<a_i |psi>|^2 to be in state corresponding to eigenstate |a_i> of A, with value a_i for the physical quantity to be measured. If you accept this, and you accept that measuring twice the same quantity in succession yields the second time the same result as the first time, this time with certainty, then where exactly is the difference between the Born rule (giving the probabilities) and the projection postulate ?

cheers,
Patrick.

nightlight

Sep28-04, 12:21 PM

vaneschI wonder what difference you see between Born's postulate and the collapse postulate ? To me, they are one and the same thing:

Unfortunately, the two are melded in the "pedagogicial" expositions so a student is left with the illusion that the projection postulate is empirically essential element of the theory. The only working part of the so-called measurement theory is the operational Born rule (as a convenient practical shortcut, in the way Shroedinger originally understood his wave function) which merely specifies the probability of a detection event without imposing any new non-dynamical evolution (the collapse/projection) on the system state. The dynamical evolution of the state is never interrupted in some non-dynamical, mysterious way by such things as human mind (as von Neumann, the originator of the QM Mystery cult, claimed) or in any other ad hoc fuzzy way.

What happens to the system state after the aparatus has triggered a macroscopic detection event is purely a matter of the specific aparatus design and it is in principle deducible from the design, initial & boundary conditions and the dynamic equations. Since the dynamical equations are local (ignoring the superficial non-locality of the limited non-relativistic approximations for potentials, such as V(r)=q/r) all changes to the state are local and continuous.

There is no coherent way to integrate the non-dynamic collapse into the system dynamics. There is only lots of dance and handwaving on the subject. When exactly does the dynamical equations get put on hold, how long are they held in suspension and when do they resume activity? It doesn't matter, the teacher said. Well, something, somewhere has to know, since it would have to perform it.

How do you know that collapse occurs at all? Well, teacher said, since we cannot attribute a definite value to the position (what exactly is the position? position of what? spread out field?) before the measurement and have the value (a value of what? the location of detector apperture? the blackened photo-grain? the electrode?) after the measurement, the definite value must have been created in a collapse which occured during the measurement. Why can't there be values before the measurement? Well, von Neumann proved that it can't be done while remaining consistent with all QM predictions. Ooops, sorry, that proof was shown invalid, it's the Kochen-Specker's theorem which shows it can't be done (after Bohm produced the counter-example to von Neumann). Ooops, again, As Bell has shown, that one had the same kind of problem as von Neumman's "proof", it's really the Bell's theorem which shows it can't be done. And what does the Bell's theorem use to show that there is a QM prediciton which violates Bell's inequality? The projection postulate, of course.

So, to show that we absolutely need the projection postulate we use projection postulate to deduce a QM prediction which violates Bell's inequality (and which no local hidden variable theory can violate). Isn't that a bit circular, a kind of cheating? That can't prove that we need projection postulate.

Well, teacher said, this QM prediction was verified experimentally, too. It was? Well, yeah, it was verified, well, other than for some tiny loopholes. You mean the actual measured data hasn't violated the Bell's inequality? It's that far off, over 90% coincidence points missing and just hypothesized into the curve? All these decades, and still this big gap? Well, the gap just appears superficially large, a purely numerical artifact, its true essence is really small, though. It's just matter of time till these minor technological glitches are ironed out.

Oh, that reminded me Mr. Teacher, I think you will be interested in investing in this neat new device I happen to have in my backpack. It works great, it has 110% of output energy vs input energy. Yeah, it can do it, sure, here is the notebook which shows how. By the way, this particular prototype has a very minor, temporary manufacturing glitch which keeps it at the 10% output vs input, just at the moment. Don't worry about it, the next batch will work as predicted.

nightlight

Sep28-04, 01:11 PM

I could say the same thing about the similar whinning people always do about QM's photon picture without realizing that if it is simply a cult not based on any form of validity, then it shouldn't WORK as well (eg. refer to the band structure of the very same semiconductors that you are using in your electronics and see how those were verified via photoemission spectroscopy).

That's the point I was addressing -- you can take the projection/collapse postulate out of the theory, it makes no difference for anything that has any contact with empirical reality. The only item that would fall would be Bell's theorem (since it uses the projection postulate to produce the alleged QM "prediction" which violates Bell's inequality). Since no actual experimental data has ever violated the inequality, there is nothing empirical that must be explained.

Since the Bell's theorem on impossibility of LHV is the only remaining rationale for the projection postulate (after von Neumann's & Kochen-Specker's HV "impossibility theorems" were found empirically irrelevant), and since its proof uses in an essential way the projection postulate itself, the two are a closed circle with no connect or usefulness to anything but to each other.

If you think you are correct, then put your money where you mouth is and try to have it published in a peer-reviewed journal. Till you are able to do that, then all your whinning are nothing more than bitterness without substance.

And who do you imagine might be a referee in this field who decides whether the paper gets published or not? The tenured professors and highly reputabe physicists who founded entire branches of research (e.g. Trevor Marshall, Emilio Santos, Asim Barut, E.T. Jaynes,...) with hundreds of papers previously published in reputable journals could not get passed the QM cult zealots to publish a paper wich directly and unambiguosly challenges the QM Mystery religion (Marshall calls them the "priesthood"). The best they would get is a highly watered down version with key points edited or dulled out and any back-and-forth arguments spanning several papers cut-off with the last word always for the opponents.

Being irrelevant and useless, this parasitic branch will die off eventually of its own. After all, how many times can one dupe the money man with the magical quantum computer tales, before he gets it and requests that they either show it work or go find another sucker.

vanesch

Sep28-04, 01:21 PM

And what does the Bell's theorem use to show that there is a QM prediciton which violates Bell's inequality? The projection postulate, of course.

Not to my understanding. He only needs the Born rule, no ? Bell's inequalities are just expressions of probabilities, which aren't satisfied by some probabilities predicted by QM. If you accept the Hilbert state description and the Born rule to deduce probabilities, that's all there is to it.

Let's go through a specific example, as given in Modern Quantum Mechanics, by Sakurai, paragraph 3.9. But I will adapt it so that you explicitly don't need any projection.

The initial state is |psi> = 1/sqrt(2) [ |z+>|z-> - |z->|z+> ] (1)
which is a spin singlet state.

(I take it that you accept that).

The probability to have an |a+>|b+> state is simply given (Born rule) by:

P(a,b) =|( <a+|<b+| ) |psi> |^2 = 1/2 | <a+|z+><b+|z-> - <a+|z-><b+|z+> |^2

Let us assume that a and b are in the xz plane, and a and b denote the angle with the z-axis.
In that case, <u+|z+> = cos (u/2) and <u+|z-> = - sin (u/2)

So P(a,b) = 1/2 | - cos(a/2)sin(b/2) + sin(a/2)cos(b/2) |^2

or P(a,b) = 1/2 { sin( (a-b)/2 ) }^2 (2)

So the probability to measure particle 1 in the spin-up state along a and particle 2 in the spin-up state along b is given by P(a,b) as given in (2) and we deduced this simply using the Born rule.

Now one of Bell's inequalities for probabilities if we have local variables determining P(a,b) is given by:

P(a,b) is smaller or equal than P(a,c) + P(c,b).

Fill in the formula (2), and we should have:

Sin^2((a-b)/2) < = Sin^2((a-c)/2) + Sin^2((c - b)/2)

Now, take a = 0 degrees, b = 90 degrees, c = 45 degrees,

sin^2(45) <= ? sin^2(22.5) + sin^2(22.5)

0.5 < ? 0.292893...

See, I didn't need any projection as such...

cheers,
Patrick.

nightlight

Sep28-04, 02:32 PM

vanesch Not to my understanding.

The state of the subsystem B which is (in the usual pedagogical description) a mixed state: 1/2 |+><+| + 1/2 |-><-|, becomes a pure state |+> for the sub-ensemble of B for which we get (-1) result on A. This type of composite system measurement treatment and the sub-system state reduction are the consequences of the projection postulate -- the reasoning is an exact replica of the von Neumann's original description of the measured system and the aparatus where he introduced the projection postulate along with the speculation that it was the observer's mind which created the collapse. Without the collapse in this model the entangled state remains entangled, since the unitary evolution cannot, in this scheme of measurement, pick-out of the superposition the specific outcome or a pure resulting sub-ensemble.

Of course, there is a grain of truth in the projection. There is a correlation of cos^2(theta) burried in the coincidence counts as Glauber's Quantum Optics multi-point correlation functions or the actual Quantum Optics experiments show. In terminology of photons, the problem is when one takes the particle picture literally and claims there is exactly one such "particle" (a member of correlated pair) and that we're measuring properties of that one particle. In fact, the photon number isn't a conserved quantity in QED.

The fully detailed QED treatment of the actuall Bell inequality experiments, which takes into account the detection process and the photon number uncertainty, would presumably, at least in principle, reproduce the correct correlations observed, including the actual registered coincidence counts, which don't violate Bell's inequality. The full events for the two detectors of subsystem B include: 1) no trigger on + or -, 2) (+) only trigger, 3) (-) only trigger, 4) (+) and (-) trigger. The pair coincidence counts then consist of all 16 combinations of possible outcomes.

The "pedagogical" scheme (and its von Neumann template) insists that only (2) and (3) are the "legitimate" single particle results and only their 4 combinations, out of 16 that actually occur, the "legitimate" pair events (I guess, since only these fall within its simple-minded approach), while labeling euphemistically (1) and (4), and the 12 remaining pair combinations, which are outside of the scheme, as artifacts of the technological "non-ideality" to be fixed by the future technological progress. The skeptics are saying that it is the "pedagogical" scheme (the von Neumann's collapse postulate with its offshoots, the measurement theory and Bell's QM "prediction" based on it) itself that is "non-ideal" since it doesn't correspond to anything that actually exists, and it is the eyesore which needs fixing.

vanesch

Sep28-04, 02:48 PM

The "pedagogical" scheme (and its von Neumann template) insists that only (2) and (3) are the "legitimate" results (I guess, since only these two fall within its simple-minded approach), while labeling euphemistically (1) and (4), which are outside of the scheme, as artifacts of the technological "non-ideality" to be fixed by the future technological progress.

I don't understand what you are trying to point out. Do you accept, or not, that superpositions of the type |psi> = 1/sqrt(2) (|+>|-> - |->|+>) can occur in nature, where the first and the second kets refer to systems that can be separated by a certain distance ?

If you don't, you cannot say that you accept QM and its dynamics and Born's rule, no ? If you do, I do not need anything else to show that Bell's inequality is violated, and especially, I do not need the projection postulate.
In the state |psi>, the state |+>|+> has coefficient 0, so probability 0 (Born) to occur, just as well as the state |->|->. So these are NOT possible outcomes of measurement if the state |psi> is the quantum state to start with. No projection involved.

I know that with visible photon detection, there are some issues with quantum efficiency. But hey, the scheme is more general, and you can take other particles if you want to. Your claim that quantum mechanics, with the Born rule, but without the projection postulate, does not violate Bell's inequalities is not correct, as I demonstrated in my previous message.

cheers,
patrick.

nightlight

Sep28-04, 04:51 PM

vanesch I don't understand what you are trying to point out. Do you accept, or not, that superpositions of the type |psi> = 1/sqrt(2) (|+>|-> - |->|+>) can occur in nature, where the first and the second kets refer to systems that can be separated by a certain distance ?

I am saying that such |psi> for the entangled photons is a schematized back-of-the-envelope sketch, adequate for a heuristic toy model and not a valid model for any physical system. Its "predictions" don't match (not even closely) any actually measured data. To make it "match" the data, over 90% of the "missing" coincidence data points have to be hand-put into the "matching curve" under the "fair sampling" and other speculative conjectures (see the earlier discussion here (http://www.physicsforums.com/showthread.php?t=12311) with details and references on this point).

If you don't, you cannot say that you accept QM and its dynamics and Born's rule, no ? If you do, I do not need anything else to show that Bell's inequality is violated, and especially, I do not need the projection postulate.

You've got the Born rule conceptually melded with the whole measurement theory which came later. The original rule (which Born introduced as a footnote in a paper on scattering) I am talking about is meant in the sense Schroedinger used to interpret his wave function with: it is an operational shortcut, not a foundamental axiom of the theory. There is no non-dynamical change of state or fundamental probabilistic axiom in this interpretation -- the Psi evolves by dynamical equations at all times. All its changes (including any localization and the focusing effects) are due to the interaction with the aparatus. There are no fundamental probabilities or suspension and resumption of the dynamical evolution.

The underlying theoretical foundation that Schroedinger assumed is the interpretation of the |Psi(x)|^2 as a charge/matter density, or in the case of photons as the field energy density. The probability of detection is the result of the specific dynamics between the aparatus and the matter field (the same way one might obtain probabilities in a classical field measurements). You can check the numerous papers and preprints of Asim Barut and his disciples which show how this original Schroedinger view can be consistently carried out for atomic systems including the correct predictions of QED radiative corrections (their self-field electrodynamics, which was a refinement of the eralier "neoclassical electrodynamics" of E.T. Jaynes).

In the state |psi>, the state |+>|+> has coefficient 0, so probability 0 (Born) to occur, just as well as the state |->|->. So these are NOT possible outcomes of measurement if the state |psi> is the quantum state to start with.

And if that simple model of |psi> corresponds to anything real at all. I am saying it doesn't, it is a simple-minded toy model for an imaginary experiment. You would need to do the full QED treatment to make any prediction that could match the actual coincidence results (which don't violate even remotely the Bell's inequality).

No projection involved.

Of course it does have projection (collapse). You've just got used to the usual pedagocial omissions and shortcuts you can't notice it any more. You simply need to include the aparatus in the dynamics and evolve the composite state to see that no (+-) or (-+) result occurs under the unitary evolution of the composite system until something collapses the superposition of the composite system (this is the von Neumann's measurement scheme, which is the bases of the QM measurement theory). That is the state collapse that makes (+) or (-) definite on A and which induces the sub-ensemble state as |-> or |+> on B, which Bell's theorem uses in an essential way to assert that there is a QM "prediction" which violates his inequality.

The full system dynamics (of A,B plus the two polarizers and the 4 detectors) cannot produce via unitary evolution of the full composite system a pure state with a definite polarization of A and B, such as |DetA+>|A+>|DetB->|B->. It can produce only a superposition of such states. That's why von Neumann had to postulate the extra-dynamical collapse -- the unitary dynamics by itself cannot produce such transition within his/QM measurement theory.

Without this extra-dynamical global collapse, you only have A, B, the two polarizers and and the four detectors evolving the superposition via purely local field interactions, incapable even in principle of yielding any prediction that excludes LHV (since the unknown local fields are LHVs themselves). It is precisely this conjectured global extra-dynamical overall state collapse to a definite result which results in the apparent non-locality (no LHV) prediction. Without it, there is no such prediction.

I know that with visible photon detection, there are some issues with quantum efficiency.

This sounds nice and soft, like the Microsoft marketing describing the latest "issues" with IE (the most recent in never ending stream of the major security flaws).

Plainly speaking, the QM "prediction" of the Bell's theorem which violates his inequality, doesn't actually happen in real data. No coincidence counts ever violated the inequality.

Your claim that quantum mechanics, with the Born rule, but without the projection postulate, does not violate Bell's inequalities is not correct, as I demonstrated in my previous message.

You seem unaware of how the projection postulate fits in the QM measurement theory or maybe you don't realize that the Bell's QM prediction is deduced using the QM measurement theory. All you have "demonstrated" so far is that you can superficially replay the back-of-the-envelope pedagogical cliches.

vanesch

Sep28-04, 10:47 PM

The underlying theoretical foundation that Schroedinger assumed is the interpretation of the |Psi(x)|^2 as a charge/matter density, or in the case of photons as the field energy density.

Ok, so you do not accept superpositions of states in a configuration space that describes more than one particle ; so you introduce a superselection rule here. BTW, this superselection rule IS assumed to be there for charged particles, but not for spins or neutral particles.

In the state |psi>, the state |+>|+> has coefficient 0, so probability 0 (Born) to occur, just as well as the state |->|->. So these are NOT possible outcomes of measurement if the state |psi> is the quantum state to start with.

And if that simple model of |psi> corresponds to anything real at all. I am saying it doesn't, it is a simple-minded toy model for an imaginary experiment. You would need to do the full QED treatment to make any prediction that could match the actual coincidence results (which don't violate even remotely the Bell's inequality).

Well, that's a bit easy as a way out: "you guys are only doing toy QM. I'm doing 'complicated' QM and there, a certain theorem holds. But I can't prove it, it is just too complicated."

No projection involved.

Of course it does have projection (collapse). You've just got used to the usual pedagocial omissions and shortcuts you can't notice it any more.

Well, tell me where I use a collapse. I just use the Born rule which states that the probability of an event is the absolute value squared of the inproduct of the corresponding eigenstate and the state of the system. But I think I know what you are having a problem with. It is not the projection or collapse, it is the superposition in a tensor product of Hilbert spaces.

You simply need to include the aparatus in the dynamics and evolve the composite state to see that no (+-) or (-+) result occurs under the unitary evolution of the composite system until something collapses the superposition of the composite system (this is the von Neumann's measurement scheme, which is the bases of the QM measurement theory). That is the state collapse that makes (+) or (-) definite on A and which induces the sub-ensemble state as |-> or |+> on B, which Bell's theorem uses in an essential way to assert that there is a QM "prediction" which violates his inequality.

But that's not true ! Look at my "toy" calculation. I do not need to "collapse" anything, I consider the global apparatus "particle 1 is measured along spin axis a and particle 2 is measured along spin axis b". This corresponds to an eigenstate <a|<b|. I just calculate the in-product and that's it.

That's why von Neumann had to postulate the extra-dynamical collapse -- the unitary dynamics by itself cannot produce such transition within his/QM measurement theory.

Yes, I know, that's exactly the content of the relative-state interpretation.
But it doesn't change anything to the predicted correlations. As I repeat: you do not have a problem with collapse, but with superposition. And that's an essential ingredient in QM.

cheers,
Patrick.

nightlight

Sep29-04, 01:22 AM

Well, that's a bit easy as a way out: "you guys are only doing toy QM. I'm doing 'complicated' QM and there, a certain theorem holds. But I can't prove it, it is just too complicated."

You're using a 2(x)2 D Hilbert space. That is a toy model considering that the system space has about infinitely many times more dimensions, even before accounting for the quantum field aspect which is ignored all together (e.g. the indefinitness of the photon number would give application of Bell's argument here a problem). The ignored spatial factors are essential in the experiment. The spatial behavior is handwaved into the resoning in an "idealized" (fictitious) form which goes contrary to the plain experimental facts (the "missing" 90 percent of coincidences) or any adequate theory of the setup ("adequate" in the sense of predicting quntitatively these facts).

A non-toy physical model ought to describe quantitatively what is being measured, not just what might be measured if the world were doing what you imagine it ought to be doing if it were "ideal".

Well, tell me where I use a collapse. I just use the Born rule which states that the probability of an event is the absolute value squared of the inproduct of the corresponding eigenstate and the state of the system.

Then you either don't know that you're using the QM measurement theory for the composite system here (implicit in the formulas for the joint event probabilities) or you don't know how any definite result occurs in the QM measurement theory (via the extra-dynamical collapse).

Just step back and think for a second here to see the blatant self-contradictory nature of your claim (that you're not assuming any non-dynamical state evolution/collapse). Let's say you're correct, you only assume dynamical evolution of the full system state according to QM (or QED, ultimately) and you never claimed, or believe, that the system state stops following the dynamical evolution.

Now, look what happens if you account for the spatial degrees of freedom and follow (at least in principle) the multiparticle Schroedinger-Dirac equations for the full system (the lasers, PDC crystals or atoms for cascade, A,B, polarizers, detectors, computers counting the data). Taken all together, you have a gigantic set of coupled partial differential equations that fully describe what is going on once you give the initial and the boundary conditions (we can assume boundary conditions 0, i.e. any subsystems which might interact are included in the "full" system already in the equations). We also cannot use the approximate non-relativistic instantaneous potentials/interactions since that would be putting in the superficial non-locality by hand into the otherwise local dynamics. This excludes the non-relativistic, explicitly non-local point-particle models with the instantaneous potentials (which are only an approximation for QED interactions), such as Bohm's formalism (which is equivalent to the non-relativistic QM formalism).

The fields described by these equations evolve purely locally (they're 2nd order or some such PDEs, linear or non-linear). Therefore these coupled fields following the local PDEs are local "hidden" variable model all by themselves, if all that is happening is accounted for by these equations.

Yet, you claim that this very same dynamical evolution, without ever having to be suspended and amended by an extra-dynamical deus-ex-machina, yield result which prohibits any local hidden variables from being able to account for the result of their evolution.

A purely dynamical evolution via a set of local PDEs cannot yield result which shows that purely local PDEs cannot describe the system. That's the basic self-contradiction of your claim "I am using no collapse."

You seem unaware of the reasoning behind the probabilistic rules of QM measurement theory you're applying, which bridges gap between the purely local evolution and the "no-local hidden variables" prediction -- a suspension of the dynamics has to occur to make such prediction possible since the dynamics by itself is a local "hidden" variable theory. And that is the problem of the conventional QM measurement theory.

My starting point, several messages back, is that you can drop this suspension of dynamics (which has to be there to yield the alleged system evolution which contradicts the local hidden variables), and nothing will be affected in the application of quantum theory to anything.

Nothing depends on it but the Bell's theorem which would have to be declared void (i.e. no such QM prediction exists if you drop the non-dynamical state collapse). Recall also that the only reason the non-dynamical collapse was introduced into quantum theory was to explain the earlier faulty proofs of impossibility of any hidden variables (von Neumann's, Kochen-Specker's). The only remaining rationale is the Bell's theorem which seemingly prohibits any LHVs, thus one needs some way to make system produce measured values, since the classical view (of pre-existent values) could not work.

Thus the two, the non-dynamical evolution (collapse) and the Bell's QM prediction are a circular system -- the Bell's prediction requires for its deduction the non-dynamical evolution (via QM measurement theory) and the reason we need any collapse at all is the alleged impossibility of the pre-existent values for the variables/observables, and the claimed impossibility hinges solely on the Bell's proof itself. Nothing else in physics requires either. The two are a useless parasitic attachment serving nothing but to support itself.

vanesch

Sep29-04, 01:49 AM

You're using a 2(x)2 D Hilbert space. That is a toy model considering that the system space has about infinitely many times more dimensions, even before accounting for the quantum field aspect which is ignored all together (e.g. the indefinitness of the photon number would give application of Bell's argument here a problem). The ignored spatial factors are essential in the experiment.

Well, you should know that in all of physics, making a model which only retains the essential ingredients is a fundamental part of it, and I claim that the essential part is the 2x2 D Hilbert space of spins. Of course, a common error also in physics is that an essential component is overlooked, and that seems to be what you are claiming. But then it is up to you to show me what that is. You now seem to imply that I should also carry with me the spatial parts of the wave function for both particles. OK, I can do that, but you can already guess that this will factor out if I take a specific model, such as a propagating gaussian bump for each one. But then you will claim that I don't take into account the specific interaction in the photocathode of that particular photomultiplier. I could introduce a simple model for it, but you won't accept that. So you are endlessly complicating the issue, so that in the end nothing can be said, and all claims are open. You are of course free to do so, but no advancement is made nowhere. Witches exist. So now it is up to you to do a precise calculation with the model you can accept as satisfying (it will always be a model, and you'll never describe completely all aspects) and show me what you get, which is different from what the simple 2x2D model gives you, after introducing finite efficiencies for both detectors.

You are making the accusation that I do not know what I'm using in QM measurement theory, but it was YOU who claimed that you accepted the Born rule (stating that the probability for an event to occur is given by |<a|psi>|^2). It is what I used, in my model.

cheers,
Patrick.

vanesch

Sep29-04, 01:55 AM

The fields described by these equations evolve purely locally (they're 2nd order or some such PDEs, linear or non-linear). Therefore these coupled fields following the local PDEs are local "hidden" variable model all by themselves, if all that is happening is accounted for by these equations.

As a specific remark, the Schroedinger equation is not a local PDE equation. Well, it is local in configuration space, but it is not in real space, because the wave function is a function over configuration space. So nothing stops you from coupling remote coordinates.

cheers,
Patrick.

nightlight

Sep29-04, 02:52 AM

vanesch As a specific remark, the Schroedinger equation is not a local PDE equation. Well, it is local in configuration space, but it is not in real space, because the wave function is a function over configuration space. So nothing stops you from coupling remote coordinates.

The PDEs are non-local only if you use the non-local (non-relativistic) approximations for the interaction potentials, such as the non-relativistic Coulomb potential approximation. If you allow these potentials in, you don't need QM or Bell's theorem to show that no local hidden variable theory could reproduce the effects of such non-local potentials: as soon as you move particle A its Coulomb potential at the position of a far away particle B changes and affects the B. It's surprising to see such discussion non-sequitur even brought up after I already excluded it upfront, explicitly and with a color emphasis.

The fully relativistic equations do not couple field values at the space-like separations. They are strictly local PDEs.

vanesch

Sep29-04, 03:04 AM

The fully relativistic equations do not couple field values at the space-like separations. They are strictly local PDEs.

Oh, but I agree with you that there is nothing spacelike going on. I had a few other posts here concerning that issue. Nevertheless, the correlations given by superpositions of systems which are separated in space are real, if you believe in quantum superposition, and that the "toy" models you attack do give you the essential facts. You WILL see correlations in the statistics, and no, the fact that we do not get the RAW DATA to be that way is not something deep, but just due to finite efficiencies. A very simple model of the efficiencies of the detectors give a correct description of the data taken.
My point (which I think is not very far from yours) is that one should only consider the measurement complete when the data are brought together (and hence are not separated spacelike) by one observer. Until that point, I do consider that the data of the other "observation" is in superposition.
But that is just interpretational. There's nothing very deep here. And no, I don't think you have to delve into QED (which is really opening a Pandora Box!) for such a simple system, because people use photons, but you could think just as well of electrons or whatever other combination. Only, the experiments are difficult to perform.

cheers,
Patrick.

nightlight

Sep29-04, 04:02 AM

vanesch Well, you should know that in all of physics, making a model which only retains the essential ingredients is a fundamental part of it, and I claim that the essential part is the 2x2 D Hilbert space of spins. ... But then it is up to you to show me what that is.

The essential part of the Bell's inequalities is that the counts which violate the inequality in the QM "prediction" include nearly all pairs (equivalent to requiring around 82% of setup efficiency). Otherwise if one allows lower setup efficiency, the counts will not violate the inequality. Thus the spatial aspects and an adequate model of detection are both essential to evaluate the maximum setup efficiency. If you can't predict from QM (or Quantum Optics) the setup efficiency sufficient to violate inequalities, you don't have a QM prediction but an idea, a heuristic sketch of a prediction. And that is the phase that this alleged QM "prediction" never outgrew. It is a back of the envelope hint for a prediction.

You now seem to imply that I should also carry with me the spatial parts of the wave function for both particles. OK, I can do that, but you can already guess that this will factor out if I take a specific model, such as a propagating gaussian bump for each one.

All I am saying, go predict something that you actually could measure. Predict the 90% missing coincidences and then change the model of the setup, the apertures, detector electrode materials, lenses, source intensities or wavelengths,... whatever you need, and then show how these changes can be made so that the setup efficiency falls within the critical range to violate the inequalities. No "fair sampling" or other such para-physical/speculative ad-hockery allowed. Just the basic equations and the verifiable properties of the materials used.

So now it is up to you to do a precise calculation with the model you can accept as satisfying (it will always be a model, and you'll never describe completely all aspects) and show me what you get, which is different from what the simple 2x2D model gives you, after introducing finite efficiencies for both detectors.

All I am saying is that there is no QM prediction which violates Bell's inequalities and which doesn't rely on a non-dynamical, non-local and empirically unverfied and unverifiable state evolution (collapse). The non-locality is thus put in by hand upfront in the premise of the "prediction".

Secondly, after over three decades of trying, there is so far no experimental data which violates the Bell inequalities, either. There are massive extrapolations of the obtained data which put in by hand the 90% of the missing coincidences (handwaved in with a wishfull ad hoc unverifiable conjectures, such as the "fair sampling"), and to everyones big surprise, the massively extrapolated data violates the Bell's inequality.

So there is neither prediction nor data which violates the inequality. Luckily nothing else in the practical applications of physics needs that violation or the non-dynamical collapse (used to deduce the "prediction"), for anything. (Otherwise it would have been put on hold until the violation is achieved.)

You are making the accusation that I do not know what I'm using in QM measurement theory, but it was YOU who claimed that you accepted the Born rule (stating that the probability for an event to occur is given by |<a|psi>|^2). It is what I used, in my model.

I explained in what sense I accepted the "Born rule" --- the same sense that Schroedinger assumed in his interpretation of the wave function --- as a practical, although limited, operational shortcut (the same way the classical physics had used probabilities, e.g. for the scattering theory), not as a fundamental postulate of the theory and certainly not as an all-powerful deus-ex-machina of the later QM measurement theory (which is what Bell used), capable of suspending the dynamical evolution of the system state and then resuming the dynamics after the "result" is produced.

That is an absurdity that will be ridiculed by the future generations as we ridicule the turtle on a turtle... model of earth. Why turtles? Why non-dynamical collapse? What was wrong with those people? What were they thinking.

Kane O'Donnell

Sep29-04, 04:10 AM

Hi nightline,

I'm new to this forum so I'm not really clear on what etiquette is followed here. I just wanted to know what background you have in Physics.

Cheers,

Kane

vanesch

Sep29-04, 04:23 AM

The essential part of the Bell's inequalities is that the counts which violate the inequality in the QM "prediction" include nearly all pairs (equivalent to requiring around 82% of setup efficiency).

Yes, but why are you insisting on the experimental parameters such as efficiencies ? Do you think that they are fundamental ? That would have interesting consequences. If you claim that ALL experiments should be such that the raw data satisfy Bell's inequalities, that gives upper bounds to detection efficiencies of a lot of instruments, as a fundamental statement. Don't you find that a very strong statement ? Even though for photocathodes in the visible light range with today's technologies, that boundary is not reached ? You seem to claim that it is a fundamental limit.

But what is wrong with the procedure of taking the "toy" predictions of the ideal experiment, apply efficiency factors (which can very easily be established also experimentally) and compare that with the data ? After all, experiments don't serve to measure things but to falsify theories.

cheers,
Patrick.

nightlight

Sep29-04, 05:15 AM

Oh, but I agree with you that there is nothing spacelike going on.

The QM measurement theory has a spacelike collapse of a state. As explained earlier, it absolutely requires the suspension of the dynamical evolution to perform its magical collapse that yields "result" then somehow lets go, and the dynamics is resumed. That kind of hocus-pocus I don't buy.

Nevertheless, the correlations given by superpositions of systems which are separated in space are real, if you believe in quantum superposition, and that the "toy" models you attack do give you the essential facts. You WILL see correlations in the statistics,

You can't make the prediction of the sharp kind of correlations that can violate the Bell's inequality. You can't get them (and nobody else has done it so far) from QED and using the known properties of the detectors and sources. You get them only using the QM measurement theory with its non-dynamical collapse.

and no, the fact that we do not get the RAW DATA to be that way is not something deep, but just due to finite efficiencies. A very simple model of the efficiencies of the detectors give a correct description of the data taken.

Well, for the Bell's inequality violation, the setup efficiency is the key question. Without the certain minimum percentage of pairs showing violation local models are still perfectly fine. If you can't create a realistic model which can violate the inequality (the sources and the detectors design which could do it if made by the specs), there is no prediction, just an idea of a prediction.

My point (which I think is not very far from yours) is that one should only consider the measurement complete when the data are brought together (and hence are not separated spacelike) by one observer. Until that point, I do consider that the data of the other "observation" is in superposition.

I think that QM should work without any measurement theory beyond the kind of normal operational rules used in classical physics. The only rigorous rationale why the QM measurement theory (with its collapse) was needed was the faulty von Neumann's proof of impossibility of any hidden variables. Without hidden variables possible one has to explain how a superposition can yield a specific result at all. With hidden variables one can simply treat it as in the classical physics - the specific result was caused by the values of stochastic variables which were not controlled in the experiment. So, von Neumann invented the collapse (which was earlier used in an informal way) and conjectured that it was the observers mind which causes it, suspending the dynamical evolution, magically creating a definite result then the dynamical evolution resumes its operation.

After that "proof" (and its Kochen-Specker temporary patch) were shown to be irrelevant, having already been refuted by Bohm's counterexample, it was the Bell's theorem which became the sole basis for excluding the hidden variables (since non-local ones are problematic), thus that is the only remaining rationale for maintaining the collapse "solution" to the "no-(local)-hidden-variable" problem. If there were no Bell's no-LHV prediction of QM, there would be no need for a non-dynamical collapse "solution" since there would be no problem to solve. (Since one could simply look at the quantum probabilities as being merely the result of the underlying stochastic variables.)

The Achilles Heel of this new scheme is that in order to prove his theorem Bell needed QM measurement theory and the collapse, otherwise there is no prediction (based on more rigorous QED and a realisitc source and detection treatment) which would be sharp/efficient enough to violate the Bell's inequality.

What we're left with is the Bell's prediction which needs the QM collapse premise and we have the collapse "solution" for the measurement problem, the problem created because the collapse premise yields, via Bell's prediction, to a prohibition of LHVs. So the two, the Bell's prediction and the collapse, form a self-serving closed loop, soleley existing to prop each other up, while nothing else in physics needs either. It is a tragic and shameful waste of time to teach kids and have them dwell on that kind of useless nonsense that future generations will laugh at (once they snap out from the spell of this logical viscious circle).

vanesch

Sep29-04, 05:53 AM

You can't make the prediction of the sharp kind of correlations that can violate the Bell's inequality. You can't get them (and nobody else has done it so far) from QED and using the known properties of the detectors and sources. You get them only using the QM measurement theory with its non-dynamical collapse.

I wonder what you understand by QED, if you don't buy superpositions of states...

cheers,
Patrick.

nightlight

Sep29-04, 06:37 AM

vanesch Yes, but why are you insisting on the experimental parameters such as efficiencies ? Do you think that they are fundamental ?

For the violation of inequality, definitely. The inequality is purely enumerative type of mathematical inequality, like a pigeonhole principle. It depends in an essential way on the fact that a sufficient percentage of result slots are filled in for different angles so they cannot be rearranged to fit multiple (allegedly required) correlations. Check for example a recent paper by L. Sica (http://cul.arxiv.org/abs/quant-ph/0101087) where he shows that if you take a three finite arrays A[n], B1[n] and B2[n], filled with numbers +1 and -1 and you form the cross-correlation expressions (used for Bell's inequality): E1=Sum(A[j],B1[j])/n, E2=Sum(A[j],B2[j])/n and E12=Sum(B1[j],B2[j])/n, then no matter how you fill the numbers or how big the arrays are, they always satisfy the Bell's inequality:

| E1 - E2 | <= 1 - E12.

So no classical data set could violate this purely enumerative inequality, i.e. the QM prediction of violation means that if we were to turn the aparatus B from angle B1 to B2, the set of results on A must be always strictly different than what it was for B position B1 . Similarly, it implies that in the actual data, the sets of results on fixed A position, and two B positions, B1 and B2, the two sequences of A results must be strictly different from each other (they would normally have roughly equal numbers of +1's and -1's in each array, so the arrangement would have to be different between the two; they can't be the same even accidentally if the inequality is violated).

For the validity of this purely enumerative inequality, it is essential that the sufficient number of array slots is filled with +1 and -1, otherwise (e.g. if you put 0's in sufficient number of slots) the inequality doesn't hold. Some discussion of this result are in the later papers by L. Sica (http://arxiv.org/find/quant-ph/1/au:+sica/0/1/0/all/0/1) and by A. F. Kracklauer (http://arxiv.org/find/quant-ph/1/au:+Kracklauer/0/1/0/all/0/1).

That would have interesting consequences. If you claim that ALL experiments should be such that the raw data satisfy Bell's inequalities, that gives upper bounds to detection efficiencies of a lot of instruments, as a fundamental statement. Don't you find that a very strong statement ? Even though for photocathodes in the visible light range with today's technologies, that boundary is not reached ? You seem to claim that it is a fundamental limit.

There is a balancing or tradeoff between the "loopholes" in the experiments. The detection efficiency can be traded for lower polarization resolution (by going to higher energy photons). Also, the detectors can be tuned to a higher sensitivity, but then the dark current rises, blurring the results and producing more "background" and "accidental" concidences have to be subtracted (which is another big no-no for a loophole free test).

For massive particles, similar tradeoffs occur as well -- if you want better detection efficiency by going to higher energies, the spin measurement resolution drops. For ultra-relativistic particles, which are detectable almost 100%, the Stern-Gerlach doesn't work at all any more and the very lossy Compton scattering spin resolution must be used.

You can check a recent paper by Emilio Santos (http://cul.arxiv.org/abs/quant-ph/0401003) for much more discussion of these and other tradeoffs (also in his earlier papers (http://cul.arxiv.org/find/quant-ph/1/au:+Santos_E/0/1/0/all/0/1)). Basically, there is a sort of "loophole conservation" phenomenon, so that squeezing one out makes another one grow. Detector efficiency is just one of the parameters.

But what is wrong with the procedure of taking the "toy" predictions of the ideal experiment, apply efficiency factors (which can very easily be established also experimentally) and compare that with the data ? After all, experiments don't serve to measure things but to falsify theories.

Using the toy model prediction as a heuristic to come up with an experiment is fine, of course. But bridging the efficiency losses to obtain the inequality violation by the data requires the additional assumptions such as "fair sampling" (which Santos discusses in the paper above and which I had discussed in detail in an earlier thread here (http://www.physicsforums.com/showthread.php?t=12311), where the Santos' paper was discussed as well). After seeing enough of this kind of find-a-better-euphemism-for-failure games, it all starts to look more and more like perpetuum mobile inventors thinking up the excuses, blaming ever more creatively the real world's "imperfections" and "non-idealities" for the failure of their allegedly 110% overunity device.

nightlight

Sep29-04, 06:43 AM

I wonder what you understand by QED, if you don't buy superpositions of states...

Where did I say I don't buy superposition of states? You must be confusing my rejection of your QM measurement theory version of "magical" Born rule and its application to the Bell's system with my support for different Born rule (non-collapsing, non-fundamental, approximate, aparatus dependent rule) to jump to conclusion that I don't believe in superposition.

vanesch

Sep29-04, 12:01 PM

For the violation of inequality, definitely. The inequality is purely enumerative type of mathematical inequality, like a pigeonhole principle.

Good. So your claim is that we will never find raw data which violates Bell's inequality. That might, or might not be the case, depending on whether you take this to be a fundamental principle and not a technological issue. I personally find it hard to believe that this is a fundamental principle, but as it stands experimentally currently it cannot be negated (I think ; I haven't followed the most recent experiments on EPR type stuff). I don't know if it has any importance at all that we can or not have these raw data. The point is that we can have superpositions of states which are entangled in bases that we would ordinary think are factorized.

However, I find your view of quantum theory rather confusing (I have to admit I don't know what you call quantum theory, honestly: you seem to use different definitions for terms than what most people use, such as the Born rule or the quantum state, or an observable).
Could you explain me how you see the Hilbert state formalism of say, 10 electrons, and what you understand by a state of the system, and what you call the Born rule in that case ?
Do you accept that the states are all the completely assymetrical functions in 10 3-dim space coordinates and 10 spin-1/2 states, or do you think this is not adequate ?

cheers,
Patrick.

nightlight

Sep29-04, 03:14 PM

So your claim is that we will never find raw data which violates Bell's inequality.

These kind of enumerative constraints have been tightening in recent years and the field of Extremal set theory has been very lively lately. I suspect it will eventually be shown that, purely enumeratively (a la Sperner's theorem or Kraft's inequalities), the fully filled in arrays of results satisfying perhaps a larger set of correlation constraints from the QM prediction (not just the few that Bell had used), will yield a result that the measure of inequality violating sets converges to zero as the constraints (e.g. for different angles) are added in the limit of infinite arrays.

That would then put the claims of experimental inequality violation at the level of perpetuum mobile of the second kind, i.e. one could look at such claims as if someone claimed that he can flip the coin million times and get regularly the first million binary digits of Pi. If he can, he is almost surely cheating.

That might, or might not be the case, depending on whether you take this to be a fundamental principle and not a technological issue. I personally find it hard to believe that this is a fundamental principle,

Well, the inequality is of the enumerative kind of mathematical result, like a pigeonhole principle. Say, someone claimed they have a special geometric layout of holes and a special pigeon placement ordering which allows them to violate the pigeonhole principle inequalities, so they can put > N pigeons in N holes without having any hole with multiple pigeons. When asked to show it, the inventor brings out a gigantic panel of holes arranged in strange ways and in strange shapes, and starts placing pigeons jumping in some odd ways accross the pannel, taking longer and longer to pick a hole as he went on, as if calculating where to go next.

After some hours and finishing about 10% of the holes, he stops and proudly proclaims, here, it is obvious that it works, no double pigeons in any hole. Yeah, sure, just some irrelevant, minor holes left due to the required computation. If I assume that holes filled are a fair sample of all the holes and I extrapolate proportionately the area I filled to the entire board, you can see that continuing in this manner, I can put exactly 5/4 N pigeons without having to share a hole. And this is only a prototype algorithm. That's just a minor problem which will be solved as I refine the algorithm performance. After all, it would be implausible that an algorithm which worked so well so far, in just rough prototype form, would fail when polished to full strength.

This is precisely the kind of claims we have for the Bell's inequality tests with 10% of coincidences filled in, then claiming to violate the enumerative inequality for which the fillup of at least 82% is absolutely vital to even begin looking at it as a constraint. As Santos argues in the paper mentioned, the ad hoc "fair sampling" conjecture used to fast-talk over the failure, is a highly absurd assumption in this context (see also the earlier thread on this topic).

And often heard invocation of implausibility of QM failing with better detectors is as irrelevant as the pigeonhole algorithm inventor's assertion of implausibility of better algorithm failing -- it is a complete non-sequitur in the enumerative inequality context. Especially recalling the closed loop, self-serving circular nature of the Bell's No-LHV QM "prediction" and the vital tool used to prove it, the collapse postulate (the non-dynamical non-local evolution, vaguely specified suspension of dynamics), which in turn was introduced into the QM for the sole reason to "solve" the No-HV problem with measurement. And the sole reason it is still kept is to "solve" the remaining No-LHV problem, the one resulting from the Bell's theorem, which in turn requires the very same collapse in a vital manner to violate the inequality.

Since nothing else needs either of the two pieces, the two only serve to prop each other up while predicting no other empirical consequences for testing except for causing each other (if Bell's violation were shown experimentally, that would support the distant system-wide state collapse; no other test for the collapse exists).

The point is that we can have superpositions of states which are entangled in bases that we would ordinary think are factorized.

The problem is not the superposition but the adequacy of the overall model of (which the state is part of), and secondarily, attributing the particular state to a given preparation.

However, I find your view of quantum theory rather confusing (I have to admit I don't know what you call quantum theory, honestly: you seem to use different definitions for terms than what most people use, such as the Born rule or the quantum state, or an observable).

The non-collapse version of Born rule (as an approximate operational shortcut) has a long tradition. If you have learned just one approach and one perspective fed from a textbook, with usual pedagogical cheating on proofs and skirting of opposing or different approaches (to avoid confusing a novice), then yes, it could appear confusing. Any non-collapse approach takes this kind of Born rule, which goes back to Schroedinger.

Could you explain me how you see the Hilbert state formalism of say, 10 electrons, and what you understand by a state of the system, and what you call the Born rule in that case ? Do you accept that the states are all the completely assymetrical functions in 10 3-dim space coordinates and 10 spin-1/2 states, or do you think this is not adequate ?

For non-relativistic approximation, yes, it would be antisymmetrical 10*3 spatial coordinate function with Coulomb interaction Hamiltonian. This is still an external field approximation, which doesn't account for self-interaction of EM and the fermion fields. Asim Barut had worked out a scheme which superficially looks like self-consistent effective field methods (such as Hartree-Fock), but underneath it is an updated old Schroedinger's idea of treating matter fiels and EM fields as two interacting fields in a single 3D space. The coupled Dirac-Maxwell equations form a nonlinear set of PDEs. He shows that this treatment is equivalent to conventional QM 3N dimensional antisymmetrized N fermion equations, but with a fully interacting model (wich doesn't use the usual external EM field or external charge current approximations). With that approach he and his graduate students had reproduced the full non-relativistic formalism and the leading orders of radiative corrections of perturbative QED, without needing renormalization (no point particles, no divergences). You can check a large collection of their preprints (http://www-lib.kek.jp/cgi-bin/kiss_prepri?KN=&TI=&AU=barut&AF=&CL=&RP=&YR=) on this topic on the KEK server.

Regarding the Born rule for this atom, the antisymmetrization and the high interaction make the concept of individual electron here largely meaningless for any discussion of the Bell correlations (via Born rule). In Barut's approach this manifests in assuming no point electrons at all but simply using the single fermion matter field (normalized to 10 electron charge; he does have separate models of charge quantisation, these are stil somewhat sketchy) wich has the identical scattering properties as the conventional QM/QED models, i.e. Born rule is valid in the limited, non-collapsing sense. E.T Jaynes (http://bayes.wustl.edu/etj/node1.html)has a similar perspective (see his paper `Scattering of Light by Free Electrons' (http://bayes.wustl.edu/etj/articles/scattering.by.free.pdf); unfortunately, both Jaynes and Barut have died few years ago, so if you have any questions or comments, you'll probably have to wait a while since I am not sure that emails can go there and back).

nightlight

Sep29-04, 07:14 PM

vanesch Good. So your claim is that we will never find raw data which violates Bell's inequality.

Just to highlight the implications of the Sica's theorem a bit for the experimenal tests of Bell's inequality.

Say, you have an ideal setup, with 100% efficiency. You take two sets of measurements, keeping A orientation fixed and changing B from B1 to B2. You collect data as numbers +1 and -1 into arrays A[n] and B[n]. Since p(+)=p(-)=1/2, there will be roughly same number of +1 and -1 entries in each data array, i.e. this 50:50 ratio is insensitive to the orientation of the polarizers.

You have now done (A,B1) test and you have two arrays of +1/-1 data A1[n] and B1[n]. You are ready for the second test, you turn B to B2 direction to obtain data arrays A2[n], B2[n]. The Sica's theorem tells you that you will not get again (to any desired degree of certainty) the same sequence as A1[n], i.e. that a new sequence A2[n] must be explicitly different than A1[n], it must have +1s and -1s arranged differently (although stil in 50:50 ratio). You can keep repeating A,B2 run, and somehow the 50:50 content of A2[n] has to keep rearranging itself, while avoiding in some way arranging itself as A1[n].

Now, if you hadn't done (A,B1) test, then there is no such constraint on what A2[n] can be. To paraphrase a kid's response when told that thermos bottle keeps the hot liquids hot and cold liquids cold -- "How do it know?"

Or, another twist, you take 99 different angles for B and ontain sets of data A1[n],B1[n]; A2[n],B2[n]; ... A99[n],B99[n]. Now you're ready for the angle B100. This time the A100[n] has to keep rearranging itself to avoid matching all 99 previous arrays Ak[N].

Then you extend the above and, say, collect r=2^n data sets for 2^n different angles (they could be all the same angle, too). This time at the next angle, B_(2^n+1), the data for A_(2^n+1)[n] would have to avoid all 2^n arrays Ak[n], which it can't do. So you get that in each test there would be one failed QM prediction, for at least one angle, since that Bell inequality would not be violated.

Then you take 2^n*2^n previous test,.... and so on. As you go up, it gets harder for the inequality violator, its negative test count has a guaranteed growth. Also, I think this therem is not nearly restraining enough and the real state is much worse for the inequality violator (as simple computer enumerations suggest when counting the percentages of violation cases for the finite data sets).

Or, you go back and start testing, say, angle B7 again. Now the QM magician in heaven has to allow new A7[n] to be the same as the old A7[n], which was prohibited up to that point. You switch B to B9, and now, the QM magician, has to disallow again the match with A7[n] and allow the match with old A9[n], which was prohibited until now.

Where is the memory for all that? And what about the elaborate mechanisms or the infrastructure needed to implement the avoidance scheme? And why? What is the point of remembering all that stuff? What does it (or anyone/anything anywhere) get in return?

The conjectured QM violation of of Bell's inequality basically looks sillier and sillier once these kind of implications are followed through. It is not any more mysterious or puzzling but plainly ridiculous.

And what do we get from the absurdity? Well, we get the only real confirmation for the collapse since Bell's theorem uses collapse to produce the QM prediction which violates the inequality. And what do we need the collapse for? Well, it helps "solve" the measurement problem. And why is there the measurement problem? Well, because Bell's theorem shows you can't have LHVs to produce definite results. Anything else empirical from either. Nope. What a deal.

The collapse postulate first lends a hand to prove Bell's QM prediciton which in turn, via LHV prohibition, creates a measurement problem which then the collapse "solves" (thank you very much). So the collapse postulate creates a problem then solves it. What happens if we take out collapse postulate all together. No Bell's theorem, hence no measurement problem, hence no problem at all. Nothing else is sensitive to the existence (or the lack) of the collapse but the Bell's inequality experiment. Nothing else needs the collapse. It is a parasitic historical relic in the theory.

vanesch

Sep30-04, 01:24 AM

nightlight

Sep30-04, 03:59 AM

vanesch I don't know Sica's theorem, but what it states seems quite obvious,

It is the array correlation inequality statement I gave earlier wich also had the Sica's preprint link (http://cul.arxiv.org/abs/quant-ph/0101087).

if I understand so: a_1, a_2 ... are to be considered independent, and hence uncorrelated, or approximately orthogonal in our Euclidean space. ... Sounds perfectly all right to me. Where's the problem ???

You were looking for a paradox or a contradiction while I was pointing at the peculiarity for a specific subset of sequences. The most probable and the average behavior is, as you say, the approximate orthogonality among a1, a2,... or among b1, b2,... There is no problem here.

The Sica's result is stronger, though -- it implies that if the two sets of measurements (A,B1) and (A,B2) satisfy Bell's QM prediction then it is necessary that a1 and a2 vectors in E_N be explicitly different -- the a1 and a2 cannot be parallel, or even approximately parallel.

With just these two data sets, the odds of a1 and a2 being nearly parallel are very small, of the order 1/2^N. But if you have more than 2^N such vectors, they cannot all satisfy the QM prediction requirement that each remain non-parallel to all others. What is abnormal about this, is that this means that at least one test is guaraneed to fail, which is quite different from what one would normally expect of a statistical prediction: one or more finite tests may fail (due to a statistical fluctuation). Sica's result implies that at least one test must fail, no matter how large the array sizes.

What I find peculiar about it is that there should be any requirement of this kind at all between the two separate sets of measurements. To emphasize the peculiarity of this, consider that each vector a1 and a2 will have roughly the 50:50 split between +1 and -1 values. So it is the array ordering convention for individual results in two separate experiments that is constrained by the requirement of satisfying the alleged QM prediction.

The peculiarity of such kind of constraint is that the experimenter is free to label individual pairs of detection results in any order he wishes, i.e. he doesn't have to store the results of (A,B2) into A2[] and B2[] arrays so that array indices follow temporal order. He can store the first pair of detection results into A2[17], B2[17], the second pair at A2[5], B2[5], ... etc. This labeling is purely a matter of convention and no physics should be sensitive to such labeling convention. Yet, the Sica's result implies that there is always a labeling convention for these assignements which yields negative result for the test of Bell's QM prediction (i.e. it produces the classical inequality).

Let's now pursue the oddity one more step. The original labeling convention for the experiment (A,B2) was to map the larger time of detection to larger index. But you could have mapped it the opposite way i.e. the larger time to smaller index. The experiments should still succeed, i.e. violate the inequality (with any desired certainty, provided you pick N large enough). Now, you could have ignored the time of detection and used a random number generator to pick the next array slot to put the result in. You still expect the experiment to almost always succeed. It shouldn't matter whether you use a computer generated pseudo-random generator or flip a coin. Now, the the array a1 is equivalent to a sequence of coin flips, as random as one can get. So we use that sequence for our labeling convention to allocate next slot in the arrays a2,b2. Now with a1 used as the labeling seed, you can make a2 parallel to a1, 100% of the time. Thus there is a labeling scheme for experiments (A,B2), (A,B3),... which makes all of them always fail the Bell's QM prediction test.

Now, you may say, you are not allowed to use a1 for your array labeling convention in experiment (A,B2). Well, Ok, so this rule for the labeling must be added to the QM postulates since it doesn't follow from the existent postulates. And we now have another postulate that says, roughly:

COINCIDENCE DATA INDEX LABELING POSTULATE: if you are doing a photon correlation experiment and your setup has the efficiency above 82%, and you desire to uphold the collapse postulate, you cannot label the results in any order you wish. Specifically, your labeling algorithm cannot use the data from any other similar photon correlation experiment which has one polarizer axis parallel to your current test and which has the setup efficiency above 82%. If none of the other experiment's axis is parallel to yours, or if their efficiency is below 82%, then you're free to use the data of said experiment in your labeling algorithm. Also, if you do not desire to uphold the collapse postulate, you're free to use any labeling algorithm and any data you wish.

That's what I see as peculiar. Not contradictory or paradoxical, just ridiculous.

vanesch

Sep30-04, 06:12 AM

vanesch I don't know Sica's theorem, but what it states seems quite obvious,

It is the array correlation inequality statement I gave earlier wich also had the Sica's preprint link (http://cul.arxiv.org/abs/quant-ph/0101087).

I'll study it... even if I still think that you have a very peculiar view of things, it merits some closer look because I can learn some stuff too...

cheers,
Patrick.

vanesch

Sep30-04, 07:57 AM

I'll study it... even if I still think that you have a very peculiar view of things, it merits some closer look because I can learn some stuff too...

cheers,
Patrick.

Ok, I read the paper you indicated and I have to say I'm disappointed, because there seems to be a blatant error in the reasoning.
If you have 2 series of measurements, (a,b) and (a',b'), and you REORDER the second stream so that a = a', then of course the correlation <a.b'> = <a.b> is conserved, but you've completely changed <b.b'>, because the b hasn't permuted, and the b' has. From there on, there's no reason why this re-calculated <b.b'> (which enters in the Bell inequality, and must indeed be satisfied) has anything to do with the completely different prediction of <b.b'> by quantum theory.
So the point of the paper escapes me completely.

Look at an example.
Suppose we had some Bantum Theory, which predicts that <a.b> = 0, <a.b'> = 1 and <b.b'> = 1. You cannot have any harder violation of equation (3). (Quantum theory is slightly nicer).
Now, Bantum theory also only allows you to confront two measurements at a time.

First series of experiments: a and b:
(1,1), (1,-1),(-1,1),(-1,-1),(1,1), (1,-1),(-1,1),(-1,-1)

Clearly, we have equal +1 and -1 in a and in b, and we have <a.b> = 0.

Second series of experiments: a and b':
(1,1),(1,1),(-1,-1),(-1,-1),(1,1),(1,1),(-1,-1),(-1,-1),

Again, we have equal amount of +1 and -1 in a and b', and <a.b'> = 1.
Note that I already put them in order of a.

Third series of experiments: b and b':
(1,1),(1,1),(-1,-1),(-1,-1),(1,1),(1,1),(-1,-1),(-1,-1)

Note that for the fun of it, I copied the previous one. We have <b.b'> = 1, and an equal amount of +1 and -1 in b and b'.

There is no fundamental reason why we cannot obtain these measurement results, is there ? If experiments confirm this, Bantum theory is right. Nevertheless, |<ab> - <ab'>| <? 1 - <b.b'>
or |0 - 1| < 1 - 1 or 1 < 0 ???

cheers,
Patrick.

vanesch

Sep30-04, 09:56 AM

If you have 2 series of measurements, (a,b) and (a',b'), and you REORDER the second stream so that a = a', then of course the correlation <a.b'> = <a.b> is conserved, but you've completely changed <b.b'>, because the b hasn't permuted, and the b' has. From there on, there's no reason why this re-calculated <b.b'> (which enters in the Bell inequality, and must indeed be satisfied) has anything to do with the completely different prediction of <b.b'> by quantum theory.

I can even add that (a,b) and (a',b') have absolutely nothing to do with (b,b') as a new measurement. I have seen this kind of reasoning to refute EPR kinds of experiments or theoretical results several times now, and they are all based on a fundamental misunderstanding of what exactly quantum theory, as most people accept it, really predicts.

This doesn't mean that these discussions aren't interesting. However, you should admit that your viewpoint isn't so obvious as to call the people who take the standard view blatant idiots. Some work on the issue can be done, but one should keep an open mind. I have to say that I have difficulties seeing the way you view QM, because it seems to jump around certain issues in order to religiously fight the contradiction with Bell's identities. To me, they don't really matter so much, because the counterintuitive aspects of QM are strongly illustrated in EPR setups, but they are already present from the moment you accept superposition of states and the Born rule.

I've seen up to now two arguments: one is that you definitely need the projection postulate to deduce Bell's inequality violation, which I think is a wrong statement, and second that numerically, out of real data, you cannot hope to violate systematically Bell's inequality, which I think is also misguided, because a local realistic model is introduced to deduce these properties.

cheers,
Patrick.

nightlight

Oct1-04, 12:59 AM

vanesch Ok, I read the paper you indicated and I have to say I'm disappointed, because there seems to be a blatant error in the reasoning.

... the correlation <a.b'> = <a.b> is conserved, but you've completely changed <b.b'>, because the b hasn't permuted, and the b' has. From there on, there's no reason why this re-calculated <b.b'> (which enters in the Bell inequality, and must indeed be satisfied) has anything to do with the completely different prediction of <b.b'> by quantum theory.

The indicated statements show you have completely missed the several pages of discussion in the Sica's paper on his "data matching" procedure where he brings out that question and explicitly preserves <b.b'>. Additional analysis of the same question is in his later paper (http://cul.arxiv.org/abs/quant-ph/0211031). It is not necessary to change the sum <b1.b2> even though individual elements of the arrays b1[] and b2[] are reshuffled. Namely there is a great deal of freedom when matching a1[] and a2[] elements since any +1 from a2[] can match any +1 from a1[], allowing thus for [(N/2)!]^2 ways to match N/2 of +1's and N/2 of -1's between the two arrays. The constraint from <b1.b2> requires only that the sum is preserved in the permutation, which is a fairly weak constraint.

Although Sica's papers don't give a blow by blow algorithm for adjusting b2[], there is enough description in the two papers to work out a simple logistics for the swapping moves between the elements of b2[] which don't change the correlation <a.b2> and which monotonically (in steps of 2 per move) approach the required correlation <b1.b2> until reaching it within the max error of 1/N.

Let me know if you have any problem replicating the proof, then I'll take the time to type it in (it can be seen from a picture of the three arrays almost at a glance, although typing it all in would be a bit of a tedium).

vanesch

Oct1-04, 03:08 AM

The indicated statements show you have completely missed the several pages of discussion in the Sica's paper on his "data matching" procedure where he brings out that question and explicitly preserves <b.b'>.

Ok, I can understand that maybe there's a trick to reshuffle the b2[] in such a way as to rematch <b.b'> that would be present if there was a local realistic model (because that is hidden in Sica's paper, see below). I didn't check it and indeed I must have missed that in Sica's paper. However, I realized later that I was tricked into the same reasoning error as is often the case in these issues, and that's why I posted my second post.
There is absolutely no link between the experiments [angle a, angle b] and [angle a, angle b'] on one hand, and a completely new experiment [angle b, angle b']. The whole manipulation of series of data tries to find a correlation <b.b'> from the first two experiments, and because there is a notational equivalence (namely the letters b and b') between the second datastreams of these first two experiments, and the first and second datastream of the third experiment. So I will now adjust the notation:
First experiment: analyser 1 at angle a, and analyser 2 at angle b, results in a data stream {(a1[n],b1[n])}, shortly {Eab[n]}
Second experiment: analyser 1 at angle a, and analyser 2 at angle b', results in a datastream {(a2[n],b'2[n])} , shortly {Eab'[n]}.
Third experiment: analyser 1 at angle b, and analyser 2 at angle b', results in a datastream {(b3[n],b'3[n])}, shortly {Ebb'[n]}.

There is no way to deduce <b3.b'3> from the first two experiments UNLESS you assume an underlying model which has a "master distribution" from which all these series are drawn ; this is nothing else but a local realistic model, for which indeed, Bell's inequalities must hold. The confusion seems to come from the fact that one tries to construct a <b.b'> from data that haven't been generated in the Ebb' condition, but from the Eab and Eab' conditions. Indeed, if these b and b' streams were to be predetermined, this reasoning would hold. But it is the very prediction of standard QM that they aren't. So the Ebb' case has the liberty of generating completely different correlations than those of the Eab and Eab' cases.

That's why I gave my (admittedly rather silly) counter example in Bantum mechanics. I generated 3 "experimental results" which

Although Sica's papers don't give a blow by blow algorithm for adjusting b2[], there is enough description in the two papers to work out a simple logistics for the swapping moves between the elements of b2[] which don't change the correlation <a.b2> and which monotonically (in steps of 2 per move) approach the required correlation <b1.b2> until reaching it within the max error of 1/N.
Contrary to what Sica writes below his equation (3) in the first paper, he DID introduce an underlying realistic model, namely that the correlations of b and b' in the case of Eab and Eab' have anything to do with the correlations of Ebb'.

Let me know if you have any problem replicating the proof, then I'll take the time to type it in (it can be seen from a picture of the three arrays almost at a glance, although typing it all in would be a bit of a tedium).

I'll give it a deeper look ; indeed it excaped me, it must be what phrase starting on line 14 of p6 alludes to (I had put a question mark next to it!), but even if I agree with it, the point is moot, because, as I said, THIS correlation between the b and b' trains (in my notation b1 and b'2) should a priori have nothing to do with the correlation between b3 and b'3. In fact, I now realise that you can probably fabricate every thinkable correlation between b1 and b'2 that is compatible with (3) by reshuffling b'2[n], so this correlation is not even well-defined. Nevertheless, by itself the result is interesting, because it illustrates very well a fundamental misunderstanding of standard quantum theory (at least I think so :-). I think I illustrated the point with my data streams in Bantum theory ; however, because i tricked them by hand you might of course object. If you want to, I can generate you a few more realistic series of data which will ruin what I think Sica is claiming when he writes (lower part of p9) "However, violation of the inequality by the correlations does imply that they cannot represent any data streams that could possibly exist or be imagined".

cheers,
Patrick.

nightlight

Oct1-04, 03:27 AM

vanesch I can even add that (a,b) and (a',b') have absolutely nothing to do with (b,b') as a new measurement.

You may need to read the part two (http://cul.arxiv.org/abs/quant-ph/0211031) of the paper where the connection is made more explicit, and also check the original Bell's 1964 paper (especially Bell's Eq's (8) and (13) which utilize the perfect correlations for the parallel and anti-parallel aparatus orientations, to move implicitly between the measurements on B and A, in the QM or in the classical model; these are essential steps for the operational interpretation of the three correlations case).

I have seen this kind of reasoning to refute EPR kinds of experiments or theoretical results several times now, and they are all based on a fundamental misunderstanding of what exactly quantum theory, as most people accept it, really predicts.

That wasn't a refutation of Bell's theorem or experiments, merely a new way to see the nature of the inequality. It is actually quite similar to an old visual proof of Bell's theorem by Henry Stapp from late 1970s (I had it while working on masters thesis on this subject, it was an ICTP preprint that my advisor brought back from a conference in Trieste).

However, you should admit that your viewpoint isn't so obvious as to call the people who take the standard view blatant idiots.

I wouldn't do that. I was under the spell for quite a few years, even though I did masters degree on the topic and have read quite a few papers and books at the time and had spent untold hours discussing it with the advisors and the colleagues. It was only after leaving the academia and forgetting about it for few years, then happening to get involved a bit helping my wife (also a physicist, but experimental) with some quantum optics coincidence setups, that it struck me as I was looking at the code that processed the data -- wait a sec, this is nothing like I imagined. All the apparent firmness of assertions, such as A goes here, B goes there, ... in textbooks or papers, rang pretty hollow.

On the other hand, I do think, it won't be too long before the present QM mystification is laughed at by the next generation of physicists. Even the giants like Gerard 't Hooft (http://arxiv.org/find/quant-ph/1/au:+hooft/0/1/0/all/0/1) are ignoring the Bell's and other no-go theorems and exploring the purely local sub-quantum models (the earlier heretics such as Schroedinger, Einstein, de Broglie, later Dirac, Barut, Jaynes,.. weren't exactly midgets, either).

...Bell's identities. To me, they don't really matter so much, because the counterintuitive aspects of QM are strongly illustrated in EPR setups, but they are already present from the moment you accept superposition of states and the Born rule.

There is nothing odd about superposition at least since Maxwell and Faraday. It might surprise you, but plain old classical EM fields can do the entanglement, GHZ state, qubits, quantum teleportation, quantum error correction,... and the rest of the buzzwords, just about all but the non-local, non-dynamical collapse - that bit of magic they can't do (check papers by Robert Spreeuw (http://cul.arxiv.org/abs/quant-ph/0009066), also some more on his home page (http://remote.science.uva.nl/~spreeuw/lop.htm)).

I've seen up to now two arguments: one is that you definitely need the projection postulate to deduce Bell's inequality violation, which I think is a wrong statement

What is your (or rather, the QM Measurement theory's) Born rule but a projection -- that's where your joint probabilities come from. Just recall that the Bell test can be viewed as a preparation of a system B in, say, pure |B+> state, which appears as a sub-ensemble of B for which A produced the (-1) result. The state of A+B which is a pure state initially collapses into a mixture rho = 1/2 |+><+|x|-><-| + 1/2 |-><-|x|+><+| from which one can identify the sub-ensemble of a subsystem, such as |B+> (without going to mixture the statements such as "A produced -1" are meaningless since the initial state is a superposition and spherically symmetrical). Unitary evolution can't do that without non-dynamical collapse (see von Neumann's chapter on measurement process and his infiite chain problem and why you have to have it).

You may imagine that you never used state |B+> but you did since you used the probabilities for B system (via the B subspace projector within your joint probabilities calculation) which only that state can reproduce (the state is unique once all the probabilities are given, according to Gleason).

Frankly, you're the only one ever to deny using collapse in deducing Bell's QM prediction. Only a suspension of the dynamic evolution can arrive from the purely local PDE evolution equations (the 3N coordinate relativistic Dirac-Maxwell equations for the full system, including the aparatus) to a prediction which prohibits any purely local PDE based mechanism from reproducing such prediction. (You never explained how can local PDEs do it without suspension of dynamics; except for trying to throw into the equations, as a premise, the approximate, explicitly non-local/non-relativistic instantaneous potentials.)

and second that numerically, out of real data, you cannot hope to violate systematically Bell's inequality, which I think is also misguided,

I never claimed that the Sica's result rules out, mathematically or logically, the experimental confirmation of the Bell's QM prediction. It only makes those predictions seem stranger than one would have thought from usual descriptions.

The result also sheds light on the nature of Bell's inequalities -- they are enumerative constraints, a la pigeonhole principle. Thus the usual euphemisms and excuses used to soften the plain simple fact of over three decades of failed tests, are non-sequiturs (see couple messages back for the explanation).

vanesch

Oct1-04, 03:49 AM

What is your (or rather, the QM Measurement theory's) Born rule but a projection -- that's where your joint probabilities come from.

Yes, that was indeed the first question I asked you: to me, the projection postulate IS the Born rule. However, I thought you aimed at the subtle difference between calculating probabilities (Born rule) and the fact that AFTER the measurement, the state is assumed to be the eigenstate corresponding to the measurement result, and I thought it was the second part that you were denying, but accepting the absolute square of inproduct as the correct probability prediction. As you seem to say yourself, it is very difficult to disentangle both!

The reason why I say that you seem to deny superposition in its general sense is that without the Born rule (inproduct squared = probability) the Hilbert space has no meaning. So if you deny the possibility for me to use that rule on the product space, this means you deny the existance of that product space, and hence the superpositions of states such that the result is not a product state. You need that Born rule to DEFINE the Hilbert space. It is the only link to physical results. So in my toy model in 2x2 D hilbert space, I can think of measurements (observables, Hermitean operators) which can, or cannot factor into 1 x A or A x 1, it is my choice. If I choose to have a "global measurement" which says "result +1 for system 1 and result -1 for system 2", then that is ONE SINGLE MEASUREMENT, and I do not need to use any fact of "after the measurement, the state is in an eigenstate of...". I need such kind of specification in order for the product space to be defined as a single Hilbert space, and hence to allow for the superposition of states across the products. Denying this is denying the superposition.
However, you need a projection, indeed, to PREPARE any state. As I said, without it, there is no link between the Hilbert space description and any physical situation. The preparation is here the singlet state. But in ANY case, you need some link between an initial state in Hilbert space, corresponding to a physical setup.

Once you've accepted that superposition of the singlet state, it should be obvious that unitary evolution cannot undo it. So, locally (meaning, acting on the first part of the product space), you can complicate the issue as much as you like, there's no way in which you can undo the correlation. If you accept the Born rule, then NO MATTER WHAT HAPPENS LOCALLY, these correlations will show up, violating Bell's inequalities in the case of 100% efficient experiments.

cheers,
Patrick.

nightlight

Oct1-04, 03:50 AM

vanesch

Oct1-04, 05:29 AM

vanesch There is no way to deduce <b3.b'3> from the first two experiments UNLESS you assume an underlying model which has a "master distribution" from which all these series are drawn ; this is nothing else but a local realistic model, for which indeed, Bell's inequalities must hold.

The whole point of reshuffling was to avoid the need for an underlying model (the route Bell took) in order to get around the non-commutativity of b,b' and the resulting counterfactuality (thus having to do the third experiment; as any Bell inequality test does) when trying to compare their correlations in the same inequality (that was precisely the point of the Bell's original objection to von Neumann's proof).

Ah, well, I could have helped them out back then :rofl: :rofl:. It was exactly the misunderstanding of what exactly QM predicts that I tried to point out. The very supposition that the first two b[n] and b'[n] series should have anything to do with the result of the third experiment means that 1) one didn't understand what QM said and didn't say, but also 2) that one supposes that these series were drawn from a master distribution, which would have yielded the same b[n] and b'[n] if we happened to have choosen to measure those instead of (a,b) and (a,b'). This supposition by itself (which comes down to saying that the <b1[n],b'2[n]> correlation (which, I repeat, is not uniquely defined by Sica's procedure) has ANYTHING to do with whatever should be measured when performing the (b,b') experiment IS BY ITSELF a hidden-variable hypothesis.

cheers,
Patrick.

nightlight

Oct1-04, 05:43 AM

Yes, that was indeed the first question I asked you: to me, the projection postulate IS the Born rule.

In the conventional textbooks QM measurement axiomatics the core empirical essence of the original Born rule (as Schoredinger intepreted it in his founding papers; Born introduced a related rule as a footnote for interpreting the scattering amplitudes) is hopelessly entangled with the Hilbert space observables, projectors, Gleason's theorem, etc.

However, I thought you aimed at the subtle difference between calculating probabilities (Born rule) and the fact that AFTER the measurement, the state is assumed to be the eigenstate corresponding to the measurement result, and I thought it was the second part that you were denying,

Well, that part, the non-destructive measurement, is mostly von Neumman's high abstraction which has little relevance or physical content (any discussion on that topic is largely a slippery semantic game, arising from the overload of term "measurement" and shifting its meaning between the prepartion and detection -- that whole topic is empty). Where is the photon A in Bell's experiment after it triggered the detector? Or for that matter any photon after detection in any Quantum Optics experiment?

but accepting the absolute square of inproduct as the correct probability prediction.

That is an approximate and limited operational rule. Any claimed probability of detection ultimately has to check against the actual design and the settings of the aparatus. Basically, the presumed linear response of an apartus to the Psi^2 is a linear approximation to a more complex non-linear response (e.g. check the actual photodetectors sensitivity curves, they are sigmoid with only one section approximately linear). Talking of "probability of detecting a photon" is somewhat misleading, often confusing, and it is less accurate than talking about degree and nature of response to an EM field.

In the usual Hilbert space formulation, the Born rule is a static, geometric property of vectors, projectors, subspaces. It lacks the time dimension, thus the connection to the dynamics which is its real origin and ultimate justification and delimiter.

The reason it is detached from the time and the dynamics is precisely in order to empower it with the magic capability of suspending the dynamics, producing the "measurement" result with such and such probability, then resuming the dynamics. And without ever defining how and when exactly this suspension occurs, what and when restarts it... etc. It is so much easier to forget about time and dynamics if you smother them with ambiguous verbiage ("macroscopic" and other such obfuscations) and vacuous but intricate geometric postulates. By the time student gets through all of it, his mind will be too numbed, his eyes too glazed to notice that emperor wears no trousers.

The reason why I say that you seem to deny superposition in its general sense is that without the Born rule (inproduct squared = probability) the Hilbert space has no meaning.

It is a nice idea (linearization) and a useful tool taken much too far. The actual PDEs and the integral equations formulations of the dynamics are mathematically much richer modelling medium then their greately impoverishing abstraction, the Hilbert space.

Superposition is as natural with any linear PDEs and integral equations as it is with Hilbert space. On the other hand, the linearity is almost always an approximation. The QM (or of QED) linearity is an approximation for the more exact interaction between the matter fields and EM field. Namely the linearization arises from assuming that the EM fields are "external" (such as Coulomb potential or an external EM fields interacting with the atoms) and that the charge currents giving rise to quantum EM fields are external. Schroedinger's original idea was to put the Psi^2 (and its current) as the source terms in the Maxwell equations, obtaining thus the coupled non-linear PDEs. Of course, at the time and in that phase that was much too ambitious project which never got very far. It was only in late 1960s that Jaynes picked up the Schroedinger's idea and developed somewhat flawed "neoclassical electrodynamics". That was picket in mid-1980s by Asim Barut which worked out more accurate "self-field electrodynamics" which reproduces not only the QM but the leading radiative corrections of QED, without ever quantizing (which amounts to linearizing the dynamics then adding the non-linearities via perturbative expansion) the EM field. He viewed the first quantization not as some fancy change of classical variables to operators, but as a replacement of the Newtonian-Lorentz particle model with the Fraday-Maxwell type matter field model, resolving thus the particle-field dichotomy (which was plagued with the point-particle divergencies). Thus for him (or for Jaynes) the field quantization was unneccessary, non-fundamental, at best a computational linearization procedure.

On the other hand, I think the future will favor neither, but rather the completely different, new modelling tools (physical theories are models) more in tune with the technology (such as Wolfram's automata, networks, etc). The Schroedinger, Dirac and Maxwell equations can already be rederived as macroscopic approximation of the dynamics of simple binary on/off automata (see for example some interesting papers by Garnet Ord (http://www.scs.ryerson.ca/~gord/)). These kind of tools are hugely richer modelling medium than either PDEs or Hilbert space.

So if you deny the possibility for me to use that rule on the product space, this means you deny the existance of that product space, and hence the superpositions of states such that the result is not a product state.

I am only denying that this abstraction/generalization automatically applies that far in such simple-minded, uncritical manner in the Bell experiment setup. Just calling all Hermitean operators observable, doesn't make them so, much less at the "ideal" level. The least one needs to do in the modelling in this manner the Bell's setup is to include projectors to no_coincdince and no_detection subspaces (these would be from orbital degrees of freedom) so the prediction has some contact with the reality instead of bundling all the unknowns it into the engineering parameter "efficiency" so all the ignorance can be swept under the rug, while wishfully and imodestly labeling the toy model "ideal". What a joke. The most ideal model is one that predicts the best what actually happens (which is 'no violation') and not the one which makes the human modeler appear in the best light or in control of the situation the most.

vanesch

Oct1-04, 05:46 AM

[/color](the 3N coordinate relativistic Dirac-Maxwell equations for the full system, including the aparatus) to a prediction which prohibits any purely local PDE based mechanism from reproducing such prediction. (You never explained how can local PDEs do it without suspension of dynamics; except for trying to throw into the equations, as a premise, the approximate, explicitly non-local/non-relativistic instantaneous potentials.)

I don't know what 3N coordinate relativistic Dirac-Maxwell equations are. It sounds vaguely as the stuff an old professor tried to teach me instead of QFT. True QFT cannot be described - as far as I know - by any local PDE ; it should fit in a Hilbert state formalism. But I truely think you do not need to go relativistically in order to talk about Bell's stuff. In fact, the space-like separation is nothing very special to me. As I said before, it is just an extreme illustration of the simple superposition + Born rule case you find in almost all QM applications. So all this Bell-stuff should be explainable in simple NR theory, because exactly the same mechanisms are at work when you calculate atomic structure, when you do solid-state physics or the like.

cheers,
Patrick.

vanesch

Oct1-04, 06:03 AM

In the usual Hilbert space formulation, the Born rule is a static, geometric property of vectors, projectors, subspaces. It lacks the time dimension, thus the connection to the dynamics which is its real origin and ultimate justification and delimiter.

You must be kidding. The time evolution is in the state in Hilbert space, not in the Born rule itself.

And without ever defining how and when exactly this suspension occurs, what and when restarts it... etc. It is so much easier to forget about time and dynamics if you smother them with ambiguous verbiage ("macroscopic" and other such obfuscations) and vacuous but intricate geometric postulates.

Well, the decoherence program has something to say about this. I don't know if you are aware of this.

It is a nice idea (linearization) and a useful tool taken much too far. The actual PDEs and the integral equations formulations of the dynamics are mathematically much richer modelling medium then their greately impoverishing abstraction, the Hilbert space.

Superposition is as natural with any linear PDEs and integral equations as it is with Hilbert space. On the other hand, the linearity is almost always an approximation. The QM (or of QED) linearity is an approximation for the more exact interaction between the matter fields and EM field.

Ok this is what I was claiming all along. You DO NOT ACCEPT superposition of states in quantum theory. In quantum theory, the linearity of that superposition (in time evolution and in a single time slice) is EXACT ; this is its most fundamental hypothesis. So you shouldn't say that you are accepting QM "except for the projection postulate". You are assuming "semiclassical field descriptions".

Namely the linearization arises from assuming that the EM fields are "external" (such as Coulomb potential or an external EM fields interacting with the atoms) and that the charge currents giving rise to quantum EM fields are external. Schroedinger's original idea was to put the Psi^2 (and its current) as the source terms in the Maxwell equations, obtaining thus the coupled non-linear PDEs.

I see, that's indeed semiclassical. This is NOT quantum theory, sorry. In QED, but much more so in non-abelian theories, you have indeed a non-linear classical theory, but the quantum theory is completely linear.

Of course, at the time and in that phase that was much too ambitious project which never got very far. It was only in late 1960s that Jaynes picked up the Schroedinger's idea and developed somewhat flawed "neoclassical electrodynamics".

Yeah, what I said above. Ok, this puts the whole discussion in another light.

That was picket in mid-1980s by Asim Barut which worked out more accurate "self-field electrodynamics" which reproduces not only the QM but the leading radiative corrections of QED, without ever quantizing (which amounts to linearizing the dynamics then adding the non-linearities via perturbative expansion) the EM field. He viewed the first quantization not as some fancy change of classical variables to operators, but as a replacement of the Newtonian-Lorentz particle model with the Fraday-Maxwell type matter field model, resolving thus the particle-field dichotomy (which was plagued with the point-particle divergencies). Thus for him (or for Jaynes) the field quantization was unneccessary, non-fundamental, at best a computational linearization procedure.

Such semiclassical models are used all over the place, such as to calculate effective potentials in quantum chemistry. I know. But I consider them just as computational approximations to the true quantum theory behind it, while you are taking the opposite view.

You tricked me into this discussion because you said that you accepted ALL OF QUANTUM THEORY except for the projection, so I was shooting at the wrong target ; nevertheless, several times it occured to me that you were actually defying the superposition principle, which is at the heart of QM. Now you confessed :tongue: :tongue:

cheers,
Patrick.

seratend

Oct1-04, 06:46 AM

I’ve read this interesting discussion and I’d like to add the following comments.

Bell’s inequalities and more precisely EPR like states help in understanding how quantum states behave. There are many papers in arxiv about theses inequalities. Many of them show how classical statistics can locally break these inequalities even without the need to introduce local (statistical) errors in the experiment.

Here are 2 examples extracted form arxiv (far from being exhaustive).

Example 1 : quant-th/0209123 Laloë 2002 extensive paper on QM interpretation questions (to my opinion against local hidden variable theory, but open mind => lot of pointers and examples)
Example 2: quant-ph/0007005 Accardi 2000 (and later). An Example of how a classical probability space can break bell inequalities (contextual).

The approach of Nightlight, if I have correctly understood, is another way (I’ve missed it: thanks a lot for this new possibility): instead of breaking the inequalities, the “statistical errors” (some events not counted by the experiment, or the way the experiment data is calculated), if included in the final result, force the experiment to follow the bell inequalities. This is another point of view on what is “really” going on with the experiment.

All of these alternative examples use a classical probability space, i.e. the Kolmogorov axiomatization, where one take the adequate variables such that they can violate the Bell’s inequalities (and now, a way to enforce them).

Now, if the question is to know whether the bell’s inequalities experiments are relevant or not, one conservative approach is to try to know (at least feel, and the best, demonstrate), if in “general”, “sensible” experiments (quantum or classical or whatever we want) are most likely to break the bell’s inequalities or not. If the answer is no, then we must admit that aspect type of experiments have detected a rare event and that the leaving “statistical errors” seem not to help (in breaking the inequalities). If the answer is yes, well, we can say what we want :).

The papers against bell’s inequalities experiments, to my modest opinion, demonstrate that a sensible experiment is more likely to detect the inequalities breaking so that we can say what we want! That’s a little bit disappointing, because in this case we still not know if any quantum state may be described by any “local” classical probability space or not. I really prefer to get an good and solid explaination.

To end, I did not know before the Sica’s papers. But, I would like to understand the mechanism he (and Nightlight) used in order to force the Bell’s inequality matching. I follow Vanesh reasoning without problem, but the Nighlight one is a little bit more difficult to understand: where is the additional freedom used to enforce the inequality.

So, lets try to understand this problem in the special case of the well known Aspect et al experiment 1982, phys.rev. letters (where only very simple mathematics are used). I like to use a particular case before making a generalisation; it is easier to see where the problem is.

First let’s take 4 ideal discrete measurements (4 sets of data) of an Aspect type experiment with no lost sample during the measurement process.

If we take the classical expectations formulas with have :

S+= E(AB)+E(AB’)=1/N sum_i1 [A(i1)B(i1)]+ 1/N sum_i2 [A(i2)B’(i2)]
= 1/N sum_i1_i2[A(i1)B(i1)+ A(i2)B’(i2)] (1)

Where A(i1),B(i1) is the data collected by the first experiment and A(i2),B(i2) the data collected by the second experiment. With N --> ∞ (we also take the same sample number for each experiment).

In our particular case A(i1) is the result of the spin measurement of photon 1 on the A (same name as the observable) axis (+1 if spin |+>, -1 if spin |->) while B(i1) is the result of the spin measurement of photon 2 on the B axis (+1 if spin |+>, -1 if spin |->).
Each ideal measurement (given by label i1 or i2) thus gives two spin results (the two photons must be detected).
Etc … For the other measurement cases.

We thus have the second equation:

S-= E(A’B)-E(A’B’)=1/N sum_i3 [A’(i3)B(i3)]- 1/N sum_i4 [A’(i4)B’(i4)]
= 1/N sum_i3_i4[A(i3)B(i3)- A(i4)B(i4)] (2)

Labelling equation (1) or (2), ie, changing the ordering of label i1,i2,i3,i4 does not change the result (sum is commutative).

Now, If we want get the inequality S+=|E(AB)+E(AB’)|≤ 1+E(BB’), we first need to make a filter to the rhs equation (1), otherwise A cannot be factorized: we must select a subset of experiment samples with A(i1)=A(i2).

If we take a large samples number N, equation (1) is not changed with this filtering and we get:

|S+|= |E(AB)+E(AB’)|= 1/N |sum_i1_i2[A(i1)B(i1)+ A(i2)B’(i2)] |
= 1/N |sum_i1[A(i1)B(i1)+ A(i1)B’(i1)] |=
≤1/Nsum_i1 |[A(i1)B(i1)+ A(i1)B’(i1)]|

We then used the simple inequality |a.b+a.c|≤ 1+ a.c (|a|,|b|,|c| ≤1) for each label i1

|S+|= |E(AB)+E(AB’)| ≤1+1/N sum_i1[B(i1)B’(i1)] (3)

Remind that B’(i1) is the data of the second experiment relabelled with a subset of label i1. Now this re-labelling has a freedom because we may have several experiment results (50%) where A(i1)=A(i2).

So in equation (3) |sum_i1[B(i1)B’(i1)]]| depends on the artificial label order.

We also have almost the same inequality for equation (2)

|S+|= |E(A’B)-E(A’B’)|= 1/N |sum_i3_i4[A’(i3)B(i3)- A’(i4)B’(i4)] |
= 1/N |sum_i3[A’(i3)B(i3)- A’(i3)B’(i3)] |=
≤1/Nsum_i3 |A’(i3)B(i3)- A’(i3)B’(i3)|

We then used the simple inequality |a.b-a.c|≤ 1- a.c (|a|,|b|,|c| ≤1)

|S+|= |E(A’B)-E(A’B’)| ≤1-1/N sum_i3[B(i3)B’(i3)] (4)

So in equation (4) |sum_i1[B(i3)B’(i3)]]| depends on the artificial label ordering i3.

Now, we thus have the bell inequality:

|S=S++S-|≤ S++ S-= 2+1/N sum_i1_i3[B(i1)B’(i1)-B(i3)B’(i3)] (5)

where sum_i1_i3[B(i1)B’(i1)-B(i3)B’(i3)] depends on the labelling order we have used to filter and get this result.

I think that (3) and (4) may be the labelling order pb remarked by Nighlight in this special case.

Up to know, we have only spoken of collection of measurement results of values +1/-1.

Now if B is a random variable that depends only on the local experiment apparatus (the photon polarizer) we have B=B(apparatus_B, hv) where hv is the local hidden variable, we should have:

1/N.sum_i1[B(i1)B’(i1)= 1/N.sum_i3B(i3)B’(i3)] = <BB’> when N--> ∞.
(so we have the Bell inequality |S|≤2).

So, now I can use the Nighlight argument, ordering of B’(i1) and B’(i3) is totally artificial then the question is: should I got 1/N.sum_i1[B(i1)B’(i1)<> 1/N.sum_i3B(i3)B’(i3)] or the equality?

Moreover, Equation (5) seems to show that this kind of experiments are more likely to see a violation of a bell inequality as B(i1),B’(i2),B(i3)B’(i4) comes from 4 different experiments.

Seratend

P.S. Sorry if some minor mistakes are left.

seratend

Oct1-04, 06:52 AM

Sorry, my post was supposed to follow this one:

vanesch Ok, I read the paper you indicated and I have to say I'm disappointed, because there seems to be a blatant error in the reasoning.

... the correlation <a.b'> = <a.b> is conserved, but you've completely changed <b.b'>, because the b hasn't permuted, and the b' has. From there on, there's no reason why this re-calculated <b.b'> (which enters in the Bell inequality, and must indeed be satisfied) has anything to do with the completely different prediction of <b.b'> by quantum theory.

The indicated statements show you have completely missed the several pages of discussion in the Sica's paper on his "data matching" procedure where he brings out that question and explicitly preserves <b.b'>. Additional analysis of the same question is in his later paper (http://cul.arxiv.org/abs/quant-ph/0211031). It is not necessary to change the sum <b1.b2> even though individual elements of the arrays b1[] and b2[] are reshuffled. Namely there is a great deal of freedom when matching a1[] and a2[] elements since any +1 from a2[] can match any +1 from a1[], allowing thus for [(N/2)!]^2 ways to match N/2 of +1's and N/2 of -1's between the two arrays. The constraint from <b1.b2> requires only that the sum is preserved in the permutation, which is a fairly weak constraint.

Although Sica's papers don't give a blow by blow algorithm for adjusting b2[], there is enough description in the two papers to work out a simple logistics for the swapping moves between the elements of b2[] which don't change the correlation <a.b2> and which monotonically (in steps of 2 per move) approach the required correlation <b1.b2> until reaching it within the max error of 1/N.

Let me know if you have any problem replicating the proof, then I'll take the time to type it in (it can be seen from a picture of the three arrays almost at a glance, although typing it all in would be a bit of a tedium).

Seratend,
It takes time to answer :)

vanesch

Oct1-04, 07:38 AM

Example 2: quant-ph/0007005 Accardi 2000 (and later). An Example of how a classical probability space can break bell inequalities (contextual).

I only skimmed quickly at this paper, but something struck me: he shows that Bell's equality can also be satisfied with a non-local model. Bell's claim is the opposite: that in order NOT to satisfy the equality, you need a non-local model.

A => B does not imply B => A.

The "reduction" of the "vital assumption" that there is one and only one underlying probability space is in my opinion EXACTLY what is stated by local realistic models: indeed, at the creation of the singlet state with two particles, both particles carry with them the "drawing of the point in the underlying probability universe", from which all potential measurements are fixed, once and for all.

So I don't really see the point of the paper! But ok, I should probably read it more carefully.

cheers,
Patrick

nightlight

Oct1-04, 07:47 AM

vanesch you accepted ALL OF QUANTUM THEORY except for the projection, so I was shooting at the wrong target ; nevertheless, several times it occured to me that you were actually defying the superposition principle, which is at the heart of QM. Now you confessed :tongue: :tongue:

Projection postulate itself suspends the linear dynamical evolution. It just does it on the cheap, in a kind of slippery way, without explaining how, why and when does it stop functioning (macroscopic device ? consciousness? a friend of that consciousness? decoherence? consistent histories? gravity? universe branching? jhazdsfuty?) and how it resumes. That is a tacit recognition that linear evolution such as the linear Schrodinger or Dirac equations, don't work correctly throughout. So when the limitation of the linear approximation reaches a critical point, the probability mantras get chanted, the linear evolution is stopped in a non-dynamic, abrupt way, and temporarily substituted with a step-like, lossy evolution (the projector) to a state in which it ought to be, then when in the safe waters again, the probability chant stops, and the regular linear PDE resumes. The overall effect is at best analogous to a piecewise linear approximation of a curve which, all agree, cannot be a line.

So this is not a matter who is for and who is against the linearity -- since no one is "for" with the only difference that some know that. The rest believe they are in the "for" group and they despise the few who don't believe so. If you believe in projection postulate, you believe in temporary suspension of linear evolution equations, however ill-defined it may be.

Now that we agreed we're all against linearity, what I am saying is that this "solution," the collapse, is an approximate stop-gap measure, due to intractability of already known non-linear dynamics, which in principle can produce collapse-like effects when they're called for, except in a lawful and clean way. The linearity would hold approximately as it does now, and no less than it does now, i.e. it is analogous to smoothing the sharp corners of the piecewise linear approximation with a mathematically nicer and more accurate approximation.

While you may imagine that non-linearity is a conjecture, it is the absolute linearity that is a conjecture, since non-linearity is a more general scheme. Check von Neumman's and Wigner's writings on the measurement problem to see the relation between the absolute linearity and the need for the collapse.

A theory cannot be logically coherent if it has an ill-defined switch between the two incompatible modes of operation, the dynamic equations and the collapse (which grew out of the similarly incoherent seeds, the Bohr's atom model and the first Plank's theory). The whole theory in this phase is like a hugely magnified version of the dichotomies of the originating embryo. That's why there is so much philosophizing and nonsense on the subject.

nightlight

Oct1-04, 08:16 AM

You must be kidding. The time evolution is in the state in Hilbert space, not in the Born rule itself.

That is the problem I am talking about. We ought not to have dynamical evolution interrupted and suspended by "measurement" which turns on the Born rule, to figure out what it really wants to do next, then somehow the dynamics is allowed to run again.

Well, the decoherence program has something to say about this. I don't know if you are aware of this.

It's a bit decoherent for my taste.

vanesch

Oct1-04, 08:20 AM

Projection postulate itself suspends the linear dynamical evolution. It just does it on the cheap, in a kind of slippery way, without explaining how, why and when does it stop functioning (macroscopic device ? consciousness?

The relative-state (or many worlds) proponents do away with it, and apply strict linearity. I have to say that I think myself that there is something missing in thas picture. But I think that quantum theory is just a bit too subtle to replace it with semiclassical stuff. I'd be surprised that such a model can predict the same things as QFT and most of quantum theory. In that it would be rather stupid, no? I somehow have the feeling - it is only that of course - that this semiclassical approach would be the evident way to try stuff before jumping on the bandwagon of full QM, and that people have turned that question in all possible directions, so that the possibilities have been exhausted there. Of course, one cannot study all "wrong" paths of the past and one has to assume that this has been looked at somehow, otherwise nobody gets nowhere if all wrong paths of the past are re and re and reexamined. So I didn't look in all that stuff, accepting that it cannot be done.

cheers,
Patrick.

nightlight

Oct1-04, 09:15 AM

But I think that quantum theory is just a bit too subtle to replace it with semiclassical stuff.

I didn't have in mind the semiclassical models. The semiclassical scheme merely doesn't quantize EM field, but it still uses the external field aproximation, thus, although practical, it is limited and less accurate than QED (when you think of the difference in heavy gear involved, it's amazing it works at all). Similar problems plague Stochastic Electrodynamics (and its branch Stochastic Optics). While they can model many of the the so called non-classical effects touted in Quantum Optics (including the Bell's inequality experiments), they are also an external field approximation scheme, just using the ZPF distribution as the boundary/intial conditions for the classical EM field.

To see the difference from the above approaches, write down Dirac equation with minimal EM coupling, then add below the inhomogenious wave equation for the 4-potential A_mu (the same one from the Dirac equation above it) with the right hand side using the Dirac's 4-current. You have a set of coupled nonlinear PDEs without external field or external current approximation. See how far you get with that kind of system.

That's a variation of what Barut started with (and also with Schroedinger-Pauli instead of Dirac) and then managed to reproduce the results of the leading orders of QED expansion (KEK preprint server (http://www-lib.kek.jp/cgi-bin/kiss_prepri?KN=&TI=&AU=barut&AF=&CL=&RP=&YR=) has 55 of his papers and preprints scanned; those from mid 1980s and on are mostly on his self-field). While this scheme alone obviously cannot be the full theory, it may be a at least knock on the right door.

vanesch

Oct1-04, 09:30 AM

To see the difference from the above approaches, write down Dirac equation with minimal EM coupling, then add below the inhomogenious wave equation for the 4-potential A_mu (the same one from the Dirac equation above it) with the right hand side using the Dirac's 4-current. You have a set of coupled nonlinear PDEs without external field or external current approximation. See how far you get with that kind of system.

This is exactly what my old professor was doing (and in doing so, he neglected to teach us QFT, the bastard). He was even working on a "many particle dirac equation". And indeed, this seems to be a technique that incorporates some relativistic corrections for heavy atoms (however, there the problem is that there are too many electrons and the problem becomes untractable, so it would be more something to handle an ion like U+91 or so).

Nevertheless, I'd still classify this approach as fully classical, because there is no "quantization" at all, and the matter fields are considered as classical fields just as well as the EM field. In the language of path integrals, you wouldn't take into account anything besides the classical solution.
Probably this work can be interesting. But you should agree that it is still a far way to go to have a working theory, so you shouldn't sneer at us low mortals who, for the moment, take quantum theory in the standard way, no ?
My feeling is that it is simply too cheap, honestly.

cheers,
Patrick.

nightlight

Oct1-04, 10:09 AM

This is exactly what my old professor was doing (and in doing so, he neglected to teach us QFT, the bastard).

What's his name. (Dirac was playing in later years with that stuff, too, so it can't be that silly.)

He was even working on a "many particle dirac equation".

What Barut found (although only for the non-relativistic case) was that for the N particle QM, he can obtain the equivalent result to conventional N particle QM, in a form superficially resembling the Hartree-Fock self-consistent field, using electron Psi_e and a nucleon Psi_n (all normalized to correct number of particles instead of to 1), as nonlinearly coupled classical matter fields in 3-D instead of the usual 3N-Dimensional configuration space, and unlike Hartree-Fock, it was not an approximation.

Nevertheless, I'd still classify this approach as fully classical, because there is no "quantization" at all, and the matter fields are considered as classical fields just as well as the EM field. In the language of path integrals, you wouldn't take into account anything besides the classical solution.

Indeed, that model alone doesn't appear to be the key by itself. For example the charge quantization doesn't come out of it and must be put in by hand, although no one has really solved anything without the substantial approximations, so no one knows what these equations are really capable of producing (charge quantization seems very unlikely, though, without additional fields or some other missing ingredient). But many have gotten quite a bit of mileage out of much much simpler non-linear toy models, at least in the form of insights about the spectrum of phenomena one might find in such systems.

seratend

Oct1-04, 12:22 PM

Seratend reply:
================================================== =====
Before, here is below the place in time, when I started to reply:

vanesch you accepted ALL OF QUANTUM THEORY except for the projection, so I was shooting at the wrong target ; nevertheless, several times it occured to me that you were actually defying the superposition principle, which is at the heart of QM. Now you confessed :tongue: :tongue:

Projection postulate itself suspends the linear dynamical evolution. It just does it on the cheap, (...)

(...)A theory cannot be logically coherent if it has an ill-defined switch between the two incompatible modes of operation, the dynamic equations and the collapse (which grew out of the similarly incoherent seeds, the Bohr's atom model and the first Plank's theory). The whole theory in this phase is like a hugely magnified version of the dichotomies of the originating embryo. That's why there is so much philosophizing and nonsense on the subject.

first,

(...) I only skimmed quickly at this paper, but something struck me: he shows that Bell's equality can also be satisfied with a non-local model. Bell's claim is the opposite: that in order NOT to satisfy the equality, you need a non-local model.

(...) So I don't really see the point of the paper! But ok, I should probably read it more carefully.
cheers,
Patrick

Vanesh, do not loose your time with Accardi Paper. It is only an example: one attempt, among many others, surely not the best, of a random variable model that breaks the bell inequalities. If I correctly understand, the results of spin measurement depend on the apparatus settings (local random variables: what they call “cameleon effect”).
It has been a long time I’ve looked at this paper :), but the first pages, before their model, are a very simple introduction to the probability and bell inequalities on a general probability space, and after how to construct, a model that breaks this inequality (local or global). This kind of view has led to the creation of a school QM interpretation (“quantum probability”, that is slightly different from orthodox interpretation).

Second and last, I have some other comments on physics and the projection postulate and its dynamics.

In the usual Hilbert space formulation, the Born rule is a static, geometric property of vectors, projectors, subspaces. It lacks the time dimension, thus the connection to the dynamics which is its real origin and ultimate justification and delimiter. (…)

(…) Thus for him (or for Jaynes) the field quantization was unneccessary, non-fundamental, at best a computational linearization procedure.

The Schroedinger, Dirac and Maxwell equations can already be rederived as macroscopic approximation of the dynamics of simple binary on/off automata (see for example some interesting papers by Garnet Ord). These kind of tools are hugely richer modelling medium than either PDEs or Hilbert space.

I appreciate, when someone likes to check other possibilities in physical modelling (or theory if we prefer), it is a good way to discover new things. However, please, avoid saying that a model/theory is better than another does as the only thing we can say (to my modest opinion) is that each model has its unknown domain of validity.
Note I do not reject the possibility of a perfect model (full domain of validity), but I prefer to think it currently does not exist.

The use of PDE models is interesting. It has already proved its value in many physical branches. We can use the PDE to model the classical QM, as well as the relativistic one, this is not the problem.
For example you have bohemian mechanics (1952): you can get all the QM classical results with this model as well as you can write an ODE that complies with QM. (insertion of a Brownian motion like term in newton’s equation – Nelson 1966 or your more recent “simple binary on/off automata” of Garnet Ord that seems to be the binary random walk of the Brownian motion –not enough time to check it :(
The main problem is to know if we can get the results of the experiments in a simpler way using such a method.

The use of Hilbert space tools in quantum mechanics formulation is just a matter of simplicity. It is interesting when we face discrete value problems (eg. Sturm-Liouville like problems). It shows,, for example, how a set of discrete values of operators change in time. Moreover it shows simply the representation relativity (e.g. quantum q or p basis) by a simple basis change. It then shows in a simplistic way the connection (a basis change) between a continuous and discrete basis (eg. {p,q} continuous basis and {a,a+} discrete basis).
In this type of case, the use of PDE may become very difficult. For example, the use of non gentle functions of L2(R,dx) spaces introduces less intuitive problems of continuities requiring for example the introduction of extension of the derivation operators to follow the full solutions of an extended space. This is not my cup of tea so I won’t go further on.

The text follows in the next post. :cry:

Seratend

seratend

Oct1-04, 12:24 PM

:surprised
Now let’s go back to the projection postulate and time dynamics in the Hilbert space formulation.

In the usual Hilbert space formulation, the Born rule is a static, geometric property of vectors, projectors, subspaces. It lacks the time dimension, thus the connection to the dynamics which is its real origin and ultimate justification and delimiter.

The reason it is detached from the time and the dynamics is precisely in order to empower it with the magic capability of suspending the dynamics, producing the "measurement" result with such and such probability, then resuming the dynamics. And without ever defining how and when exactly this suspension occurs, what and when restarts it... etc. It is so much easier to forget about time and dynamics if you smother them with ambiguous verbiage ("macroscopic" and other such obfuscations) and vacuous but intricate geometric postulates. By the time student gets through all of it, his mind will be too numbed, his eyes too glazed to notice that emperor wears no trousers.

Projection postulate (PP) is one of the orthodox/Copenhagen postulates that is not well understood by many people even if it is one of the most simple (but may be subtle).

PP is not completely outside the QM it mimics the model of scattering theory. The only thing that we have to know about PP is the description of the result of the unknown interaction between a quantum system (a system with N variables) and a measurement system (a quantum system of may be an infinite number of quantum variables: 10^23 variables, or more):
-- From an input state of the quantum system, PP gives an output state of the quantum system like in the quantum scattering theory except that we assume that the time of interaction (the state update) is as short as we want and that the interaction may be huge:
|in> --measurement--> |out>
-- Like scattering theory, the projection postulate does not need to know the evolution of the “scattering center” (the measurement system): in scattering theory we often assume a particle with an infinite mass, this is not much different from a heavy measurement system.
-- Like the scattering theory, you have a model: the state before the interaction, and the sate after the interaction. You do not care about what occurs during the interaction. And it is perfect, because you avoid manipulating incommensurable variables and energies due to this huge interaction and where the QM may become wrong. However, before and after the interaction we are in the supposed validity domain of QM: that’s great and its exactly we need for our experiments! Then we apply the Born rules: we then have our first explanation why born rules apply to the PP model: it is only an extension of the scattering theory rather than an “of the hat” postulate.

What I also claim with the PP, is that I have a “postulate”/model that gives me the evolution of a quantum system interaction with a huge system and that I can verify in the everyday quantum experiments.
I am not saying that I have a collapse or a magical system evolution just what is written on most of schoolbooks: I have a model of the time evolution of the system in interaction with the measurement system. Therefore, I also need to describe this evolution on all the possible states of the quantum state.

Now most of the people using the PP always forget the principal thing: the description of the complete modification of the quantum system by the measurement “interaction”. The missing of such complete specification almost always leads to these “collapse” and others stuffs. When we look at the states issued by the measurement apparatus this is not a problem, but the paradoxes (and questions about projection postulate or not) occur for the other states.

For example, when we say that we have an apparatus that measures the |+> spin. It is common to read/see this description:
1) We associate to the apparatus the projector P_|+>= |+><+|. We thus say that we have an apparatus that acts on the entire universe forever (even before its beginning).
2) For a particle in a general state |in>, we find the state after measure:
|out>= P_|+>|in>= |+> (we skip the renormalisation)
And most of the people are happy with this result.
So if we take now a particle |in>=|-> and apply the projector we get |out>= P_|+>|in>= 0.
Is there any problem?
I say: what is a particle with a state equal to a null vector? Consider now two particles in the state |in>=|in1>|-> where the measurement apparatus acts on:
|out>= P_|+>|in>=<+|->|in1>|+>=0|in1>|+>=0, the first particle has also disappeared during the measurement of the second particle.

What’s wrong: In fact, like in scattering theory, you must describe the measurement interaction output states for all input states otherwise you will get in trouble. Classical QM as well as field/relativistic QM formalism does not like the null state as the state of a particle (it is one of the main mathematical reasons why we need to add a void state /Hilbert void space to the states of fields ie <void|void> <>0).
Therefore, we have to specify also the action of the measurement apparatus on the sub Hilbert space orthogonal to the measured values!
In our simple case |out>= P_|->|in>= |somewhere> : we just say for example that particles of spin |-> will be stopped by the apparatus or, if we like, will disappear (in this case we need to introduce the creation/annihilation formalism: the jump to the void space). We may also take |somewhere(t)>: to say that after the interaction the particle has a new non permanent state: it is only a description of what the apparatus do on particles.

So if we take our 2 particles we have:
|out>=sum P_|>|in1>|->= (|+><+|+|somewhere><-|)||in1>|+>= |in1>|somewhere>

Particle doesn’t 1 disappear and is unchanged by the measurement (we do not need to introduce the density operator to check it).

Once we begin to define the action of the PP on the complete Hilbert space (or at least the sub Hilbert space under interest), everything becomes automatic and the magical stuff disappears.

Even better, you can define exactly, and in a very simple way, where and when the measurement occurs and describes local measurement apparatuses. Let’s go back to our spin measurement apparatus:
Here is the form a finite spatial extension apparatus measuring the |+> spin:
P_|+>=|there><there||+><+| (1)
Where <x|there>=There(x)~there. There(x) is different from 0 only on a small local zone of the apparatus. It is where the measurement will take place.

We thus have to specify the action on the other states (rest of the universe, rest of the spin states) otherwise P_|+> will make the particles “disappear” if particles are not within the spatial domain of the apparatus. For example:

P_|->=|there><there||somewhere><-|+ |everywhere - there>< everywhere - there|(|+><+| +|-><-|)

And, if we take |in>=|x_in(t)>|+> a particle moving along the x axis (very small spatial extension), we approximately know the measurement time (we do not break the uncertainty principle :): time of interaction tint occurs at |x_in(tint)>=|there>.

So once we take the PP in the write manner (the minimum: only a state evolution), we have all the information to describe the evolution of the particle. And it is not hard to see and to describe the dynamical evolution of the system and to switch on and off the measurement apparatus during the time.

Seratend.

nightlight

Oct1-04, 07:59 PM

seratend The use of PDE models is interesting. It has already proved its value in many physical branches. We can use the PDE to model the classical QM, as well as the relativistic one, this is not the problem.

Hilbert space is an abstraction of the linear PDEs. There is nothing abot it that PDEs don't have, i.e. it doesn't add properties but it subtracts them. That is fine, as long as one understands that every time you make abstraction, you throw out quite a bit from the more specific model you are abstracting away. Which means you may be abstracting away something which is essential.

In the Hilbert space abstraction we subtract the non-linearity traits of the PDE (or integral eqauations) modelling tool. That again is perfectly fine, as long as one understands that linear modelling in any domain is generally an approximation for the more detailed or deeper models. Our models are always an approximation to a domain of phenomena, like a Taylor expansion to a function within a proper domain.

While the linear term of Taylor series is useful, it is by no means the best math for everything and for all times. And surely one would not take the linear term and proclaim that all functions are really linear functions and then to avoid admitting it ain't so, one then proceeds using piecewise linear approximations for everything. That could be fine too, but it surely cannot be said that it is the best one can do with functions, much less that it is the only thing valid about them.

This kind of megalomany is precisely what the Hilbert space abstraction (the linear approximation) taken as a foundation of the QT has done -- this is how all has to work or it isn't the truest and the deepest physics.

Since the linearity is a very limited model for much of anything, and it certainly was never a perfect approximation for all the phenomena that QT was trying to describe, the linear evolution is amended -- it gets suspended in an ill-defined slippery maner (allegedly only when "measurement" occurs, whatever that really means) the "state" gets changed to where its linear model shadow, the state vector (or statistical operator), ougth to be, then the linear evolution gets resumed.

That too is all fine, as long as one doesn't make such clumsy rigging and ad-hockery into the central truth about universe. At least one needs to be aware that one is merely rectifying the inadequacies of the linear model while trying to describe phenomena which don't quite fit the first term of Taylor expansion. And one surely ought not to make the ham-handed ways we use to ram it in, into the core principle and make way too much out of it. There is nothing deep about projection (collapse) postulate, it's a underhanded slippery way to acknowledge 'our model doesn't work here'. It is not a virtue, as often made to look like; it is merely a manifestation of a model defect, of the ignorance.

Bell's theorem is precisely analogous of deifying the piecewise linear approximation model and proclaiming that the infinities of its derivatives are fundamental trait of the modelled phenomenon. Namely, the Bell's QM "prediction" is a far stretch of the collapse postulate (which is detached from and declared contrary and an override of the dynamics, instead of being recognized for what it is -- a kludgey do-hickey patching over the inadequacies of the linear approximation, the Hilbert space axiomatics, for the dynamics) to the remote non-interacting system and then proclaiming this shows fundamental non-locality. The non-locality was put in by hand through the inappropriate use of the piecewise linear approximation for the dynamics (i.e. throught the misuse of the projection postulate of the standard QM axiomatics). It applies the instantaneous projection to the remote system, disregarding the time, distance and the lack of interaction. It is as hollow as making a big ado about the infinites in the derivatives of piecewise linear approximations. It's a waste of time.

humanino

Oct1-04, 10:46 PM

Hilbert space is an abstraction of the linear PDEs. There is nothing abot it that PDEs don't have, i.e. it doesn't add properties but it subtracts them.
You have such an ego, this is amazing. You pretend to know everything about both domains, which is simply impossible for a single one !

What about fractal dimension as computed with wavelets ? This is a great achievement of the Hilbert space formalism. The reason Hilbert spaces were discovered, was to understand how Fourier could write his meaningless equations, and get so powerful results at the end of the day. How come when PDEs get too complicated to deal with, we reduce them to strange attractors, and analyze these with Hilbert space technics ?

It is not because a computation is linear, that it is trivial. It makes it doable. If you are smart enough to devise a linear algorithm, you could presumably deal with any problem. The Lie algebra, reduces the study of arbitrary mappings, to those linear near the identity : does it substract properties : yes, global ones. Does it matter ? Not so much, they can be dealt with afterwards.

Your objections are formal, and do not bring very much. You are very gifted at hands waving.

vanesch

Oct2-04, 12:19 AM

Bell's theorem is precisely analogous of deifying the piecewise linear approximation model and proclaiming that the infinities of its derivatives are fundamental trait of the modelled phenomenon. Namely, the Bell's QM "prediction" is a far stretch of the collapse postulate (which is detached from and declared contrary and an override of the dynamics, instead of being recognized for what it is -- a kludgey do-hickey patching over the inadequacies of the linear approximation, the Hilbert space axiomatics, for the dynamics) to the remote non-interacting system and then proclaiming this shows fundamental non-locality. The non-locality was put in by hand through the inappropriate use of the piecewise linear approximation for the dynamics (i.e. throught the misuse of the projection postulate of the standard QM axiomatics). It applies the instantaneous projection to the remote system, disregarding the time, distance and the lack of interaction. It is as hollow as making a big ado about the infinites in the derivatives of piecewise linear approximations. It's a waste of time.

I personally think that although this idea is interesting, it is very speculative and you should keep an open mind towards the standard theory too. After all, under reasonable assumptions of the behaviour of photon detectors (namely that they select a random fraction of the to be detected photons, with their, very measurable efficiency epsilon), we DO find the EPR type correlations, which are hard to reproduce otherwise. So, indeed, not all loopholes are closed, but there is VERY REASONABLE EXPERIMENTAL INDICATION that the EPR predictions are correct (EDIT: what I mean by this is that if it weren't for an application in an EPR experiment, but say, to find the coincidences of the two photons in a PET scanner, you wouldn't probably object to the procedure at all ; so if presented with data (clicks in time) of an experiment of which you don't know the nature, and people ask you to calculate the original correlation when the efficiencies of the detectors are given, you'd probably calculate without hesitation the things you so strongly object to in the particular case of EPR experiments). Until you really can come up with a detailled and equally practical scheme to obtain these results, you should at least show the humility of considering that result. It is a bit easy to say that you have a much better model of QM, except for those results that don't fit in your conceptual scheme, which have to be totally wrong. Also, I think you underestimate the effort that people put into this, and are not considered as heretics. But saying that "young student's minds are misled by the priests of standard theory" or the like make you sound a bit crackpottish, no ? :tongue2:
I repeat, this is not to say that work like you are considering should be neglected ; but please understand that it is a difficult road full of pitfalls which has been walked before by very bright minds, and who came back empty hands. So I'm still convinced that it is a good idea to teach young students the standard approach, because research in this area is still too speculative (and I'd say the same about string theory !).

cheers,
Patrick.

seratend

Oct2-04, 07:13 AM

nightlight Hilbert space is an abstraction of the linear PDEs. There is nothing abot it that PDEs don't have, .

The reciprocal is also true. I think you really have problems/belief with mathematical toys: they all say the same thing in different ways. One of the problems with these toys is the domain of its validity we assume. The other problem is the advance in the mathematical research that can restrict, voluntary, the domain of validity (e.g. Riemann integration of 19th century and the 20th general theory of integration).
Please do not forget, that I have no preference concerning PDE or Hilbert spaces, because I cannot have an objective demonstration that one formulation gives a domain of solutions larger or smaller than the other one.
So you say, that PDE are better than the Hilbert space (I don’t know what is “better” in your mind), then, please try to give a rigorous mathematical demonstration. I really think you have no idea (or may be you do not want to have) on how they may be close.
Like projection postulate, you give an affirmation but not a piece of demonstration, because if you give a demonstration, you have to give its domain of validity. Therefore you may see that you therorem depends on the assumed domain of validy of PDE or Hilbert spaces (like restricting the domain of validity of the integrals to the 19th century).
You are like some people saying that probability has nothing to do with integration theory.

I like PDE and Hilbert spaces and probability, I always try to see what IS different and what SEEMS different and thus I peek what is the more adequate to solve a problem.

nightlight
i.e. it doesn't add properties but it subtracts them. That is fine, as long as one understands that every time you make abstraction, you throw out quite a bit from the more specific model you are abstracting away. Which means you may be abstracting away something which is essential.

In the Hilbert space abstraction we subtract the non-linearity traits of the PDE (or integral eqauations) modelling tool. That again is perfectly fine, as long as one understands that linear modelling in any domain is generally an approximation for the more detailed or deeper models. Our models are always an approximation to a domain of phenomena, like a Taylor expansion to a function within a proper domain.
.

I think you block with linearity, like a schoolchild with the addition and multiplication. He may think that addition has nothing to do with multiplication until discovering that a multiplication is only an addition.

You seem to view Hilbert space linearity like the first new comers in quantum area: you are trying to see what it is not here.
Linearity of Hilbert spaces just allows saying that ANY UNTHINKABLE vector MAY describe a system and that’s all:
We may choose the Hilbert space we want: L2(R,dx), L1(R,dx), any Hilbert space, it seems to have no importance, it is only a matter of representation. So how can you tell that linearity “doesn’t add properties but it subtracts them” , but I say linearity says NOTHING. It says just what is evident: all solutions are possible: the belong to the Hilbert space.

You say that linearity of the Hilbert spaces imposes more restriction that the use of PDE while you may use this “awful linearity” without problem when you write your PDE in an abstract Euclidian space. I assume that you know that an Euclidian space is only a real Hilbert space. How do you manage this kind of linearity?

nightlight
While the linear term of Taylor series is useful, it is by no means the best math for everything and for all times. And surely one would not take the linear term and proclaim that all functions are really linear functions and then to avoid admitting it ain't so, one then proceeds using piecewise linear approximations for everything. That could be fine too, but it surely cannot be said that it is the best one can do with functions, much less that it is the only thing valid about them.
.

Please try to define what is “by no means the best math for everything for all times”. Such an assertion is very large and may lead to the conclusion the definite use of a math toy is given only once in time by the current knowledge we have about it.

Once again, you are restricting the domain of validity of the “Taylor” mathematical toy (as well as the Hilbert spaces). You are like a 19th century mathematician discovering the meaning of continuity. You think, with your implicit restricted domain of validity, that Taylor series does only apply to analytic functions. Try to expand your view, like the PDE toy, think for example the Taylor series in a different topological space with a different continuity. Think for example on the Stone Weistrass theorem, and the notion of complete spaces.

Like Hilbert spaces, PDE, probability theory, etc… Taylor series are only a toy with its advantage and disadvantage that can evolve with the advance in the mathematics.

nightlight

This kind of megalomany is precisely what the Hilbert space abstraction (the linear approximation) taken as a foundation of the QT has done -- this is how all has to work or it isn't the truest and the deepest physics.

Since the linearity is a very limited model for much of anything, and it certainly was never a perfect approximation for all the phenomena that QT was trying to describe, the linear evolution is amended -- it gets suspended in an ill-defined slippery maner (allegedly only when "measurement" occurs, whatever that really means) the "state" gets changed to where its linear model shadow, the state vector (or statistical operator), ougth to be, then the linear evolution gets resumed.
.

I think you mix Linearity of the operator space with the linearity of Hilbert spaces. How can you manage such a mix (an operator space is not an Hilbert space)? I really think you really need to have a look on papers like Paul J. Werbos (arxiv). Such papers may help you in understanding better the difference of linearity of a vector space and the non linearity of operators space. May be, its papers will help you to better understand how Hilbert spaces toys are connected to ODE and PDE toys.

You even mix linearity with unitary evolution! How can you really speak about measurement if you do not seem to see the difference?
Look: Unitary evolution assumes the continuity of evolution like the assumption of continuity in PDE or ODE. It is not different. You can suppress this requirement if you want like in PDE or ODE (in some limit conditions) there is no problem, only short mind.
Suppression of this requirement is equivalent to consider the problem of the domain of definition of unbounded operators in Hilbert spaces and the type of discontinuities they have (i.e reduction of the Hilbert space where the particle stays).

nightlight

That too is all fine, as long as one doesn't make such clumsy rigging and ad-hockery into the central truth about universe. At least one needs to be aware that one is merely rectifying the inadequacies of the linear model while trying to describe phenomena which don't quite fit the first term of Taylor expansion. And one surely ought not to make the ham-handed ways we use to ram it in, into the core principle and make way too much out of it. There is nothing deep about projection (collapse) postulate, it's a underhanded slippery way to acknowledge 'our model doesn't work here'. It is not a virtue, as often made to look like; it is merely a manifestation of a model defect, of the ignorance. …

.

Once again, I think you do not understand the projection postulate or you attach too many things to a simple state evolution (see my precedent post).
May be is it the term postulate that you do not like or may be is it the fact it is said that an apparatus not fully described by the theory gives results of this theory? Tell me, what theory does not use such a trick to describe results that are in final seen by the human?
The main difference comes from the fact that quantum theory has written this fact explicitly, so our attention is called to it and it is good: we must not forget that we are far from having described how everything works and if it is possible without requiring, for example, black boxes.

Please tell us what you really understand by projection postulate! It’s a good way to improve our knowledge and may be detect some errors.

Seratend

seratend

Oct2-04, 07:16 AM

:smile: Continuation:

nightlight
Bell's theorem is precisely analogous of deifying the piecewise linear approximation model and proclaiming that the infinities of its derivatives are fundamental trait of the modelled phenomenon. Namely, the Bell's QM "prediction" is a far stretch of the collapse postulate (which is detached from and declared contrary and an override of the dynamics, instead of being recognized for what it is -- a kludgey do-hickey patching over the inadequacies of the linear approximation, the Hilbert space axiomatics, for the dynamics) to the remote non-interacting system and then proclaiming this shows fundamental non-locality. The non-locality was put in by hand through the inappropriate use of the piecewise linear approximation for the dynamics (i.e. throught the misuse of the projection postulate of the standard QM axiomatics). It applies the instantaneous projection to the remote system, disregarding the time, distance and the lack of interaction. It is as hollow as making a big ado about the infinites in the derivatives of piecewise linear approximations. It's a waste of time.
.

I may repeat vanesh, but what do you intend by “collapse” or “collapse postulate” ? . We have only a “projection postulate” - see my previous post: We even may get a unitary evolution model of the particles in the Bell type experiment if we want! I really would like to know where you think there is a “fundamental” problem with this experiment/theorem.

As said before, I think you mix several types of linearity in your discussion and you confuse linearity with unitary evolution.

You also attach too many deductions from what Bell theorem says: two calculus models of a 2 particle system gives 2 different values. Then we have experiments, with certain assumptions as always in physics, who gives also the known results. That’s all. So where is the problem?

After, you have the interpretation (yours, and everybody) and the corrections of the model and theorem: we have had a lot of ones since 1964. And one of the interpretations is centred on non-locality of variables. Ok, this interpretation of the theorem disturbs you and me, that’s all (not the linearity of Hilbert spaces or what else):

The non-locality is not given by the theorem itself, it is interpreted from the single “classical” model” used in the theorem (its domain of validity): This model is incompatible with the model used in the QM formalism.
Bell, in its initial paper has given its definition of “locality” and therefore one of its interpretation of the theorem: “the vital assumption is that the result B for particle 2 does not depend on the setting a of the magnet for particle A on b”. But we can also prove easily that some “non local” variables may match the bell inequality if we want (e.g. Accardi 2000).
So the real question, I think is: does “the classical model of bell” contain all possible local variable models? Rather than does the theorem implies that QM formulation is not compatible with non local hidden variables.

Concerning the relevance of the experiments, a lot of work is done since 1964. And we must say yes, we may have some errors and explicit filters and assumptions, etc … in the experiment, but the numeric results of the experiments just give the expectation value of QM with a good confidence and only after the break of the bell inequality. So all of the errors must comply gently with the QM model: that only what is mainly searched in physics (or at least in technology): an experimental(“real”) numeric value that complies with the abstract model (or the opposite :biggrin: ).

Seratend :bugeye:

nightlight

Oct2-04, 12:26 PM

vanesch VERY REASONABLE EXPERIMENTAL INDICATION that the EPR predictions are correct

I don't find it a "reasonable experimental indication" at all.

The presence of the cos(2a) modulation on top of a larger "non-ideality" is a trait shared with the most natural classical physics of this setup. And that is all that gets tested.

If you could show the experimental results to any physicist, from Malus through Lorenz, they wouldn't be surprised with the data in the least. Maxwell could have probably writen down a fairly accurate model for the actual data, since the classical EM fields have all the main "non-classical" traits of the quantum amplitudes, including entaglement (see papers by Robert Spreeuw (http://cul.arxiv.org/abs/quant-ph/0009066), and some more on his home page (http://remote.science.uva.nl/~spreeuw/lop.htm)).

So this argument is barking up the wrong tree. There is nothing distinguishing about cos(2a) modulated correlation. When you enhance the simple classical models with a detector model, which models detection noise (via the Stochastic Electrodynamics, the classical EM model with ZPF boundary conditions) along with the detector sensitivity curves and perform the same kind of subtractions and data adjustments as the experimenters do, you get exactly what the experimenters have obtained (see numerous Marshall & Santos papers on this; they've been battling this battle for the last 25 years).

What distinguishes the alleged QM "prediction" from the classical one is the claim that such setup can produce a pure, unmodulated cos(2a). That is a conjecture and not a prediction. Namely, the 2x2 space model gives you only a hint of what kind of modulation to expect and says nothing about the orbital degrees of freedom, much less about dynamics of the detectior trigger. To have a proper prediction, one needs to have error bounds of the prediction (this is not a sampling error but the prediction limits) so that one can say e.g. the data which gets measured will be in [a,b] 95% of the time (in the limit of infinite sample). If I were in a hurry to make a prediction with the error bounds, such that I had to put my money on the prediction, I would at least include the 'loss projectors' to "missed_aperture" and "failed_to_trigger" ... subspaces, based on known detector efficiencies, and thus predict a wide, modulated cos(2a) correlation, indistingushable from the classical models.

In other words, to have a QM prediction which excludes all classical models, one needs to examine any setup candidate through the natural classical models then deduce a trait from the QM model which cannot be reproduced first by the natural classical models and then, if the prediction passes this basic preliminary citeria, analyse to which degree any other type of classicality can be excluded by the prediction.

In the case of the Bell's setup, one would have immediately found that the classical EM predicts a modulated cos(2a) correlation, so one would have to conclude that the prediction of the 2x2 model (which in order to have error bounds has to include the loss projectors to cover for all the skipped over and thus unknown details) is not sharp enough to draw the line between the QM and the classical models.

One would then evalute the sharpest cos(2a) modulation that natural classical models produce (which amounts to 1/2 photon equivalent of noise added to QM model). With this least of the QM-EM distingusihibility thresholds at hand, one can now focus the QM modelling to this distinction line. One would analyse the orbital propagation, the apertures, the unsharpness of the source particle number, etc, using of course any relevant empirical data available (such as detector response curves) looking to shrink the wide "loss projectors" spread of the toy model, so the more accurate QM prediction wich includes its error margin now falls beyond the classical line. Then you would have a proper QM prediction that excludes at least the straightforward classical models. At this point, it would become clear that with the present knowlede and empirical data on apartus properties, the best proper prediction of QM is indistungushable from the prediction of the natural classical models.

One has thus given up the proper QM prediciton, leaving it as a conjecture, something the experiment will have to resolve. And it's here that the Bell's inequality would come in to exclude the artificial classical models, provided the experiments show the actual data violates the inequality.

The theory (aided by empirical aparatus data) does not have a prediction which distinguishes even the natural classical models from the QM model for this setup. The Bell's inequality itself isn't a QM prediction, it is a classical prediction. And the error margins of the toy model are too large to make a distinction.

You may reply here that you don't need any such procedure, when QM already has projection postulate which predicts the inequality violation.

Ok, so, in order to distinguish the prediction from classical models, tell me what error margin for the prediction does the postulate give? None that I know of (ignoring the finite sample error which is implicitly understood and can be made as small as necessary).

Does that absence of mention of error margin mean that error margin is 0 percent? If it does, than the postulate is plainly falsified with any measurement. Clearly, there is an implicit understanding here that if you happen to require an error margin for any particular setup, you will have to evaluate it from the specific setup and a model (or use empirical data) for the detectors. Since we do need a good error margin here to be distingushable even if only to separate from the weaker threshold of natural models, we can't avoid the kind of estimation sketched earlier.

You might try refining the response saying: the absence of mention of error margin means that the "ideal system" has error margin 0. Which axiom defines the "ideal system"? Is that any system that one can construct in the Hilbert space? If so, why bother with all the arguments about the shaky projection postulate, when one can simply construct a non-local Hamiltonian that no local model can reproduce?

what I mean by this is that if it weren't for an application in an EPR experiment, but say, to find the coincidences of the two photons in a PET scanner, you wouldn't probably object to the procedure at all ; ...

Why would I object. For the prediction here the distingushability from classical models is irrelevant, it is not a requirement. Therefore the constraints on the error margins of the prediction are much weaker. Why would the experiment designer care here whether any classical model might be able to replicate the QM prediction. He has entirely different requirements. He might even bypass much of the error margins computations and simply let the setup itself "compute" what these are. For him it may not matter whether he has a genuine prediction or a just a heuristic toy model to guide the trial and error -- he is not asserting a theorem (as Bell's QM "prediction" is often labeled) claiming that there is a prediction with such and such error margins.

Until you really can come up with a detailled and equally practical scheme to obtain these results, you should at least show the humility of considering that result.

I did put quite bit of thought and effort on this problem over the years. And for several years I believed with the utmost humility and the highest respects the conventional story line.

It was only after setting foot into the real life Quantum Optics lab that I realized that the conventional presentations were largely misleading and are continuing as a waste of physics students' time and creativity. It would be better for almost everyone if the their energies were redirected away from this tar pit.

But saying that "young student's minds are misled by the priests of standard theory" or the like make you sound a bit crackpottish, no ?

I didn't 'invent' the "priesthood" label. I heard it first in this context from Trevor Marshall, who, if anyone, knows what he is talking about.

So I'm still convinced that it is a good idea to teach young students the standard approach

Well, yes, the techniques have to be taught. But if I were to teach my own kids, I would tell them to forget the projection postulate as an absolute rule and to take it as a useful but limited approximation and as a prime example of its misuse and the pitfalls to watch for I would show them the Bell's theorem.

vanesch

Oct3-04, 02:01 AM

If you could show the experimental results to any physicist, from Malus through Lorenz, they wouldn't be surprised with the data in the least. Maxwell could have probably writen down a fairly accurate model for the actual data, since the classical EM fields have all the main "non-classical" traits of the quantum amplitudes, including entaglement (see papers by Robert Spreeuw (http://cul.arxiv.org/abs/quant-ph/0009066), and some more on his home page (http://remote.science.uva.nl/~spreeuw/lop.htm)).

I think I'm beginning to see what you are alluding to. Correct me if I'm wrong. You consider the parametric down conversion as a classical process, out of which come two continuous EM waves, which are then "photonized" only locally in the detector, is that it ?

EDIT: have a look at quant-ph/9810035

cheers,
Patrick.

vanesch

Oct3-04, 03:04 AM

nightlight

Oct3-04, 03:43 AM

vanesch You consider the parametric down conversion as a classical process, out of which come two continuous EM waves, which are then "photonized" only locally in the detector, is that it ?

The classicality of PDC is not my conjecture but a mathematical result of the same kind as the similar 1963 Sudarshan-Glauber result (cited earlier) showing the same for the thermal and laser sources -- there is no multipoint coincidence setup for these sources that can yield correlations distinguishable from the classical EM filed interacting with a square law detector (which in turn can be toy-modelled as an ionisation of a Schrodinger's atom). Marshall, Santos and their collaborators/disciples have shown this equivalence for type I and || PDC sources. Here are just couple (among over a dozen) of their papers on this question:
Trevor W. Marshall Do we need photons in parametric down conversion? (http://cul.arxiv.org/abs/quant-ph/9711029)

The phenomenon of parametric down conversion from the vacuum may be understood as a process in classical electrodynamics, in which a nonlinear crystal couples the modes of the pumping field with those of the zeropoint, or "vacuum" field. This is an entirely local theory of the phenomenon, in contrast with the presently accepted nonlocal theory. The new theory predicts a hitherto unsuspected phenomenon - parametric up conversion from the vacuum.
Alberto Casado, Trevor W. Marshall, Emilio Santos
Type-II parametric down conversion in the Wigner-function formalism. Entanglement and Bell's inequalities (http://cul.arxiv.org/abs/quant-ph/9711042)

We continue the analysis of our previous articles which were devoted to type-I parametric down conversion, the extension to type-II being straightforward. We show that entanglement, in the Wigner representation, is just a correlation that involves both signal and vacuum fluctuations. An analysis of the detection process opens the way to a complete description of parametric down conversion in terms of pure Maxwell electromagnetic waves.

The essential new ingredient in their approach is the use of the vacuum fluctuations (they call it Zero Point Field, ZPF, when referring to it as the special initial & boundary conditions of classical EM field; the ZPF distribution is not some kind of adjustible fudge factor since it is uniquely determined by the requirements of Lorenz invariance) and its relation to the detection. That addition also provides a more concrete physical interpretation of the somewhat abstract 1963 results for the thermal and laser sources.

Namely, the ZPF background (which amounts to an equivalent of 1/2 photon per mode and which the "normal ordering" of operators in QED, used for computing the multipoint correlations, discards from the expressions) allows one to have, among other effects, a sub-ZPF EM wave, with energy below the background (result of a superposition with the source field e.g. on the beam splitter), but which carries the phase info of the original wave and can interfere with it, yet it is normally not detected (since it falls below the detector's dark-current trigger cutoff which is callibrated to register no events for the vacuum fluctuations alone; this is normally accomplished by a combination of adjustments to the detector's sensitivity and the post-detection subtracion of the backgorund rate).

This sub-ZPF component (a kind of "dark wave"; I recall Marshall using term "ghost" or "ghost field" for it) behaves formally as a negative probability in the Wigner's joint distribution formalism (it has been know for a long time that allowing for negative probabilities yields at least formally the classical-like joint distributions; the sub-ZPF component provides a simple and entirely non-mysterious interpretation of these negative probabilities). It is conventionally undetectable (in the coincidence experiments it gets callibrated & subtracted away to match the correlations computed using the normal ordering rule; it shows as a negative dip below the baseline rate=0 in some more detailed data presentations), yet it travels the required path and picks all the inserted phase shifts along the way so the full intereference behavior is preserved, while any detection on each path shows just one "photon" (the averaging over the ZPF and source distributions smoths out the effect, matching quantitatively the photon anti-correlation phenomenon which is often mentioned as demonstrating the "particle" aspect of photons).

{ Note that ZPF alone plus classical point particles cannot reproduce the Schroedinger or Dirac equations (that goal used to be the "holy grail" in the early years of the Stochastic ED, 1960s & 1970s). Although there were some limited successes over the years, Marshall now admits it can't work; this realization has nudged this approach to Barut's Self-field ED, except with the advantage of the ZPF tool.}

nightlight

Oct3-04, 04:15 AM

vanesch See, I didn't need any projection as such...

I think John Bell's last paper "Against Measurement" (http://www-lib.kek.jp/cgi-bin/kiss_prepri?KN=&TI=against+measurement&AU=bell&AF=&CL=&RP=&YR=) should suffice to convince you that you're using the non-dynamical collapse (Dirac's quantum jump). He explains it by picking apart the common obfuscatory verbiage, using the Landau-Lifsh-itz** and Gottfried's QM textbooks as the examples. You'll also find that his view of the collapse, measurement and teaching of the two is not very different of what I was saying here. Among other points I agree with, he argues that the collapse should be taught as a consequence of the dynamics, not in addition to it (as a postulate). He returns to and discusses the Schroedinger's original interpretation (the view that |Psi|^2 is a density of "stuff"). Then he looks at the ways to remedy the packet spread problem that Schroedinger found (the schemes such as de Broglie-Bohm's theory and the Ghirardi-Rimini-Weber dynamical, thus non-linear, collapse). Note that this is an open problem in Barut's approach as well, even though he had some toy models for the matter field localizations (from which he managed to pull out a rough approximation for the fine structure constant).

{ ** The PF's 4-letter-word filter apparently won't allow the entry of the Lanadau's coauthor.}

vanesch

Oct3-04, 05:53 AM

this is normally accomplished by a combination of adjustments to the detector's sensitivity and the post-detection subtracion of the backgorund rate).

Well, you're now in my field of expertise (which are particle detectors) and this is NOT how this works, you know. When you have a gas or vacuum amplification, this is essentially noiseless ; the "detector sensitivity" is completely determined by the electronic noise of the amplifier and the (passive) capacitive load by the detector and can be calculated using simple electronics simulations which do not take into account any detector properties except for its capacity (C).
A good photomultiplier combined with a good amplifier has a single-photon signal which stands out VERY CLEARLY (tens of sigma) from the noise. So the threshold of detection is NOT adjusted "just above the vacuum noise" as you seem to imply (or I misunderstood you).

cheers,
Patrick.

PS: you quote a lot of articles to read ; I think I'll look at (some) of them. But all this takes a lot of time, and I'm not very well aware of all these writings. I'm still convinced those approaches are misguided, but I agree that they are interesting, up to a point. Hey, maybe I'll change sides :-)) Problem is, there's SO MUCH to read.

seratend

Oct3-04, 05:56 AM

vanesch

Oct3-04, 06:18 AM

Nightlight ... I think John Bell's last paper "Against Measurement" (http://www-lib.kek.jp/cgi-bin/kiss_prepri?KN=&TI=against+measurement&AU=bell&AF=&CL=&RP=&YR=)

I is a good paper for a first introduction to the decoherence program.
Attention that "collapse" does not mean that the quantum state |psi> has really collapsed into a new state |An>.

Yes, exactly. In fact, the funny thing is that the decoherence program seems to say that people who insist on the nonlinearity of the measurement process didn't take the linearity seriously enough :tongue:
However, it is true that the decoherence program, in itself, still doesn't solve completely the measurement problem, and any work that can shed more light on it can be interesting.
What disturbes me a bit in the approach suggested by nightlight and the people he cites is not so much that "standard theory is offended" but that they obstinately seem to refute the EPR experimental results EVEN if by fiddling around a lot, there are still many ways to explain the results by semiclassical approaches (or at least POTENTIALLY explain them). I'm maybe completely missing the point, but I think that there are 2 ways of comparing experimental results to theoretical predictions. One is to try to "correct the measurements and extract the ideal quantities". Of course that looks like fudging the data. But the other is: taking the ideal predictions, applying the experimentally expected transformations (like efficiencies and so on), and compare that with the raw data. Both procedures are of course equivalent, but the second one seems to be much more "acceptable". As far as I know, all EPR type experiments agree with the predictions of QM EVEN IF ONE COULD THINK OF SPECIFIC SEMICLASSICAL THEORIES almost made up for the purpose to obtain the same results - potentially. This, to me, is for the moment sufficient NOT TO REJECT the standard theory, which, at least, with simple "toy models" and "toy experimental coefficients" obtains correct results.

cheers,
Patrick.

nightlight

Oct3-04, 07:38 AM

A good photomultiplier combined with a good amplifier has a single-photon signal which stands out VERY CLEARLY (tens of sigma) from the noise. So the threshold of detection is NOT adjusted "just above the vacuum noise" as you seem to imply (or I misunderstood you).

You can change the PM's bias voltage and thus shift on its sensitivity curve (a sigmoid type function). That simply changes your dark current rate/vacuum fluctuations noise. The more sensitive you make it (to shrink the detection loophole) the larger the dark current, thus the larger explicit background subtraction. If you wish to have lower background subtractions you select lower PM sensitivity. It is a tradeoff between the detection and the subtraction "loopholes".

In the original Aspect's experiment, they found the setup to be the most efficient (most accepted data points per unit time) when they tune the background subtraction rate to be equivalent exactly to the background DC offset on the cos^2() that natural classical model predicts as necessary.

This was pointed out by Marshall, who demonstrated a simple classical, non-ZPF EM model, with exactly the same predictions as the pre-subtraction coincidence rates Aspect reported. After some public back and forth via letters and papers, Aspect repeated the experiments where he reduced the subtractions below the simple classical model (by lowering the sensitivity of the detectors) and still "violated" the Bell's inequality (while the subtraction loophole shrunk, the detection loophole grew). Then Marshall & Santos worked out the initial versions of their ZPF based model (without a good detection model at the time) which matched the new data, but by this time the journals had somehow lost the interest in the subject leaving Aspect with the last word in the debate.

In adition to tuning the particular PM, changing the type of the detector as well as the photon wavelengths (this change affects the analyzing efficiency of the polarizer, basically offseting any efficiency gains you made on the detection), selects by itself different tradeoff points between the dark rate and the quantum efficiency.

Since the classical predictions are within 1/2 photon equivalent from the "ideal" QM prediction and since more realistic QED models do use the "normal ordering" of a+, a- operators (which amounts to subtracting the divergent vacuum energy of 1/2 photon per mode; different ordering rules change the joint distributions types e.g. from Husimi to Wigner), it is highly doubtful that anything decisive can come out of the photon experiments ever. Separately, the popular source of recent years, PDC, is 100% equivalent to the classical ZPF based EM predictions for any coincidence measurements, with any number of detectors and any number of linear components (polarizers, beam splitters, etc). Just as one didn't have to bother debunking blow by blow any non-classicality claim based on linear optical components and thermal sources from 1956 (Hanbury Brown & Twiss effect) or laser sources from 1963 (Sudarshan, Glauber), since the late 1990s one doesn't need to do it with PDC sources either. The single atomic sources are still usable (if one is a believer in the remote, non-dynamical, instant collapse), but the three body problem has kept these setups even farther from the "ideal".

nightlight

Oct3-04, 05:27 PM

vanesch but let's do a very simple calculation. ...

Simple, indeed. I don't wish to excessively pile on references, but there is an enormous amount of detailed analysis on this setup.

Take detector 1 as the "master" detector. ... Each time that detector 1 has seen a photon, we ASSUME - granted - that there has been a photon in branch 2 of the experiment,

The master may be a background, as well. Also, you have 2 detectors for A and 2 for B and thus you have 2^4-1 combinations of events to deal with (ignoring the 0,0,0,0).

and that two things can happen: or that the second photon was in the wrong polarization state, or that it was in the right one.

Or that there is none since the "master" trigger was the vacuum fluctuation, amplification or any other noise. Or that there is more than one photon (note that the "master" has a dead time after a trigger). Keep in mind that even if you included the orbital degrees of freedom and followed up the amplitudes in space and time, you are still putting in the assumption of non-relativistic QM approximation of the sharp, conserved particle number which isn't true for QED photons.

If you compute QED correlations for the coincidences using "normal operator ordering" (the Glauber's prescription, which is the cannonical Quantum Optics way) you're modelling a detection process which is calibrated to subtract vacuum fluctuations, which yields Wigner's joint distributions (in phase space variables). The "non-classicality" of these distribution (the negative probability regions) is always equivalent for any number of correlations to the classical EM with ZPF subtractions (see the Marshall & Santos (http://arxiv.org/find/quant-ph/1/AND+au:+OR+marshall+santos+abs:+wigner/0/1/0/all/0/1) papers for these results).

If your correlation computation doesn't use normal operator ordering to remove the divergent vacuum fluctuations from the Hamiltonian and instead uses high frequency cutoff, you get Husimi joint distribution in phase space which has only positive probabilites, meaning it is a perfectly classical stochastic model for all photon correlations (it is mathematically equivalent to the Wigner's distribution with smoothed out negative probability regions by a Gaussian; the smoothing is physically due to the indeterminacy of the infrared/soft photons). Daniele Tommasini (http://arxiv.org/find/quant-ph/1/AND+au:+tommasini+abs:+epr/0/1/0/all/0/1) has several papers on the QED "loophole" topic (it surely takes some chutzpah to belittle the more accurate QED result as a "loophole" for the approximate QM result).

So I'd guess that the quantum prediction to have coincidences in channel 2, if channel 1 triggered, to be equal to e2xC_ideal....

What you're trying to do is rationalize the fair sampling assumption. The efficiencies are features of averages of detections over Gaussian (for high rates) or Poisson (for low rates) detection event distributions, neither of which is usable for Bell's violation tests, since classical models trigger rates are equivalent to the "ideal" QM prediction smoothed out/smeared by precisely these types of distributions.

The QED "loophole" is not a problem in the routine Quantum Optics applications. But if you're trying to distinguish QM "ideal" model from a classical model, you need much sharper parameters than the averages over Poisson/Gaussian distributions.

In addition to the QED "loophole, the assumption that the average ensemble properties (such as the coincidence detection efficiency, which is a function of individual detectors quantum efficiencies) must also be properties of the individual pairs has another, even more specific problem in this context.

Namely, in a classical model you could have a hidden variable shared by the two photons (which was set at the pair creation time and which allows the photons to correlate nearly perfectly for the parallel polarizers). In the natural classical models this variable is a common and specific polarization orientation. For the ensemble of pairs this polarization is distributed equally in each direction. But for any individual pair it has a specific value (thus the rotational symmetry of the state is an ensemble property which need not be a property of individual pair in LHV theories; and it is not rotationally symmetrical for individual pairs even in the most natural classical models i.e. you don't need some contrived toy model to have this rotational asymmetry at the individual pair level while retaining the symmetry at the ensemble level).

Now, the splitting on the polarizer breaks the amplitudes into sin() and cos() projections relative to the polarizer axis for (+) and (-) result. But since the detection probability is sensitive to the squares of amplitude incident on each detector, this split automatically induces a different total probability of coincident detection for individual pair (for the general polarizer orientations). The quantum efficiency figure is an average insensitive to this kind of systematic bias which correlates the coincidence detection probability of an individual pair with the hidden polarization of this pair thus with the result of the pair.

This classically perfectly natural trait is a possibility that "fair sampling" assumption excludes upfront. The individual pair detection (as a coincidence) may be sensitive to the orientation of a hidden polarization relative to the two polarizer orientations even though the ensemble average may lack this sensitivity. See Santos paper (http://cul.arxiv.org/abs/quant-ph/0401003) on the absurdity of "fair sampling" (due to this very problem) and also a couple of papers by Khrennikov which propose a test of the "fair sampling" (http://arxiv.org/find/quant-ph/1/AND+au:+khrennikov+abs:+AND+fair+sampling/0/1/0/all/0/1) for the natural classical models (which yield a prediction for detecting this bias).

vanesch

Oct4-04, 02:11 AM

vanesch but let's do a very simple calculation. ...

Simple, indeed. I don't wish to excessively pile on references, but there is an enormous amount of detailed analysis on this setup.

May I ask you something ? Could you indicate me a "pedagogical reading list" in the right order for me to look at ? I'm having the impression in these papers I'm being sent from reference to reference, with no end to it (all papers have this treat of course, it is just that normally, at a certain point, this is absorbed by "common knowledge in the field").
I think this work is interesting because it illustrates what exactly is "purely quantum" and what not.

cheers,
Patrick

nightlight

Oct4-04, 04:13 AM

vanesch May I ask you something ? Could you indicate me a "pedagogical reading list" in the right order for me to look at ?

I am not sure what specific topic for the list are you referring to. In any case, I haven't used or have any such list. Marshall & Santos have perhaps couple hundred papers, most of which I have in the paper preprint form. I would say that one can find their more recent equivalents/developments of most that was worth pursuing (Marshall's home page (http://homepages.tesco.net/~trevor.marshall/antiqm.html) has few basic reference lists with informal intros into several branches of their work). The phase space distributions are a well developed field (I think Marshall & Santos work here was the first rational interpretation of the negative probabilities appearing in these distributions).

KEK (http://www-lib.kek.jp/cgi-bin/kiss_prepri?KN=&TI=&AU=barut&AF=&CL=&RP=&YR=) and CERN (http://cdsweb.cern.ch/search.py?sc=1&ln=en&p=barut&f=author&action=Search&cc=Articles+%26+Preprints&c=Published+Articles&c=Preprints&c=Theses&c=Reports&c=CERN+Internal+Notes&c=CERN+Committee+Documents)servers have most of Barut's stuff (I did have to get some which are missing as paper copies via mail from ICTP and some hard to find from his former students).

There is also E.T. Jaynes publication (http://bayes.wustl.edu/etj/node1.html) archive (I found especially interesting #71 (http://bayes.wustl.edu/etj/articles/scattering.by.free.pdf), #74 (http://bayes.wustl.edu/etj/articles/backward.look.pdf), #68 (http://bayes.wustl.edu/etj/articles/prob.in.qm.pdf), #67 (http://bayes.wustl.edu/etj/articles/cmystery.pdf), and the unpublished paper on Dyson (http://bayes.wustl.edu/etj/articles/disturbing.memory.pdf)). His classic probability theory book (http://www-laplace.imag.fr/Jaynes/prob.html) is also online.

Of other people you may have not heard of, an applied math professor Garnet Ord (http://www.scs.ryerson.ca/~gord/) has found an interesting combinatorial origin of all the core equations of physics (Maxwell, Schroedinger, Dirac) - they're all contnuum limits of the combinatorial/enumerative properties of the fluctuations of the plain Brownian motion (obtained without analytic continuation, but purely combinatorially; Gerard 't Hooft (http://arxiv.org/find/quant-ph/1/au:+hooft/0/1/0/all/0/1) has been playing with similar models lately, apparently having lost the faith in the QM orthodoxy and the physical relevance of the no-go "theorems").

Another collection of interesting and often rare papers and preprints is the Toffoli's quantum computation archive (http://kh.bu.edu/qcl/) (ironically he is one of the few [open] Quantum Computing skeptics and much of the stuff there, thankfully, has no relation to Quantum Computing). His main interest is "computational mechanics" which comes down to modelling all of the physics through local cellular automata instead of PDEs, Hilbert space,... (which his papers there cover). Thus the collection gathers papers with the related ideas as well as lots on the EPR/Bell topic (which in his mind was the main impediment to overcome). Of special interest: paper on Schroedinger's (http://kh.bu.edu/qcl/pdf/aebi___r199678747472.pdf) analysis of diffusion (1931) anticipating Ord's models; and another precursor (http://kh.bu.edu/qcl/pdf/aron___j19797c150601.pdf), plus many of Toffoli's papers.

vanesch

Oct4-04, 07:24 AM

Now, the splitting on the polarizer breaks the amplitudes into sin() and cos() projections relative to the polarizer axis for (+) and (-) result. But since the detection probability is sensitive to the squares of amplitude incident on each detector, this split automatically induces a different total probability of coincident detection for individual pair (for the general polarizer orientations). The quantum efficiency figure is an average insensitive to this kind of systematic bias which correlates the coincidence detection probability of an individual pair with the hidden polarization of this pair thus with the result of the pair.

This classically perfectly natural trait is a possibility that "fair sampling" assumption excludes upfront.

I think I understand what you mean. To you, a "photon" is a small, classical wavetrain of EM radiation, and the probability of detection depends on the square of its amplitude. I tried to find quickly a counter example, and indeed, in most if not all "single photon events" the behaviour seems identical with the "QED photon". So you claim that if we send a polarized EM beam under 45 degrees onto a detector, each little wavetrain arrives "fully" at the photocathode and hence has a probability epsilon to be detected. However, if we now put an X polarizer into the beam, contrarily to the QED view, we do not block half of the "photons" (wave trains), but we let through ALL of them, but they have diminished (by sqrt(2)) wave train amplitudes, namely purely their X component, which results, you claim, in half of the detection efficiency, and so it is only the detector who sees half of them, us naive physicists thinking that there physically are only half of them present. It is just that they are 'half photons'. By turning the polarizer, we can make "tiny tiny photons" which still encode the wavelength or frequency, but have a very very small probability to be detected.
Right. So you will agree with me that you are essentially refuting the photon as a particle, and just as a detection phenomenon of classical EM radiation ; in that case I also understand your insistence on how you refuse the fair sampling idea.
How do you explain partial absorption in a homogeneous material ? Loss of a number of wavetrains, or diminishing the amplitude of each one, keeping the total number equal ?

cheers,
Patrick.

nightlight

Oct4-04, 02:43 PM

vanesch To you, a "photon" is a small, classical wavetrain of EM radiation, and the probability of detection depends on the square of its amplitude.

The QM (or Quantum Optics) amplitude does exactly the same here. Check any computation for the free space propagation or through the polarizer or other linear elements -- it follows precisely the Maxwell's equations. The only difference is that I don't imagine a marble floating somehow inside this amplitude packet. It is not necessary, it makes no empirical difference (and one can't even define a consistent theoretical position operator for the photon). The a+, a- operators don't give you any marble-like localization hint, they're field modes (which are spatially extended) creators and destructors.

Of course, it is fine to use any visual mnemonic one finds helpful for some context, but one has to be aware that that's all it is and not create "paradoxes" by attributing ontology to a private visual mnemonic device.

So you claim that if we send a polarized EM beam under 45 degrees onto a detector, each little wavetrain arrives "fully" at the photocathode and hence has a probability epsilon to be detected.

The Quntum Optics amplitude does exactly the same split since it follows the same equations for orbital propagation. For any thermal, laser or PDC source you cannot set-up any configuration of linear optical elements and square law detectors that will predict any difference in coincidence counts.

Of course, I am not including in the term "prediction" here the predictions of some QM toy-model since that is not a model of an actual system and it doesn't predict what is actually measured (the full raw counts, the existence, much less the rate, of background counts or the need and the model for the background subtractions). It predicts the behavior of some kind of "ideal" system (which has no empirical counterpart), that has no vacuum fluctuations (which are in QO/QED formally subtracted by normal ordering convention, and this subtraction is mirrored by the detector design, threshold calibration and background subtractions to exclude the vaccum events) and that has a sharp, conserved photon number.

(-- interrupted here--)

nightlight

Oct4-04, 05:00 PM

vanesch ... us naive physicists thinking that there physically are only half of them present. It is just that they are 'half photons'. ...

What's exactly the empirical difference? The only sharp test that can exclude the natural classical field models (as well as any local model) is the Bell's inequality test, and so far it hasn't done it.

Dropping the "loophole" euphemistics, the plain factual situation is that these tests have excluded all local theories which satisfy the "fair sampling" property (which neither the classical EM fields nor the QED/QO amplitudes satisfy). So, the test has excluded the theories that never existed in the first place. Big deal.

So you will agree with me that you are essentially refuting the photon as a particle, and just as a detection phenomenon of classical EM radiation ; in that case I also understand your insistence on how you refuse the fair sampling idea.

In which sense is the photon a particle in QED? I mean, other than jargon (or a student taking the Feynman's diagrams a bit too literally). You prefer to visualise counting marbles while I prefer to imagine counting modes since it has neither position nor individuality.

The discreteness of the detector response is the design decision (the photo-ionisation in detectors is normally treated via semi-clasical model; even the few purely QED treatments of the detection don't invoke any point-like photons and show nothing different or new). Detectors could also perfectly well measure and correlate continuous photo-currents. (Of course, even in the continuous detection mode a short pulse might appear as a sharp spike, but that is a result of the amplitude modulation which is not related to a pointlike "photon." )

One needs also to keep in mind that the engineering jargon of Quantum Optics uses label non-classical in much weaker sense than the fundamental non-classicality we're discussing (for which the only sharp test is some future Bell type test which could violate the Bell's inequalities).

Basically, for them anything that the most simple minded boundary & initial conditions of classical EM model cannot replicate is "non-classical" (such as negative regions of Wigner distributions). Thus their term "classical" excludes by definition the classical EM models which account for the vacuum fluctuations (via the ZPF initial & bounday conditions).

How do you explain partial absorption in a homogeneous material ? Loss of a number of wavetrains, or diminishing the amplitude of each one, keeping the total number equal ?

What is this, a battle of visual mnemonic devices? Check the papers by Jaynes (http://bayes.wustl.edu/etj/node1.html) (esp. 71 (http://bayes.wustl.edu/etj/articles/scattering.by.free.pdf) and 74 (http://bayes.wustl.edu/etj/articles/backward.look.pdf) the QED section) about the needs for quantization of the EM field. With Jaynes' and Barut's results included, you need to go beyond the first order of radiative corrections to even get to the area where they haven't carried out the computations and where the differences may appear (they've both passed away, unfortunately). The Quantum Optics, or some statistical physics bulk material properties are far away from the fundamental (as opposed to computationally practical) necessity to quantize the EM field. The Quantum Optics doesn't have a decisive test on this question (other than those for the weak non-classicality or some new design of the Bell's test). The potentially distinguishing efects are couple QED perturbative orders below the phenomena of Quantum Optics or the bulk material properties.

What you're talking above is the battle of visual mnemonic devices. For someone doing day to day work in QO it is perfectly fine to visualize photons as marbles somehow floating inside the amplitudes or collapsing out of amplitudes, if that helps them think about it or remember the equations better. That has nothing to do with the absolute empirical necessity for a marble-like photon (of which there is none, not even in QED formalism it is point-like, although the jargon is particle-like).

As a computational recipe for routine problems the standard scheme is far ahead of any existent non-linear models for the QED. As Jaynes put it (in #71):

Today, Quantum Mechanics (QM) and Quantum Electrodynamics (QED) have great
pragmatic success - small wonder, since they were created, like epicycles, by
empirical trial-and-error guided by just that requirement. For example, when
we advanced from the hydrogen atom to the helium atom, no theoretical
principle told us whether we should represent the two electrons by two wave
functions in ordinary 3-d space, or one wave function in a 6-d configuration
space; only trial-and-error showed which choice leads to the right answers.

Then to account for the effects now called `electron spin', no theoretical
principle told Goudsmit and Uhlenbeck how this should be incorporated into the
mathematics. The expedient that finally gave the right answers depended on
Pauli's knowing about the two-valued representations of the rotation group,
discovered by Cartan in 1913.

In advancing to QED, no theoretical principle told Dirac that electromagnetic
field modes should be quantized like material harmonic oscillators; and for
reasons to be explained here by Asim Barut, we think it still an open question
whether the right choice was made. It leads to many right answers but also to
some horrendously wrong ones that theorists simply ignore; but it is
now known that virtually all the right answers could have been found without,
while some of the wrong ones were caused by field quantization.

Because of their empirical origins, QM and QED are not physical theories at
all. In contrast, Newtonian celestial mechanics, Relativity, and Mendelian
genetics are physical theories, because their mathematics was developed by
reasoning out the consequences of clearly stated physical
principles which constrained the possibilities. To this day we have no
constraining principle from which one can deduce the mathematics of QM and
QED; in every new situation we must appeal once again to empirical evidence to
tell us how we must choose our mathematics in order to get the right answers.

In other words, the mathematical system of present quantum theory is, like
that of epicycles, unconstrained by any physical principles. Those
who have not perceived this have pointed to its empirical success to justify
a claim that all phenomena must be described in terms of Hilbert spaces,
energy levels, etc. This claim (and the gratuitous addition that it must be
interpreted physically in a particular manner) have captured the minds of
physicists for over sixty years. And for those same sixty years, all efforts
to get at the nonlinear `chromosomes and DNA' underlying that linear
mathematics have been deprecated and opposed by those practical men who,
being concerned only with phenomenology, find in the present formalism all
they need.

But is not this system of mathematics also flexible enough to accommodate any
phenomenology, whatever it might be? Others have raised this question
seriously in connection with the BCS theory of superconductivity. We have all
been taught that it is a marvelous success of quantum theory, accounting for
persistent currents, Meissner effect, isotope effect, Josephson effect, etc.
Yet on examination one realizes that the model Hamiltonian is
phenomenological, chosen not from first principles but by trial-and-error
so as to agree with just those experiments.

Then in what sense can one claim that the BCS theory gives a physical
explanation of superconductivity? Surely, if the Meissner effect did not
exist, a different phenomenological model would have been invented, that does
not predict it; one could have claimed just as great a success for quantum
theory whatever the phenomenology to be explained.

This situation is not limited to superconductivity; in magnetic resonance,
whatever the observed spectrum, one has always been able to invent a
phenomenological spin-Hamiltonian that ``accounts'' for it. In high-energy
physics one observes a few facts and considers it a big advance - and great
new triumph for quantum theory -- when it is always found possible to invent a
model conforming to QM, that ``accounts'' for them. The `technology' of QM,
like that of epicycles, has run far ahead of real understanding.

This is the grounds for our suggestion (Jaynes, 1989) that present QM is only
an empty mathematical shell in which a future physical theory may, perhaps, be
built. But however that may be, the point we want to stress is that the
success - however great - of an empirically developed set of rules gives
us no reason to believe in any particular physical interpretation of them.
No physical principles went into them.

Contrast this with the logical status of a real physical theory; the success
of Newtonian celestial mechanics does give us a valid reason for believing in
the restricting inverse-square law, from which it was deduced; the success
of relativity theory gives us an excellent reason for believing in the
principle of relativity, from which it was deduced.

vanesch

Oct5-04, 02:05 AM

The Quntum Optics amplitude does exactly the same split since it follows the same equations for orbital propagation. For any thermal, laser or PDC source you cannot set-up any configuration of linear optical elements and square law detectors that will predict any difference in coincidence counts.

How about the following setup:
take a thermal source of light, with low intensity. After collimation into a narrow beam, send it onto a beam splitter (50-50%). Look at both split beams with a PM. In the "marble photon" picture, we have a Poisson stream of marbles, which, on the beam splitter, go left or right, and have then a probability of being seen by the PM (which is called its quantum efficiency). This means that only 3 cases can occur: a hit "left", a hit "right" or no hit. The only possibility of a "hit left and a hit right" is when there is a spurious coincidence in the Poisson stream, and lowering the intensity (so that the dead time is tiny compared to the average flux) lowers this coincidence. So in the limit of low intensities (as defined above), the coincidence rate of hits can be made as low as desired.
However, in the wavetrain picture, this is not the case. The wavetrain splits equally in two "half wavetrains" going each left and right. There they have half the probability to be detected. This leads to a coincidence rate which, if I'm not mistaking, to be e/2 where e is the quantum efficiency of the PM. Indeed, exactly at the same moment (or small lapse of time) when the left half wavetrain arrives at PM1, the right half wavetrain arrives at PM2. This cannot be lowered by lowering the intensity.
Now it is an elementary setup to show that we find anticoincidence, so how is this explained away in the classical picture ?

EDIT:
I add this because I already see a simple objection: you could say: hey, these are continuous beams, not little wavetrains, and it are both PM's which randomly (Poisson-like) select clicks as a function of intensity. But then the opposite bites you: how do you explain then that, in double cascades, or PDC, or whatever, we DO get clicks which are more correlated than a Poisson coincidence can account for ?
Now if you then object that "normal" sources have continuous wave outputs, but PDC or other "double photon emitters" do make little wavetrains, then do my proposed experiment again with such a source (but only using one of both wavetrains coming out of it, which is not difficult given the fact that they usually are emitted in opposite directions, and that we single out one single narrow beam).
What I want to say is that any classical mechanism that explains away NON-coincidence bites you when you need coincidence, and vice versa, while the "marble photon" model gives you naturally each time the right result.

cheers,
Patrick.

vanesch

Oct5-04, 03:41 AM

You can change the PM's bias voltage and thus shift on its sensitivity curve (a sigmoid type function). That simply changes your dark current rate/vacuum fluctuations noise. The more sensitive you make it (to shrink the detection loophole) the larger the dark current, thus the larger explicit background subtraction.

Have a look at:
http://www.hpk.co.jp/eng/products/ETD/pdf/PMT_construction.pdf
p 12, figure 28. You see a clear spectral (pulse height spectrum) separation between the dark current pulses, which have a rather exponential behaviour, and the bulk of "non-dark single photon" pulses, and allthough a small tradeoff can be made, it should be obvious that a lower cutoff in the amplitude spectrum clearly cuts away most of the noise, while not cutting away so much "non-dark" pulses. The very fact that these histograms have completely different signatures should indicate that the origins are quite different, no ?

cheers,
Patrick.

EDIT: but you might be interested also in other technologies, such as:

http://www.hpk.co.jp/eng/products/ETD/pdf/H8236-07_TPMO1011E03.pdf

where quantum efficiencies of ~40% are reached, in better noise conditions (look at the sharpness of the peak for single photon events !)

nightlight

Oct5-04, 04:13 AM

vanesch How about the following setup:
take a thermal source of light, with low intensity. After collimation into a narrow beam, send it onto a beam splitter (50-50%). Look at both split beams with a PM. In the "marble photon" picture, we have a Poisson stream of marbles, which, on the beam splitter, go left or right, and have then a probability of being seen by the PM (which is called its quantum efficiency). This means that only 3 cases can occur: a hit "left", a hit "right" or no hit. The only possibility of a "hit left and a hit right" is when there is a spurious coincidence in the Poisson stream, and lowering the intensity (so that the dead time is tiny compared to the average flux) lowers this coincidence. So in the limit of low intensities (as defined above), the coincidence rate of hits can be made as low as desired.
However, in the wavetrain picture, this is not the case. The wavetrain splits equally in two "half wavetrains" going each left and right. There they have half the probability to be detected. This leads to a coincidence rate which, if I'm not mistaking, to be e/2 where e is the quantum efficiency of the PM. Indeed, exactly at the same moment (or small lapse of time) when the left half wavetrain arrives at PM1, the right half wavetrain arrives at PM2. This cannot be lowered by lowering the intensity.
Now it is an elementary setup to show that we find anticoincidence, so how is this explained away in the classical picture ?

The semiclassical and QED theory of the square law detectors predicts Poisson distribution of counts P(k,n) where n is the average k (the average combines the efficiency and the incident intensity effects).

That means that classical case will have (A,B) triggers of type: (0,0), (1,0), (0,1), (2,0), (1,1), (0,2),... (with Poisson distribution applied independently on each detector). Thus, provided the average of your incident marbles Poissonian has this same n, you will have indistingushable correlations for any combination of events, since your marbles will be splitting in exactly same combinations at the same rates.

If you wish to divide the QM cases into "spurious" and "non-spurious" and start discarding events (instead of just using the incident Poissonian and computing the probabilities) and based on that predict some other kind of correlation, note that the same "refinement" of the Poisonian via spurious/non-spurious division can be included into any other model. Of course, any such data tweaking takes both models away from the Poissonian prediction (and the actual coincidence data).

It seems you're again confusing the average ensemble property (such as the efficiency e) with the individual events for the classicl case, i.e. assuming that the classical model implies a prediction of exactly 1/2 photocurrent in each try. That's not the case. The QED and the semiclassical theory of detectors yield exactly the same Poisson distribution of trigger events. The QED proper effects (which distinguish it empirically from the semiclassical models with ZPF) start at higher QED perturbative orders than those affecting the photo-ionization in detector modelling.

vanesch

Oct5-04, 04:24 AM

The semiclassical and QED theory of the square law detectors predicts Poisson distribution of counts P(k,n) where n is the average k (the average combines the efficiency and the incident intensity effects).

I was talking in cases where we have on average a hit every 200 seconds, while the hit itself takes 50 ns (so low intensity), so this means that (in the QM picture) double events are such a rarity that we can exclude them. Now you seem to say that - as I expected in my EDIT - you would now consider these beams as CONTINUOUS and not as little wavetrains ("photons") ; indeed, then you have independent Poisson streams on both sides.

It seems you're again confusing the average ensemble property (such as the efficiency e) with the individual events for the classicl case, i.e. assuming that the classical model implies a prediction of exactly 1/2 photocurrent in each try. That's not the case. The QED and the semiclassical theory of detectors yield exactly the same Poisson distribution of trigger events. The QED proper effects (which distinguish it empirically from the semiclassical models with ZPF) start at higher QED perturbative orders than those affecting the photo-ionization in detector modelling.

Indeed, I expected this remark (see my EDIT). However, I repeat my inverse difficulty then:
If light beams of low intensity are to be considered as "continuous" (so no little wave trains which are more or less synchronized in time), then how do you explain ANY coincidence which surpasses independent Poisson hits, such as there are clearly observed in PMD coincidences ?? Given the low intensity, the probability of coincidence based on individual Poisson streams is essentially neglegible, so it is extremely improbable that both detectors would trigger simultaneously, no ? So how do you explain ANY form of simultaneity of detection ?

cheers,
Patrick.

nightlight

Oct5-04, 05:27 AM

vanesch Have a look at:
http://www.hpk.co.jp/eng/products/ETD/pdf/PMT_construction.pdf
p 12, figure 28. You see a clear spectral (pulse height spectrum) separation between the dark current pulses, which have a rather exponential behaviour, and the bulk of "non-dark single photon" pulses, and allthough a small tradeoff can be made, it should be obvious that a lower cutoff in the amplitude spectrum clearly cuts away most of the noise, while not cutting away so much "non-dark" pulses. The very fact that these histograms have completely different signatures should indicate that the origins are quite different, no ?

You can get low noise for low QE. The PM tubes will have max QE about 40% which is not adequate for any non-classicality test. Also, note that the marketing brochures sent to the engineers are not exactly the same quality information source as the scientific reports. This kind of engineering literature uses also its own jargon and conventions and needs a grain of salt to interpret.

To see the problems better, take a look at the ultra-high efficiency detector (http://cul.arxiv.org/abs/quant-ph/0308054) (in a scientific report), with 85% QE, which with some engineering refinements might go to 90-95% QE. To reduce the noise, it is cooled down to 6K (not your average commercial unit). You might think that this solves the Bell test problem since the 83% ought to remove the need for the "fair sampling" assumption.

Now you read on, it says the optimum QE is obtained for the signal rates of 20,000 photons/sec. And what is the dark rate. You look around, and way back you find it as also 20,000 events/sec. The diagrams for QE vs bias voltage shows increase in QE with voltage, so it seems one could just increase the bias. Well, it doesn't work, since this also increases the dark rate much faster and for the voltage 7.4V it achieves the 85% QE and the 20,000 cps dark rate for the flux of 20,000 photons/sec. Beyond the 7.4V the detector breaks down.

So why not increase the incident flux? Well, because the detector's dead time then rises, decreasing the efficiency. The best QE they could get was after tuning the flux to 20,000. Also, decreasing the temperature does lower the noise, but requires higher voltage to get same QE, thus that doesn't help them.

Their Fig. 5 in the paper then combines all the effects relating QE to dark rate, and you see for the QE vs dark rate that as QE rises to 85% the dark rate grows exponentially to 20,000 (QE shows the same dependency as for voltage increase). As they put it:

But if we plot the quantum efficiency as a function of dark counts, as is done in Figure 5, the data for different temperatures all lie along the same curve. This suggests that the quantum efficiency and dark counts both depend on a single parameter, the electric field intensity in the gain region. The temperature and bias voltage dependance of this parameter result in the behavior shown in Figure 4. From Figure 5 we see that the maximum quantum efficiency of 85% is achieved at a dark count rate of roughly 20,000.

So, with this kind of dark rates, this top of the line detector with maxed-out QE is basically useless for Bell tests. Anything it measures will be prefectly well within the semiclassical (with ZPE) models. No matter how you tweak it, you can't get rid of the stubborn side-effects of an equivalent of 1/2 photon per mode vaccum fluctuations (since they predicted by the the theory). And that 1/2 photon equivalent noise is exactly what makes the semiclassical model with ZPF indistingushable at the Quantum Optics level (for the highers orders of perturbative QED, the semiclassical models which don't include self-interaction break down; Barut's self-field ED which models self-interaction still matches the QED to all orders it was computed).

vanesch

Oct5-04, 05:34 AM

Now you seem to say that - as I expected in my EDIT - you would now consider these beams as CONTINUOUS and not as little wavetrains ("photons") ; indeed, then you have independent Poisson streams on both sides.

I should maybe add that you have not that much liberty in the detector performance if you consider wavetrains of a duration of the order of a few ns with most of the time NOTHING happening. If you need, on the average, a certain efficiency, and you assume that it is only during these small time windows of arrival of the wavetrains that a detector can decide to click or not, then, with split wavetrains, you HAVE to have a certain coincidence rate if no "flag" is carried by the wavetrain to say whether it should click or not (and if you assume the existence of such a flag, then just do away with those wavetrains which have a "don't detect me" flag, and call those with the "detect me" flag, photons :-), because you assume these detection events to be independent in each branch.
So your only way out is to assume that the low level light is a continuous beam, right ? No wavetrains, and then nothing.

And with such a model, you can NEVER generate non-Poisson like coincidences, as far as I can see.

cheers,
Patrick.

vanesch

Oct5-04, 05:37 AM

And that 1/2 photon equivalent noise is exactly what makes the semiclassical model with ZPF indistingushable at the Quantum Optics level

Is this then also true for 1MeV gamma rays ?

cheers,
Patrick.

nightlight

Oct5-04, 06:04 AM

vanesch I was talking in cases where we have on average a hit every 200 seconds, while the hit itself takes 50 ns (so low intensity), so this means that (in the QM picture) double events are such a rarity that we can exclude them.

It doesn't matter what the Poisson average rate is. The semiclassical photodetector model predicts the trigger on average once per 200 s. There is no difference there.

However, I repeat my inverse difficulty then:
If light beams of low intensity are to be considered as "continuous" (so no little wave trains which are more or less synchronized in time), then how do you explain ANY coincidence which surpasses independent Poisson hits, such as there are clearly observed in PMD coincidences ??

The previous example of thermal source was super Poissonian (or at best Poissonian for laser beam).

On the other hand, you're correct that the semiclassical theory which does not model vacuum fluctuations cannot predict sub-Poissonian correlations of PDC or other similar sub-Poissonian experiments.

But, as explained at length earlier, if classical theory uses ZPF (boundary & initial conditions) and the correlation functions are computed to subtract the ZPF (to match what is done in the Glauber's prescription for Quantum Optics and what the detectors do by background subtractions and tuning to have null triggers when there is no signal), then it produces the same coincidence counts. The sub-Poissonian trait of semiclassical model is the result of the contribution of sub-ZPF superpositions (the "dark wave"). See the earlier message and the references there.

Given the low intensity, the probability of coincidence based on individual Poisson streams is essentially neglegible, so it is extremely improbable that both detectors would trigger simultaneously, no ? So how do you explain ANY form of simultaneity of detection ?

There is nothing to explain about vague statements such as "extremely improbable". Show me an expression that demonstrates the difference. Note that two independent Poissonans of classical model yield p^2 for trigger probability. Now if your QM marble count is Poissonian with any average, small or large (it only has to match the singles rate of classical model) it yields also the probability quadratic in p of the two marbles arriving to the splitter.

What's exactly the difference for the Poissonan source if you assume that QM photon number Poissonian has the same average singles rate as the classical model (same intensity calibration)? There is none. The Poissonian source complete clasicality for any number of detectors, polarizers, splitters (any linear elements) is an old hat (1963, Glauber Sudarshan classical equivalence for the coherent states).

NOTE: I assume here, when you insist on Poissonian classical distribution, that your marble distribution is also Poissonian (otherwise why would you mention it). For the sub-Poissonian case, classical models with ZPF can do that too (using the same kind of subtractions of vacuum fluctuation effects as QO), as explained at the top.

nightlight

Oct5-04, 06:20 AM

vanesch Is this then also true for 1MeV gamma rays ?

You still have vacuum fluctuations. But, the gamma ray photons are obviously in much better relation to any frequency cutoff of the fluctuations than optical photons, thus they indeed do have much better signal to noise on the detectiors. But this same energy advantage turns into disadvantage for non-classicality tests since the polarization coupling to atomic lattice is proportionately smaller, thus the regular polarizers (or half-silvered mirrors with preserved coherent splitting) won't work for the gamma rays.

The oldest EPR tests in fact were with gamma rays and they used Compton scattering to analyse polarization (for beam splitting), which is much less accurate than the regular optical polarizers. The net effect was much lower overall efficiency than for the optical photons. That's why no one uses gamma or X-ray photons for Bell's tests.

vanesch

Oct5-04, 06:32 AM

vanesch Is this then also true for 1MeV gamma rays ?

You still have vacuum fluctuations. But, the gamma ray photons are obviously in much better relation to any frequency cutoff of the fluctuations than optical photons, thus they indeed do have much better signal to noise on the detectiors. But this same energy advantage turns into disadvantage for non-classicality tests since the polarization coupling to atomic lattice is proportionately smaller, thus the regular polarizers (or half-silvered mirrors with preserved coherent splitting) won't work for the gamma rays.

I was not talking for EPR kinds of experiments, but to try to refute the idea that you do not need photons (that classical wave theory can do). I don't really see what's so different between gamma rays and optical photons: or both exist, or both are describable by the same semiclassical theory. And with gamma rays, there isn't this problem with quantum efficiency and dark currents, so I was wondering if this doesn't give a problem with the explanations used to explain away photons in the visible range.

cheers,
Patrick.

vanesch

Oct5-04, 06:34 AM

But, as explained at length earlier, if classical theory uses ZPF (boundary & initial conditions) and the correlation functions are computed to subtract the ZPF (to match what is done in the Glauber's prescription for Quantum Optics and what the detectors do by background subtractions and tuning to have null triggers when there is no signal), then it produces the same coincidence counts. The sub-Poissonian trait of semiclassical model is the result of the contribution of sub-ZPF superpositions (the "dark wave"). See the earlier message and the references there.

Eh, this sounds bizarre. I know you talked about it but it sounds so strange that I didn't look at it. I'll try to find your references to it.

cheers,
Patrick.

nightlight

Oct5-04, 06:54 AM

vanesch Eh, this sounds bizarre. I know you talked about it but it sounds so strange that I didn't look at it. I'll try to find your references to it.

The term "dark wave" is just picturesque depiction (a visual aid), a la Dirac hole, except this would be like a half-photon equivalent hole in the ZPF. That of course does get averaged over the entire ZPF distribution and without further adjustments of data nothing non-classical happens.

But, if you model a setup calibrated to "ignore" vacuum fluctuations (via combination of background subtractions and detectors sensitivity adjustments), the way Quantum Optics setups are (since Glauber's correlation functions subtract the vacuum contributions as well) -- then the subtraction of the average ZPF contributions makes the sub-ZPF contribution appear as having negative probability (which mirrors the negative regions in Wigner distribution) and able to replicate the sub-Poissonian effects on the normalized counts. The raw counts don't have sub-Poissonian or negative probability traits, just as they don't in Quantum Optics. Only the adjusted counts (background subtractions and/or the extrapolations of the losses via the "fair sampling" assumption) have such traits.

See those references for PDC classicality via Stochastic electrodynamics I gave earlier.

seratend

Oct5-04, 07:20 AM

I think both of you should not argument on the possibility to get a detector triggering a single photon as it is impossible (with classical or quantum physics).
Experiences with single photon are only simplification of what really occurs (i.e the problem of the double slit experiment, cavities, etc …). We just roughly say: I have an electromagnetic energy of hbar.ω.

Remind that a “pure photon” is a single energy and thus requires an infinite time of measurement: reducing this time of measurement (interaction is changed) modifies the field.

It is like trying to build a super filter that would extract a pure sinus wave from an electrical signal or a sound wave.

Don’t also forget that the quantization of the electromagnetic field gives only the well known energy eigenvalues (a number of photons) in the case of a free field (no sources) where we have a free electromagnetic Hamiltonian (Hem).
Once you interact, the eigenvalues of the electromagnetic field are changed and are given by Hem+Hint (i.e. you modify the basis of the photons number (the energy) < => you change the number of photons).

Seratend.

nightlight

Oct5-04, 07:27 AM

vanesch I was not talking for EPR kinds of experiments, but to try to refute the idea that you do not need photons (that classical wave theory can do). I don't really see what's so different between gamma rays and optical photons: or both exist, or both are describable by the same semiclassical theory. And with gamma rays, there isn't this problem with quantum efficiency and dark currents, so I was wondering if this doesn't give a problem with the explanations used to explain away photons in the visible range.

We were talking about coherent beam splitter which splits QM amplitude (or classical wave) into two equal coherent sub-packets. If you try same with the gamma rays, you have different type of split (non equal amplitudes) i.e. it would have merely classical mix (multidimensional rho instead of a single dimensional Psi in Hibert space terms) of the left-right sub-packets. This gives it a particle-like appearance, i.e. in each try it goes one way or the other but not both ways. But that type of scattering is perfectly within the semi-classical EM modelling.

Imagine a toy classical setup with a mirror containing large holes in the coating (covering half the area) and run quickly a "thin" light beam in random fashion over it. Now a pair of detectors behind will show perfect anti-correlation in their triggers. There is nothing contrary to classical EM about it, even though it appears as if particle went through on each trigger and on average half the light went each way. The difference is that you can't make the two halves interfere any more since they are not coherent. If you can detect which way "it" went you lose coherence and you won't have interference effects.

Some early (1970s) "anti-correlation" experimental claims with optical photons have made this kind of false leap. Namely they used randomly or circularly polarized light and used polarizer to split it in 50:50 ratio, then claimed the perfect anti-correlation. That's the same kind of trivially classical effect as the mirror with large holes. They can't make the two beams interfere, though (and they didn't try that, of course).

vanesch

Oct5-04, 07:42 AM

ZapperZ

Oct5-04, 08:00 AM

No, we were simply talking about photon detection and background. If the zero-point energy or whatever it is, provoques what is usually considered as being a technical difficulty, namely the "dark current noise", then why is this the limiting factor in visible light detectors, but doesn't it occur in gamma ray detectors, which are close to 100% efficient with neglegible dark currents (take MWPC for instance). I don't see why something that is "a fundamental problem" at say, 2eV is suddenly no issue anymore at 2MeV.

cheers,
Patrick.

I didn't want to jump into this and spoil the "fun", but I can't resist myself. :)

You are certainly justified in your puzzlement. Dark current, at least the ones we detect in photon detectors, has NOTHING to do with "zero-point" field. I deal with dark current all the time in accelerators. They are the result of field emission, and over the range of less than 10 MV/m, they are easily described by the Fowler-Nordheim theory of field emission. I do know that NO photodetector work with that kind of a gradient, or anywhere even close.

The most sensitive gamma-ray detector is the Gammasphere, now firmly anchored here at Argonne (http://www.anl.gov/Media_Center/News/2004/040928gammasphere.html). In its operating mode when cooled to LHe, it is essentially 100% efficient in detecting gamma photons.

Zz.

vanesch

Oct5-04, 08:14 AM

I didn't want to jump into this and spoil the "fun", but I can't resist myself. :)

No, please jump in !! I try to keep an open mind in this discussion, and I have to say that nightlight isn't the usual crackpot one encounters in this kind of discussions and is very well informed. I only regret a bit the tone of certain statements like what we are doing to those poor students and so on, but I've seen worse. What is potentially interesting in this discussion is how far one can push semiclassical explanations for optical phenomena. For instance, I remember having read that what is usually quoted as a "typical quantum phenomenon", namely the photo-electric effect, needs quantification of the solid state, but not of the EM field which can still be considered classical. Also, if it is true that semiclassical models can correctly predict higher order radiative corrections in QED, I have to say that I'm impressed. Tree diagrams however, are not so impressive.
I can very well accept that EPR like optical experiments do not close all loopholes and it can be fun to see how people still find reasonably looking semiclassical theories that explain the results.
However, I'm having most of the difficulties in this discussion with 2 things. The first one is that photon detectors seem to be very flexible devices which seem to get exactly those properties that are needed in each case to save the semiclassical explanation ; while I can accept each refutation in each individual case, I'm trying to find a contradiction between how it behaves in one case and how it behaves in another case.
The second difficulty I have is that I'm not aware of most of the litterature that is referred too, and I can only spend a certain amount of time on it. Also, I'm not very aware (even if I heard about the concepts) of these Wigner functions and so on. So any help from anybody here can do. Up to now I enjoyed the cat-and-mouse game :smile: :smile:

cheers,
Patrick.

seratend

Oct5-04, 08:26 AM

May be the principal problem is to know if the total spin 0, EPR state is possible with a classical vision.
I understand, nightlight needs to refute the physical existence of a "pure EPR state" in order to get "a classical theory" that describes the EPR experiment.

Seratend

vanesch

Oct5-04, 08:40 AM

I understand, nightlight needs to refute the physical existence of a "pure EPR state" in order to get "a classical theory" that describes the EPR experiment.

Yes, that is exactly what he does, and it took me some time to realize this in the beginning of the thread, because he claimed to accept all of QM except for the projection postulate. But if you browse back, afterwards we agreed upon the fact that he disagreed on the existence of a product hilbert space, and only considers classical matter fields (kind of Dirac equation) coupled with the classical EM field (Maxwell), such that the probability current of charge from the dirac field is the source of the EM field. We didn't delve into the issue of the particle-like nature of matter. Apparently, one should also add some noise terms (zero point field or whatever) to the EM field in such a way that it corresponds to the QED half photon contribution in each mode. He claims (well, and most authors he cites too) that the clickediclack of photons is just a property of "photon detectors" which react in such a way to continuous radiation... it is there that things seem to escape me.
However, the fun thing is that indeed, one can find explanations of a lot of "quantum behaviour" this way. The thing that bothers me are the detectors.

cheers,
Patrick.

ZapperZ

Oct5-04, 08:43 AM

What is potentially interesting in this discussion is how far one can push semiclassical explanations for optical phenomena. For instance, I remember having read that what is usually quoted as a "typical quantum phenomenon", namely the photo-electric effect, needs quantification of the solid state, but not of the EM field which can still be considered classical.

I happened to work in angle-resolved photoemission (ARPES) for the 3 years that I spent as a postdoc. So here is what I know.

While it is true that the band structure of the material being looked at can dictate the nature of the result, this is more of a handshaking process between both the target material and the probe, which is the light. While the generic photoelectric effect can find a plausible argument that light is still a wave (and not photons), this requires strictly that the target material (i) be polycrystaline (meaning no specific or prefered orientation of the crystal structure) and (ii) has a continuous energy band, as in the metallic conduction band. If you have ALL that, then yes, the classical wave picture cannot be ruled out in explaining the photoelectric effect.

The problem is, people who still hang on to those ideas have NOT followed the recent developments and advancements in photoemission. ARPES, inverse photoemission (IPES), resonant photoemission (RPES), spin-polarized photoemission, etc., and the expansion of the target material being studied, ranging from single-crystal surface states all the way to mott insulators, have made classical description of light quite puzzling. For example, the multi-photon photoemission, which I worked on till about 3 months ago, would be CRAZY if we have no photons. The fact that we can adjust the work function to have either 1-photon, 2-photon, 3-photon, etc. photoemission AND to be able to angularly map this, is damn convincing as far as the experiment goes.

There are NO quantitative semiclassical theory for ARPES, RPES, etc.. There are also NO quantitative semiclassical theory for multi-photon photoemission, or at least to explain the observation from such experiments IF we do not accept photons. I know, I've looked. It is of no surprise if I say that my "loyalty" is towards the experimental observation, not some dogma or someone's pet cause. So far, there have been no viable alternatives that are consistent to the experimental observations that I have made.

Zz.

seratend

Oct5-04, 10:21 AM

Vanesh
Yes, that is exactly what he does, and it took me some time to realize this in the beginning of the thread, because he claimed to accept all of QM except for the projection postulate. But if you browse back, afterwards we agreed upon the fact that he disagreed on the existence of a product hilbert space, and only considers classical matter fields (kind of Dirac equation) coupled with the classical EM field (Maxwell), such that the probability current of charge from the dirac field is the source of the EM field. …

… He claims (well, and most authors he cites too) that the clickediclack of photons is just a property of "photon detectors" which react in such a way to continuous radiation... it is there that things seem to escape me.
However, the fun thing is that indeed, one can find explanations of a lot of "quantum behaviour" this way. The thing that bothers me are the detectors.

Like classical mechanic can explain many things even light as particles (Newton assumption). It has taken a long time before scientist community accepted that light was a wave. Even with the initial results of young slits experiment, they have preferred to wait for another experiment, the experiment, showing the impossibility: the diffraction figure of an enlightened sphere: a light point in the middle of the shadow. This diffraction figure was predicted, if I remember, by Poisson in a demonstration to show that if light was not made of particles an incredible light point should appear :eek: .

ZapperZ
The problem is, people who still hang on to those ideas have NOT followed the recent developments and advancements in photoemission. ARPES, inverse photoemission (IPES), resonant photoemission (RPES), spin-polarized photoemission, etc., and the expansion of the target material being studied, ranging from single-crystal surface states all the way to mott insulators, have made classical description of light quite puzzling. For example, the multi-photon photoemission, which I worked on till about 3 months ago, would be CRAZY if we have no photons. The fact that we can adjust the work function to have either 1-photon, 2-photon, 3-photon, etc. photoemission AND to be able to angularly map this, is damn convincing as far as the experiment goes.

There are NO quantitative semiclassical theory for ARPES, RPES, etc.. There are also NO quantitative semiclassical theory for multi-photon photoemission, or at least to explain the observation from such experiments IF we do not accept photons. I know, I've looked. It is of no surprise if I say that my "loyalty" is towards the experimental observation, not some dogma or someone's pet cause. So far, there have been no viable alternatives that are consistent to the experimental observations that I have made.

I really think that arguing about the minimum error in the photo detectors would not solve the problem: the existence of the EPR like state and its associated results.

I think the current problem of “simple alternate classical” theories (with local interactions, local variables) lies in the lack of providing a reasonable result to EPR like states (photons, electrons): a pair of particles with a total null spin.

This state is so special: a measurement on any axis always gives a 50/50% of spin up/down for each particle of the pair. When we take a separated particle experiment, the result measurement shows that a 50/50 is only achievable on a unique orientation!

Seratend.

nightlight

Oct5-04, 10:23 AM

vanesch No, we were simply talking about photon detection and background. If the zero-point energy or whatever it is, provoques what is usually considered as being a technical difficulty, namely the "dark current noise", then why is this the limiting factor in visible light detectors, but doesn't it occur in gamma ray detectors, which are close to 100% efficient with neglegible dark currents (take MWPC for instance). I don't see why something that is "a fundamental problem" at say, 2eV is suddenly no issue anymore at 2MeV.

You may have lost the context of the arguments that brought us to the detecton question -- the alleged insufficiency of the non-quantized EM models to account for various phenomena (Bell tests, PDC, coherent beam splitters). It was in that specific context that the phenomenon of detection noise due to the vacuum fluctuation precludes any effect to help decide the EM non-classicality -- it is a problem for these specific non-classicality claims, not "a problem" for all conceivable non-classicality claims, much less that it is some kind of general technological or scientific "problem".

The low energy photons interact differently with the optical components than the gamma rays (the ratio of their energy/momenta to their interaction with atoms is hugely different), so the phenomena you used for the earlier non-classicality claims has lost their key features (such as the sharp polarization splitting or the sharp interference on the beam splitter).

Like with perpetuum mobile claims (which these absolute non-classicality claims increasingly resemble, after three, or even five, decades of excuses and ever more creative euphemisms for the failure), each device may have its own loophole or ways to create illusion of energy excess.

Now you have left the visible photons, moved to gamma rays. Present a phenomenon which makes them absolutely non-classical. You didn't even make a case how this sharper detectibility (better S/N) for these photons yields to anything that prohibits non-quantised EM field from modelling the phenomenon. I explained why the original setups don't help you with these photons.

The second confusion you may have is that between the Old Quantum Theory (before Schroedinger/Heisenberg) particle photon claims and the conventional jargon and visual mnemonics of the QED or Quantum Optics. The OQT didn't have correct dynamical theory of ionisation or of photon photo-electron scattering cross sections. So they imagined needle radiation or point-photons. After the Shoredinger-Heisenberg created QM dynamics, these phenomena became computable using purely semi-classical models (with only matter particles being quantized). The OQM arguments became irrelevant, even though you'll still see them parroted in the textbooks. The point-like jargon for photons survived into QED (and it is indeed heuristically/mnemonically useful in many cases, as long as one doesn't make ontology out of the personal mnemonic device and then claim paradoxes).

I asked you where is the point-photon in QED. You first tried via the apparent coexistence of anti-correlation and the coherence on a beam splitter. As demonstrated that doesn't work (and has been known so for 4-5 decades, it was tried first in 1950s and resolved during the Hanbury Brown and Twiss effect debates). The photon count is Poissonian, which is same as detector model response distribution. So the anti-correlation here isn't as sharp as it is usally claimed.

Then (after a brief detour into PDC) you brought up gamma rays as not having detection problem. True, they don't. But they lose the coherence and the visibility of the interference as they gain on the anti-correlation (due to sharper detection). That is a perfectly classical EM tradeoff. The less equal and less synchronized the packets after the split, the more exclusive they appear to the detectors while their intererence fringes become less sharp (lower visibility).

That is the same "complementarity" phenomenon that QM aplititudes (which follow Maxwell's equations for free space & through linear optical elements) describe. And that is identical to the semiclassical EM description since the same equations describe the propagation.

So what is the non-classicality claim about the gamma rays? The anti-correlation on the beam splitter is not relevant for that purpose for these photons.

You may wonder why is it always so that there is something else that blocks the non-classicality from manifesting. My guess is that it is so because it doesn't exist and all attempted contraptions claiming to achieve it are bound to fail one way or the other, just as perpetuum mobile has to. The reasons the failure causes shift is simply because the new contraptions which fix the previous failure shift to some other trick, confusion, obfuscation... The explanations of the flaws has to shift if the flaws shift. That is where the "shiftiness" originated.

The origin of these differences on the need of the 2nd quantization (that of the EM field) is in the different view on what was the 1st quantization all about. To those who view it as the introduction of the Hilbert space, observable non-commutativity into the classical system it is natural to try repeating the trick with remaining classical systems.

To those who view it as a solution to the classical physics dichotomy between the fields and the particles, since it replaced the particles with matter fields (Barut has shown that 3N configuration space vs 3D space issue is irrelevant here) it is sensless trying to "quantize" the EM field, since it is already "quantized" (i.e. it is a field).

In this perspective the Hilbert space formulation is a linear approximation, which due to the inherent non-linearity of the coupled matter and EM fields is limited, thus the collapse is needed which patches the approximation inadequacy via the piecewise linear evolution. The non-commutatitivity of the observables is general artifact with these kinds of piecewise linearizations, not a fundamental principle (Feynman noted and was particularly intrigued by this emergence of noncommutativity from the approximation in his checkerboard/lattice toy models of EM and Dirac equations; see Garnet Ord's (http://www.scs.ryerson.ca/~gord/) extended discussions on this topic, including the Feynman's puzzlement; note that Ord is a matematician, thus the physics in those papers is a bit thin).

ZapperZ

Oct5-04, 11:20 AM

ZapperZ You are certainly justified in your puzzlement. Dark current, at least the ones we detect in photon detectors, has NOTHING to do with "zero-point" field.

The "dark current" is somewhat fuzzy. Label it the irreducible part of the noise due to quantum vacuum fluctuations since that the part of the noise that was relevant in the detector discussion. The temperature can be lowered to 0K (the detector discussed was on 6K) and you will still have that noise.

No, what YOU think of "dark current" is the one that is fuzzy. The dark current that *I* detect isn't. I don't just engage in endless yapping about dark current. I actually measure, make spectral analysis, and other characterization of it. The field emission origin of dark current is well-established and well-tested.[1]

Zz.

1. R.H. Fowler and L. Nordheim, Proc. Roy. Soc. Lond., A119, 173 (1928).

nightlight

Oct5-04, 11:47 AM

vanesch he disagreed on the existence of a product hilbert space,

That's a bit of over-simplification. Yes, in non-relativistic QM you take each electron into its own factor space. But then you anti-symmetrize this huge product space and shrink it back to almost where it was (the 1 dimensional subspace of the symmetric group representation), the Fock space.

So the original electron product space was merely a pedagogical scaffolding to construct the Fock space. After all the smoke and hoopla has cleared, you're back where you started before constructing the 3N dimensional configuration space -- one 3-D space PDE set (Dirac Equation) describing now propagation of classical Dirac field (or the modes of quantized Dirac field represented by the Fock space) which now represents all classical electrons with one 3D matter field (similar to the Maxwell's EM field) instead of the QM amplitudes of a single Dirac electron. Plus you get around 3*(N-1) tonnes of obfuscation and vacuous verbiage on meaning of identity (that will be laughed at few generations from now). Note that Schroedinger believed from day one that these 1-particle QM amplitudes should have been interpreted as a single classical matter field of all electrons.

That's not my "theory" that's what it is for you or for anyone who cares to look it up.

The remaining original factors belong to different types of particles, they're simply different fields. Barut has shown that depending on which functions one picks for variation of the action, one gets an equivalent dynamics represented as either the 3N Dimensional configuration space fields or the regular 3 Dimensional space fields.

Apparently, one should also add some noise terms (zero point field or whatever) to the EM field in such a way that it corresponds to the QED half photon contribution in each mode.

That's not something one can fudge very much since the distribution uniquely follows from Lorenz invariance. It's not something you put in by hand and tweak as you go to fit this or that.

He claims (well, and most authors he cites too) that the clickediclack of photons is just a property of "photon detectors" which react in such a way to continuous radiation... it is there that things seem to escape me.

You never explained how QED predicts anything more marble-like about photons. Photons don't have position observable, they are not conserved, they don't have identity. They can be redefined by change of base. They propagate in space following Maxwell's equations. What is left of the marbles? That you can count them? You can count anything e.g. the QED EM field modes (which is what they are). They make clickediclacks? I'll grant you this one, they sound just like marbles droped into a box.

You must be still under the spell of the Old Quantum Theory (pre-1926) ideas of point photons (which is how this gets taught). They're not the same model as QED photons.

ZapperZ

Oct5-04, 01:31 PM

ZapperZ No, what YOU think of "dark current" is the one that is fuzzy. The dark current that *I* detect isn't.

I was talking about the usage of the term. Namely you claimed that in your field of work, the contribution of the QED vacuum fluctuation doesn't count into the "dark current." Yet, the authors of the detector preprint I cited (as well as the other Quantum Optics literature) count the vacuum fluctuations contributions under the "dark current" term. Therefore, that disagreement in usage alone demonstrates the term usage is fuzzy. QED.

The usage of the term "dark current" as used in PHOTODETECTORS (that is, after all, what we are talking about, aren't we?) has NOTHING to do with "QED vacuum fluctuation". Spew all the theories and ideology that you want. The experimental observation as applied to photodetectors and photocathodes do NOT make such connection.

This is getting way too funny, because as I'm typing this, I am seeing dark currents from a photocathode sloshing in an RF cavity. Not only that, I can control how much dark current is in there. There's so much of it, I can detect it on a phosphor screen! QED vacuum fluctuations??? It is THIS easy???!! C'mon now! Let's do a reality check here!

Zz.

nightlight

Oct5-04, 11:07 PM

vanesch What is potentially interesting in this discussion is how far one can push semiclassical explanations for optical phenomena.

If you recall that Stochastic Quantization starts by adding Gaussian noise to the classical field dynamics (in functional form and with the added imaginary time variable) to construct the quantized field (in path integrals form), you will realize that the Marshall-Santos model of Maxwell equations+ZPF (Stochastic Electrodynamics) can go at least as far as QED, provided you drop the external field and the external current approximations, thus turning it into ZPF enchanced version of the Barut's nonlinear self-field ED (which even without the ZPF reproduces the leading order of QED radiative corrections; see Barut group's KEK preprints; they had published much of it in Phys Rev as well).

The Ord's results provide much nicer, more transparent, combinatorial interpretation of the analytic continuation (of time variable) role in transforming the ordinary diffusion process into the QT wave equations -- they extract the working part of the analytic continuation step in the pure form -- all of its trick, the go of it, is contained in the simple cyclic nature of the powers if "i", which serves to separate the object's path sections between the collisions into 4 sets (this is the same type of role that powers of x in combinatorial generating functions techniques perform - they collect and separate the terms for the same powers of x).

Marshall-Santos-Barut SED model (in the full self-interacting form) is the physics behind the Stochastic Quantization, the stuff that really makes it work (as a model of natural phenomena). The field quantization step doesn't add new physics to "the non-linear DNA" (as Jaynes put it). It is merely a fancy jargon for a linearization scheme (a linear approximation) of the starting non-linear PD equations. For a bit of background on this relation check some recent papers by a mathematician Krzysztof Kowalski, which show how the sets of non-linear PDEs (the general non-linear evolution equations, such as those occuring in chemical kintecs or in population dynamics) can be linearized in the form of a regular Hilbert space linear evolution with realistic (e.g. bosonic) Hamiltonians. Kowalski's results extend the 1930s Carleman's & Koopman's PDE linearization techniques. See for example his preprints: solv-int/9801018 (http://cul.arxiv.org/abs/solv-int/9801018), solv-int/9801020 (http://cul.arxiv.org/abs/solv-int/9801020), chao-dyn/9801022 (http://cul.arxiv.org/abs/chao-dyn/9801022), math-ph/0002044 (http://cul.arxiv.org/abs/math-ph/0002044), hep-th/9212031 (http://cul.arxiv.org/abs/hep-th/9212031). He also has a textbook Methods of Hilbert Spaces in the Nonlinear Dynamical Systems (http://www.worldscibooks.com/chaos/2345.html) with much more on this technique.

vanesch

Oct6-04, 02:36 AM

You may have lost the context of the arguments that brought us to the detecton question -- the alleged insufficiency of the non-quantized EM models to account for various phenomena (Bell tests, PDC, coherent beam splitters).

No, the logic in my approach is the following.
You claim that we will never have raw EPR data with photons, or with anything for that matter, and you claim that to be something fundamental. While I can easily accept the fact that maybe we'll never have raw EPR data ; after all, there might indeed be limits to all kinds of experiments, at least in the forseable future, I have difficulties with its fundamental character. After all, I think we both agree on the fact that if there are individual technical reasons for this inability to have EPR data, this is not a sufficient reason to conclude that the QM model is wrong. If it is something fundamental, it should be operative on a fundamental level, and not depend on technological issues we understand. After all (maybe that's where we differ in opinion), if you need a patchwork of different technical reasons for each different setup, I don't consider that as something fundamental, but more like the technical difficulties people once had to make an airplane go faster than the speed of sound.

You see, what basically bothers me in your approach, is that you seem to have one goal in mind: explaining semiclassically the EPR-like data. But in order to be a plausible explaination, it has to fit into ALL THE REST of physics, and so I try to play the devil's advocate by taking each individual explanation you need, and try to find counterexamples when it is moved outside of the EPR context (but should, as a valid physical principle, still be applicable).

To refute the "fair sampling" hypothesis used to "upconvert" raw data with low efficiencies into EPR data, you needed to show that visible photon detectors are apparently plagued by a FUNDAMENTAL problem of tradeoff between quantum efficiency and dark current. If this is something FUNDAMENTAL, I don't see why this tradeoff should occur for visible light and not for gamma rays ; after all, the number of modes (and its "half photon energy") in the zero-point stuff scales up from the eV range to the MeV range. So if it is something that is fundamental, and not related to a specific technology, you should understand my wondering why this happens in the case that interests you, namely the eV photons, and not in the case that doesn't interest you, namely gamma rays. If after all, this phenomenon doesn't appear for gamma rays, you might not bother because there's another reason why we cannot do well EPR experiments with gamma rays, but to me, you should still explain why a fundamental property of EM radiation at eV suddenly disappears in the MeV range when you don't need it for your specific need of refuting EPR experiments.

Like with perpetuum mobile claims (which these absolute non-classicality claims increasingly resemble, after three, or even five, decades of excuses and ever more creative euphemisms for the failure), each device may have its own loophole or ways to create illusion of energy excess.

Let's say that where we agree, is that current EPR data do not exclude classical explanations. However, they conform completely with quantum predictions, including the functioning of the detectors. It seems that it is rather your point of view which needs to do strange gymnastics to explain the EPR data, together with all the rest of physics.
It is probably correct to claim that no experiment can exclude ALL local realistic models. However, they all AGREE with the quantum predictions - quantum predictions that you do have difficulties with explaining in a fundamental way without giving trouble somewhere else, like the visible photon versus gamma photon detection.

I asked you where is the point-photon in QED. You first tried via the apparent coexistence of anti-correlation and the coherence on a beam splitter.

No, I asked you whether the "classical photon" beam is to be considered as short wavetrains, or as a continuous beam.
In the first case (which I thought was your point of view, but apparently not), you should find extra correlations beyond the Poisson prediction. But of course in the continuous beam case, you find the same anti-correlations as in the billiard ball photon picture.
However, in this case, I saw another problem: namely if all light beams are continuous beams, then how can we obtain extra correlations when we have a 2-photon process (which I suppose, you deny, and just consider as 2 continuous beams). This is still opaque to me.

You may wonder why is it always so that there is something else that blocks the non-classicality from manifesting. My guess is that it is so because it doesn't exist and all attempted contraptions claiming to achieve it are bound to fail one way or the other, just as perpetuum mobile has to.

The reason I have difficulties with this explanation is that the shifting reasons should be fundamental, and not "technological". I can understand your viewpoint and the comparison to perpetuum mobile, in that for each different construction, it is yet ANOTHER reason. That by itself is no problem. However, each time the "another reason" should be fundamental (meaning, not depending on a specific technology, but a property common to all technologies that try to achieve the same functionality). If the reason photon detectors in the visible range are limited in QE/darkcurrent tradeoff, it should be due to something fundamental - and you say it is due to the ZPF.
However, then my legitime question was: where's this problem then in gamma photon detectors ?

cheers,
Patrick.

nightlight

Oct6-04, 05:04 AM

vanesch The reason I have difficulties with this explanation is that the shifting reasons should be fundamental, and not "technological"

Before energy conservation laws were declared the fundamental laws, you could only refute perptuum mobile claims on case by case basis. You would have to analyze and measure the forces, frictions, etc and show that the inventors claims don't add to net excess of energy.

The conventional QM doesn't have any such general principle. But in the Stochastic ED, the falsity of the violation immediately follows from the locality of the theory itself (it is an LHV theory).

In nonrelativistic QM you not only lack a general locality principle, but you have a non-local state collapse as a postulate, which is the key in deducing QM prediction that violates locality. Thus you can't have a fundamental refutation in QM -- it is an approximate theory which not only lacks but explicitly violates locality principle (via collapse and via the non-local potentials in Hamiltonians).

So, you are asking too much, at least with the current explicitly non-local QM.

The QED (the Glauber's Quantum Optics correlations) itself doesn't predict a sharp cos(theta) correlation. Namely it predicts that for the detectors and the data normalized (via background subtractions and the trigger level tuning) to the above-vacuum-fluctuations baseline counting, one will have perfect correlation for these kinds of counts.

But these are not the same counts as the "ideal" Bell's QM counts (which assume sharp and conserved photon number, none of which is true in a QED model of the setups), since both calibration operations, the subtractions and the above-vacuum-fluctuation detector threshold, remove data from the set of pair events, thus the violation "prediction" doesn't follow without much more work. Or if you're in hurry, you can just declare "fair sampling" principle is true (in the face of the fact that the semiclasical ED and the QED don't satisfy such "principle") and you spare yourself all the trouble. After all, the Phys. Rev. referees will be on your side, so why bother.

On the other hand, the correlations computed without normal ordering, thus corresponding to the setup which doesn't remove vacuum fluctuations, yields Husimi joint distributions which are always positive, hence their correlations are perfectly classical.

nightlight

Oct6-04, 05:19 AM

Let's say that where we agree, is that current EPR data do not exclude classical explanations.

We don't need to agree about any conjectures, but only about the plain facts. Euphemisms aside, the plain fact is that the experiments refute all local fair sampling theories (even though there never were and there are no such theories in the first place).

nightlight

Oct6-04, 05:41 AM

No, I asked you whether the "classical photon" beam is to be considered as short wavetrains, or as a continuous beam.

There is nothing different about "classical photon" or QED photon regarding the amplitude modulations. They both propagate via the same equations (Maxwell) throughout the EPR setup. Whatever amplitude modulation the QED photon has there, the same modulation is assumed for the "classical" one. This is a complete non-starter for anything.

While you still avoid to answer where did you get point photon idea from QED (other than through mixup with the "photons" of the Old Quantum Theory, of pre-1920s; since you're using the kind of arguments used in that era, e.g. only one grain of silver blackened modernized to "only one detector trigger", etc). It doesn't follow from QED any more than the point phonons follow from the exactly same QFT methods used in the solid state theory.

nightlight

Oct6-04, 06:32 AM

vanesch If this is something FUNDAMENTAL, I don't see why this tradeoff should occur for visible light and not for gamma rays ; after all, the number of modes (and its "half photon energy") in the zero-point stuff scales up from the eV range to the MeV range.

But the fundamental interaction constants don't scale along. The design of the detectors and the analyzers depends on the interaction constants. For example, for visible photons there is too little space left between 1/2 hv1 and 1 hv1 compared to atomic ionisation energies. At the MeV level, there is plenty of room in terms of atomic ionization energies to insert between the 1/2 hv2 and 1 hv2. The tunneling rates for these two kinds of gaps are hugely different since the interaction constants don't scale. Similarly, the polarization ineraction is negligable for MeV photons to affect their energy-momentum for analyzer design... etc.

In the current QM you don't have general locality principle to refute outright the Bell locality violation claims. So, the only thing one can do is refute particular designs, case by case. The detection problem plagues the visibile photon experiments. Analyzer problems plague the MeV photons.

To refute the perpetuum mobile claims before the energy conservation principles, one had to find friction or gravity or temperature or current of whatever other design specific mechanism ended up balancing the energy.

The situation with EPR Bell tests is only different in the sense that the believers in the non-locality are on top, as it were, so even though they never even showed anything that violates the locality, they insist that the opponents show why that whole class of experiments can't be improved in the future and made to work. That is quite a bit larger burden on the opponents. If they just showed anything that explicitly appeared to violate non-locality, one could just look their data and find error there (if locality holds). But there is no such data. So one has to look for underlying physics of the design and show how that particular design can't yield anything decisive.

vanesch

Oct6-04, 06:38 AM

There is nothing different about "classical photon" or QED photon regarding the amplitude modulations. They both propagate via the same equations (Maxwell) throughout the EPR setup. Whatever amplitude modulation the QED photon has there, the same modulation is assumed for the "classical" one. This is a complete non-starter for anything.

No, this is only true for single-photon situations. There is no classical way to describe "multi-photon" situations, and that's where I was aiming at. If you consider these "multi-photon" situations as just the classical superposition of modes, then there is no way to get synchronized hits beyond the Poisson coincidence. Nevertheless, that HAS been found experimentally. Or I misunderstand your picture.

cheers,
Patrick.

ZapperZ

Oct6-04, 06:40 AM

The reason I have difficulties with this explanation is that the shifting reasons should be fundamental, and not "technological". I can understand your viewpoint and the comparison to perpetuum mobile, in that for each different construction, it is yet ANOTHER reason. That by itself is no problem. However, each time the "another reason" should be fundamental (meaning, not depending on a specific technology, but a property common to all technologies that try to achieve the same functionality). If the reason photon detectors in the visible range are limited in QE/darkcurrent tradeoff, it should be due to something fundamental - and you say it is due to the ZPF.
However, then my legitime question was: where's this problem then in gamma photon detectors ?

cheers,
Patrick.

Here's a bit more ammunition for you, vanesch. If I substitute the photocathode in a detector from, oh, let's say, tungsten to diamond, and keeping everything else the same, the dark current INCREASES! Imagine that! I can change the rate of vacuum fluctuation simply by changing the type of media near to it! So forget about going from visible light detector to gamma ray detectors. Even just for visible light detector, you can already manipulate the dark current level. There are no QED theory on this!

I suggest we write something and publish it in Crank Dot Net. :)

Zz.

nightlight

Oct6-04, 06:46 AM

vanesch

Oct6-04, 06:53 AM

vanesch If this is something FUNDAMENTAL, I don't see why this tradeoff should occur for visible light and not for gamma rays ; after all, the number of modes (and its "half photon energy") in the zero-point stuff scales up from the eV range to the MeV range.

But the fundamental interaction constants don't scale along.

Yes if we take into account atoms, but the very fact that we take atoms to make up our detection apparatus might 1) very well be at the origin of being unable to produce EPR raw data - I don't know (I even think so), but 2) this is nothing fundamental, is it ? It is just because we earthlings are supposed to work with atomic matter. The description of the fundamental behaviour of EM fields shouldn't be dealing with atoms, should it ?

To refute the perpetuum mobile claims before the energy conservation principles, one had to find friction or gravity or temperature or current of whatever other design specific mechanism ended up balancing the energy.

Well, let us take the following example. Imagine that perpetuum mobile DO exist, when working, say, with dilithium crystals. Imagine that I make such a perpetuum mobile, where on one I put in 5000V and 2000A, and on the other side, I have a huge power output on a power line, 500000V and 20000A.

Now I cannot make a direct volt meter measuring 500000 V, so I use a voltage divider with a 1GOhm resistor and a 1MOhm resistor, and I measure 500V over my 1MOhm resistor. Also I cannot pump 20000A in my ampmeter, so I use a shunt resistance of 1milliOhm in parallel with 1 Ohm, and I measure 20 Amps in the shunt.
Using basic stuff, I calculate from my measurement that 500V on my voltmeter, times my divider factor (1000) gives me 500 000V and that my 20 Amps times my shunt factor (1000) gives me 20 000 A.

Now you come along and say that these shunt corrections are fudging the data, that the raw data give us 500V x 20A = 10 KW output, while we put 5000Vx2000A = 10MW input in the thing, and that hence we haven't shown any perpetuum mobile.
I personally would be quite convinced that these 500V and 20A, with the shunt and divider factors, are correct measurements.
Of course, it is always possible to claim that shunts don't work beyond 200A, and dividers don't work beyond 8000V, in those specific cases when we apply them to such kinds of perpetuum mobile. But I find that far-stretched, if you accept shunts and dividers in all other cases.

cheers,
Patrick.

ZapperZ

Oct6-04, 06:54 AM

ZapperZ Here's a bit more ammunition for you, vanesch. If I substitute the photocathode in a detector from, oh, let's say, tungsten to diamond, and keeping everything else the same, the dark current INCREASES! Imagine that! I can change the rate of vacuum fluctuation simply by changing the type of media near to it!

You change rate of tunneling since the ionization energies are different in those cases.

Bingo!! What did you think I meant by "field emission" and "Fowler-Nordheim theory" all along? You disputed these and kept on insisting it has something to do with "QED vacuum fluctuation"! Obviously, you felt nothing wrong with dismissing things without finding out what they are.

For the last time - dark currents as detected in photodetectors have NOTHING to do with "QED vacuum fluctuation". Their properties and behavior are VERY well-known and well-characterized.

Zz.

nightlight

Oct6-04, 06:59 AM

vanesch No, this is only true for single-photon situations. There is no classical way to describe "multi-photon" situations, and that's where I was aiming at. If you consider these "multi-photon" situations as just the classical superposition of modes, then there is no way to get synchronized hits beyond the Poisson coincidence. Nevertheless, that HAS been found experimentally. Or Imisunderstand your picture.

We already went over "sub-Poissonian" distributions few messages back -- it is the same problem as with anti-correlation. This is purely the effect of the vacuum fluctuation subtraction (for the correlation functions by using normal operator ordering), yielding negative probability regions in the Wigner joint distribution functions. The detection and the setups corresponding to correlations computed this way adjust data and tune detectors so that in the absence of signal all counts are 0.

The semiclassical theory which model this data normalization for coincidence counting, also predicts the sub-Poissonian distribution, the same way. (We already went over this at some length earlier...)

seratend

Oct6-04, 07:08 AM

Nightlight

Marshall-Santos-Barut SED model (in the full self-interacting form) is the physics behind the Stochastic Quantization , the stuff that really makes it work (as a model of natural phenomena). The field quantization step doesn't add new physics to "the non-linear DNA" (as Jaynes put it).
It is merely a fancy jargon for a linearization scheme (a linear approximation) of the starting non-linear PD equations.
For a bit of background on this relation check some recent papers by a mathematician Krzysztof Kowalski, which show how the sets of non-linear PDEs ... can be linearized in the form of a regular Hilbert space linear evolution with realistic (e.g. bosonic) Hamiltonians. .

Finally, I understand (may be not :) you agree that PDE, ODE and their non linearities may be rewritten into the Hilbert space formalism. See your example, Kowalski's paper (ODE) solv-int/9801018 (http://cul.arxiv.org/abs/solv-int/9801018).

So, it is the words “linear approximation” that seem no to be correct as the reformulation of ODE, PDE with non-linearities in Hilbert space are equivalent.
In fact, I understand what you may reject in the Hilbert space formulation is the following:

-- H is an hermitian operator in id/dt|psi>=H|psi> <=> the time evolution is unitary (what you may call the linear approximation?).

And if I have understood the paper, Kowalski has demonstrated, a well known fact of the hilbert space users, that with a simple gauge transformation (selection of other p,q type variables), you can change a non hermitian operator into an hermitian one (its relation (4.55 to 4.57)). Therefore, many non-unitary evolutions may be expressed exactly as functions of unitary evolutions.
So I still conclude that even a unitary evolution of the Shroedinger equation may represent a non linear ODE.
Therefore, I still not understand what you call the “linear approximation” as in all cases I get exact results (approximation means, for me the existence of small errors).

--All the possible solutions given by the Schrödinger type equation id/dt|psi>=H|psi> (and its derivatives in the second quantization formalism).
At least the solutions that are non-compatible with the local hidden variables theories.

So, if we interpret your possible physical interpretation stochastic electrodynamics as giving the true results, what we just need to do is to rewrite it formally into the Hilbert space formalism and look at the difference with QED?

Seratend.

P.S. For example, with this comparison, we can see effectively if the projection postulate is really critical or only a way of selecting an initial state.

P.P.S We thus may also check in a rather good confidence if the stochastic electrodynamics formulation does not contain by itself an hidden “hidden variable”.

P.P.P.S and then, if there is really fundamental difference we identify, we can update the schroedinger equation : ) as well as the other physical equations.

vanesch

Oct6-04, 07:11 AM

We already went over "sub-Poissonian" distributions few messages back -- it is the same problem as with anti-correlation. This is purely the effect of the vacuum fluctuation subtraction (for the correlation functions by using normal operator ordering), yielding negative probability regions in the Wigner joint distribution functions.

Yes, I know, but I didn't understand it.

cheers,
Patrick.

nightlight

Oct6-04, 07:24 AM

vanesch Yes if we take into account atoms, but the very fact that we take atoms to make up our detection apparatus might 1) very well be at the origin of being unable to produce EPR raw data - I don't know (I even think so), but 2) this is nothing fundamental, is it ? It is just because we earthlings are supposed to work with atomic matter. The description of the fundamental behaviour of EM fields shouldn't be dealing with atoms, should it ?

It is merely related to specific choice of the setup which claims (potential) violation. Obviously, why are the constants what they are, is fundamental.

But why the constants (in combination with laws) happen to block this or that claim in just that particular way is the function of the setup, what is the physics they overlooked to make them pick that design. That isn't fundamental.

Now you come along and say that these shunt corrections are fudging the data, that the raw data give us 500V x 20A = 10 KW output, while we put 5000Vx2000A = 10MW input in the thing, and that hence we haven't shown any perpetuum mobile.

Not quite analogical situation. The "fair sampling" is plainly violated by the natural semiclassical model (see earlier message on sin/cos split) as well as in the Quantum Optics, which will have exactly the same amplitude propagation through the polarizers to detectors and follow the same square law detector probabilities of trigger. See also Khrennikov's paper cited earlier on proposed test for the "fair sampling."

So the situation is as if you picked some imagined behavior that is contrary to the existent laws and claimed that you will assume in your setup the property holds.

Additionally, there is no universal "fair sampling" law which you just invoke without examination whether it applies in your setup. And in the EPR-Bell setups it should be at least tested since the claim is so fundamental.

nightlight

Oct6-04, 07:38 AM

nightlight

Oct6-04, 08:12 AM

seratend And if I have understood the paper, Kowalski has demonstrated, a well known fact of the hilbert space users, that with a simple gauge transformation (selection of other p,q type variables), you can change a non hermitian operator into an hermitian one (its relation (4.55 to 4.57)). Therefore, many non-unitary evolutions may be expressed exactly as functions of unitary evolutions.

That was not it. The point is the linearization procedure which is the step of construction of M, which is linear operator. That step occurs in transition between 4.44 and 4.46 where the M is obtained. The stuff you quote is the comparatively trivial part about making 4.45 look like Schroedinger equation with the hermitean operator (instead of M).

So I still conclude that even a unitary evolution of the Shroedinger equation may represent a non linear ODE.
Therefore, I still not understand what you call the “linear approximation” as in all cases I get exact results (approximation means, for me the existence of small errors).

The point of his procedure is to have as input any set of non-linear (evolution) PD equations and create a set of linear equations which approximate the nonlinear set (iterative procedure which arrives to infinite set of linear approximations). The other direction, from linear to non-linear, is relatively trivial.

So, if we interpret your possible physical interpretation stochastic electrodynamics as giving the true results, what we just need to do is to rewrite it formally into the Hilbert space formalism and look at the difference with QED?

If you want to try, check first Barut's work which should save you lots of time. It's not that simple, though.

ZapperZ

Oct6-04, 08:27 AM

nightlight You change rate of tunneling since the ionization energies are different in those cases.

ZapperZBingo!! What did you think I meant by "field emission" and "Fowler-Nordheim theory" all along? You disputed these and kept on insisting it has something to do with "QED vacuum fluctuation"! Obviously, you felt nothing wrong with dismissing things without finding out what they are.

Complete non sequitur. You stated that if you change detector materials, you will get different dark currents and that this would imply (if vacuum fluctuations had a role in dark currents) that vacuum fluctuations were changed.

It doesn't mean that vacuum fluctuations changed. If you change material and thus change the gap energies, the tunneling rates will change even though the vacuum stayed the same, since the tunneling rates depend on the gap size, which is the material property (in addition to depending on vacuum fluctuation energy).

Eh? Aren't you actually strengtening my point? It is EXACTLY what I was trying to indicate that changing the material SHOULD NOT change the nature of the vacuum beyond the material - and I'm talking about the order of 1 meter here from the material! If you argue that the dark currents are due to "QED vacuum fluctuations", then the dark current should NOT change simply because I switch the photocathode since, by your own account, vacuum fluctuations hasn't changed!

But the reality is, IT DOES! I detect this all the time! So how could you argue the dark currents are due to QED vacuum fluctuation? Just simply because a book tells you? And you're the one who are whinning about other physicists being stuck with some textbook dogma?

For the last time - dark currents as detected in photodetectors have NOTHING to do with "QED vacuum fluctuation". Their properties and behavior are VERY well-known and well-characterized.

Take any textbook on Quantum Optics and read up on photo-detectors noise and find out for yourself.

... and why don't you go visit an experimental site that you criticizing and actually DO some of these things? It appears that your confiment within theoretical boundaries are cutting you off from physical reality. Grab a photodiode and make a measurement for yourself! And don't tell me that you don't need to know how it works to be able to comment on it. You are explicitly questioning its methodology and what it can and cannot measure. Without actually using it, all you have is a superficial knowledge of what it can and cannot do.

Comments such as the one above is exactly the kind of theorists that Harry Lipkin criticized in his "Who Ordered Theorists" essay. When faced with an experimental results, such theorists typically say "Oh, that can't happen because my theory says it can't". It's the same thing here. When I tell you that I SEE dark currents, and LOTS of it, and they have nothing to do with QED vacuum fluctuations, all you can tell me is to go look up some textbook? Oh, it can't happen because that text says it can't!

If all the dark currents I observe in the beamline is due to QED vacuum fluctuation, then our universe will be OPAQUE!

Somehow, there is a complete disconnect between what's on paper and what is observed. Houston, we have a problem....

Zz.

vanesch

Oct6-04, 08:48 AM

Not quite analogical situation. The "fair sampling" is plainly violated by the natural semiclassical model (see earlier message on sin/cos split) as well as in the Quantum Optics, which will have exactly the same amplitude propagation through the polarizers to detectors and follow the same square law detector probabilities of trigger.

Well, the fair sampling is absolutely natural if you accept photons as particles, and you only worry about the spin part. It is only in this context that EPR excludes semiclassical models. The concept of "photon" is supposed to be accepted.

I've been reading up a bit on a few of Barut's articles which are quite interesting, and although I don't have the time and courage to go through all of the algebra, it is impressive indeed. I have a way of understanding his results: in the QED language, when it is expressed in the path integral formalism, he's working with the full classical solution, and not working out the "nearby paths in configuration space". However, this technique has a power over the usual perturbative expansion, in that the non-linearity of the classical solution is also expanded in that approach. So on one hand he neglects "second quantization effects", but on the other hand he includes non-linear effects fully, which are usually only dealt with in a perturbative expansion. There might even be cancellations of "second quantization effects", I don't know. In the usual path integral approach, these are entangled (the classical non-linearities and the quantum effects).

However, I still fail to see the link to what we are discussing here, and how this leads to correlations in 2-photon detection.

cheers,
Patrick.

vanesch

Oct6-04, 09:19 AM

However, I still fail to see the link to what we are discussing here, and how this leads to correlations in 2-photon detection.

I guess the crux is given by equation 27 in quant-ph/9711042,
which gives us the coincidence probability for 2 photon detector clicks in 2 coherent beams. However, this is borrowed from quantum physics, no ? Aren't we cheating here ?
I still cannot see naively how you can have synchronized clicks with classical fields...

cheers,
Patrick.

EDIT: PS: I just ordered Mandel's quantum optics book to delve a bit deeper in these issues, I'll get it next week.... (this is a positive aspect for me of this discussion)

seratend

Oct6-04, 11:12 AM

nightlight ... Therefore, many non-unitary evolutions may be expressed exactly as functions of unitary evolutions.

That was not it. The point is the linearization procedure which is the step of construction of M, which is linear operator. That step occurs in transition between 4.44 and 4.46 where the M is obtained. The stuff you quote is the comparatively trivial part about making 4.45 look like Schroedinger equation with the hermitean operator (instead of M).

Oki, for me the redefinition of M of (3.2) into the “M’” of (4.46) was trivial : ). In fact I only considered §D and §E as only a method on a well known problem of vector spaces: how to make diagonal some non hermitian operators (i.e. where solving the time evolution operator is easy in our case).
Starting from a non-hermitian operator M=M1+iM2 where M1 and M2 are hermitian, we may search a linear transformation on the Hilbert space where M becomes hermitian (and thus it may be diagonal with further transformation).

So, the important point for me, is that I think you accept that a PDE/ODE equation may be reformulated into the Hilbert space formalism, but without the obligation to get a unitary time evolution (i.e id/dt|psi>=M|psi> where M may or may not be hermitian.

nightlight The point of his procedure is to have as input any set of non-linear (evolution) PD equations and create a set of linear equations which approximate the nonlinear set (iterative procedure which arrives to infinite set of linear approximations).

So “approximation” for you mean an infinite set of equations to solve (like computing the inverse of an infinite dimensional matrix). But theoretically, you know that you have an exact result. Ok, let’s take this definition. Well, you may accept more possibilities than what I do: that a non unitary time evolution (id/dt|psi>=M|psi>) may be changed, with an adequate transformation, into a unitary one.

So, the use of stochastic electrodynamics may be theoretically transposed into an exact id/dt|psi>=H|psi> (may be in a 2nd quantification view) where H (the hypothetic Hamiltonian) may not be hermitian (and I think you assume It is not).

So if we assume (very quickly), that H is non hermitian (=H1+iH2, H1 and H2 hermitian, and with H1>> H2 for all practical purposes), we thus have a schroedinger equation that has a kind of diffusion coefficient (H2) that may approach some of the proposed modifications found in the literature to justify the “collapse” of the wave function. Decoherence program – see for example Joos quant-ph/9908008 eq. 22 and many other papers.

Thus the stochastic electrodynamics may be (?) checked more easily with experiments that measure the decoherence time of quantum systems rather than the EPR experiment where you have demonstrated that it is not possible to make the difference.

Thus, I think, that the promoters of this theory should work on a Hilbert space formulation (at least approximate, but with enough precision in order to get a non hermitian Hamiltonian). Therefore they may apply it to other experiments to demonstrate the difference (i.e different previsions between classical QM and stochastic electrodynamics through, may be, decoherence experiments) rather than working on experiments that cannot separate the theories and verifying that the 2 theories agree with the experiment:
It is their job, as their claim seem to say that classical QM is not ok.

Seratend.

nightlight

Oct6-04, 06:26 PM

vanesch Well, the fair sampling is absolutely natural if you accept photons as particles, and you only worry about the spin part. It is only in this context that EPR excludes semiclassical models. The concept of "photon" is supposed to be accepted.

I don't see how does "natural" part help you restate the plain facts: Experiments refuted the "fair sampling" theories. It seems the plain fact still stands as is.

Secondly, I don't see it natural for the particles either. Barut has some EPR-Bell papers for spin 1/2 point particles in classical SG and he gets the unfair sampling. In that case it was due to the dependence of the beam spread in the SG on the hidden classical magnetic momentum. This yields particle paths in the ambiguous, even wrong region, depending on the value of hidden spin orientation to the SG axis. Thus for the coincidence it makes the coincidence accuracy sensitive to the angle between the two SG's i.e. the "loophole" was in the analyzer violating the fair sampling (same analyzer problem happens for the high energy photons).

It seems what you mean by "particle" is strict unitary evolution with sharp particle number, and in the Bell setup with sharp value 1 for each side. That is not true of QED photon number (you neither have sharp nor conserved photon number; and specifically for the proposed setups you either can't detect them reliably enough or you can't analyze them on a polarizer reliably enough, depending on photon energy; these limitations are facts arising from the values of relevant atomic interaction constants and cross sections which are what they are i.e. you can't assume you can change those, you can only come up with another design which works around any existent flaw which was due to the relevant constants).

However, I still fail to see the link to what we are discussing here, and how this leads to correlations in 2-photon detection.

It helps in the sense that if you can show that Barut's self-field ED agrees with QED beyond the perturbative orders relevant for Quantum Optics measurements (which is actually the case), you can immediately conclude, without having to work out a detailed Quantum Optics/QED prediction (which is accurate enough to predict exactly what would actually be obtained for correlations with the best possible detectors and polarizers consistent with the QED vacuum fluctuations and all the relevant physical constants of the detectors and the polarizers) that a local model of the experiment exists for any such prediction -- the model would be the self-field ED itself.

Thus you would immediately know that however you vary the experimental setup/parameters, within the perturbative orders to which QED & self-fields agree, something will be there to block it from violating locality. You don't need to argue about detector QE or plarizer efficiency, you know that anything they cobble together within the given perturbative orders, will subject any conjecture about future technology being able to improve efficiency of a detector (or other components) beyond threshold X, to reductio ad absurdum. Thus the experimenter would have to come up with a design which relies in an essential way on the predictions of QED perturbative orders going beyond the orders of agreement with the self-field ED. Note also that the existent experiments are well within the orders of agreement of the two theories, thus for this type of tests there will always be a "loophole" (i.e. the actual data won't violate the inequality).

This is the same kind of conclusion that you would make about perpertuum mobile claim which asserts that some particular design will yield 110% efficiency if the technology gets improved enough to have some sub-component of the apratus work with the accuracy X or better. The Bell tests make exactly this kind of assertion (without the fair sampling conjecture which merely helps them claim that experiments exclude all local "fair sampling" theories, and that is too weak to exlude anything that exists, much less all future local theories) -- we could violate it if we can get X=83% or better the overall setup efficiency (which accounts for all types of losses, such as detection, polarizer, apperture efficiency, photon number spread,...).

Now, since in the perpetuum mobile case you can invoke general energy conservation law, you can immediately tell the inventor that (provided the rest of his logic is valid) his critical component will not be able to achieve accuracy X since that would violate energy conservation. You don't need to go into detailed survey of all conceivable relations between the relevant interaction constants in order to compute the limits on the accuracy X for all conceivable technological implementatons of that component. You would know it can't work since assuming otherwise would lead to reductio ad absurdum.

nightlight

Oct6-04, 08:28 PM

vanesch I guess the crux is given by equation 27 in quant-ph/9711042,
which gives us the coincidence probability for 2 photon detector clicks in 2 coherent beams. However, this is borrowed from quantum physics, no ? Aren't we cheating here ?

The whole section 2 is derivation of standard Quantum Optics prediction (in contrast to a toy QM prediction) expressed in terms of Wigner functions, which are perfectly standard tool for QED or QM. So, of course, it is all standard Quantum Optics, just using Wigner's joint distribution functions instead of the more conventional Glauber's correlation functions. The two are fully equivalent, thus that is all standard, entirely uncontroversial part. They are simply looking for a more precise expression of the standard Quantum Optics prediction showing the nature of the non-classicality in a form suitable for their analysis.

The gist of their argument is that if for a given setup you can derive strictly positive Wigner function for joint probabilities, there is nothing else to discuss, all statistics is perfectly classical. The problem is how to interpret the other case, when there are negative probability regions of W (which show up in PDC or any sub-Poissonan setup). To do that they need to examine to what kind of detection and counting does the Wigner distribution correspond operationally (to make prediction with any theoretical model you need operational mapping rules of that kind). With the correspondence established, their objective is to show that the effects of the background subtractions and the above-vacuum threshold adjustments on individual detectors (the detectors adjustments can only set the detector's Poisson average, there is no sharp decision for each try, thus there is always some loss and some false positives) are in combination always sufficient to explain the negative "probability" of the Wigner measuring setups as artifacts of the combined subtraction and losses (the two can be traded off by the experimenter but he will always have to chose between the increased losses and the increased dark currents, thus subtract the background and unpaired singles in proportions of his choice but with the total subtraction not reducible below the vacuum fluctuations limit).

That is what the subsequent sections 3-5 deal with. I recall discussing with them the problems of that paper at the time since I thought that the presentation (especially in sect 5) wasn't sharp and detailed enough for readers who weren't up to speed on their whole previous work. They had since then sharpened their detector analysis with more concrete detection models and detailed computations, you can check their later preprints in quant-ph if the sections 4 & 5 don't seem sufficient for you.

Note that they're not pushing here SED model explicitly, but rather working in the standard QO scheme (even though they know from their SED treatment where to look for the weak spots in the QO treatment). This is to make the paper more publishable, easier to get through the hostile gatekeepers (who might just say, SED who? and toss it all out). After all, it is not a question whether experiments have produced any violation -- they didn't. In a fully objective system, that would be it, no one would have to refute anything since nothing was shown that needs refuting.

But in the present system, the non-locality side has an advantage so that their handwave about "ideal" future technology is taken as a "proof" that it will work some day, which then the popularizers and the educators translate into "it worked" (which is mostly the accepted wisdom you'll find in these kind of student forums). Unfortunately, with this kind of bias, the only remaining way for critics of the prevailing dogma is to show, setup by setup, why a given setup, even when granted the best conceivable future technology can't produce a violation.

I still cannot see naively how you can have synchronized clicks with classical fields...

You can't get them and you don't get them with the raw data, which will always have either too much uncorrelated background or too much pair losses. You can always lower the sensitivity to lower the background noise in order to have smaller explicit subtractions, but then you will be discarding too many unpaired singles (events which don't have a matching event on the other side).

vanesch

Oct8-04, 02:15 AM

The gist of their argument is that if for a given setup you can derive strictly positive Wigner function for joint probabilities, there is nothing else to discuss, all statistics is perfectly classical.

This is what I don't understand (I'm waiting for my book on quantum optics..., hence my silence). After all, these Wigner functions describe - if I understand well - the Fock states that correspond closely to classical EM waves. However, the statistics derived from these Fock states for photon detection assume a second quantization, no ? So how can you 1) use the statistics derived from second quantization (admitted, for cases that correspond to classical waves) to 2) argue that you don't need a second quantization ??

You see, the way I understand the message (and maybe I'm wrong) is the following procedure:
-Take a classical EM wave.
-Find the Fock space description corresponding to it (with the Wigner function).
-From that Fock space description, calculate coincidence rates and other statistical properties.
-Associate with each classical EM wave, such statistics. (*)
-Take some correlation experiment with some data.
-Show that you can find, for the cases at hand, a classical EM wave such that when we apply the above rules, we find a correct prediction for the data.
-Now claim that these data are explainable purely classically.

To me, the last statement is wrong, because of step (*)
You needed second quantization in the first place to derive (*).

cheers,
Patrick.

EDIT: I think that I've been too fast here. It seems indeed that two-photon correlations cannot be described that way, and that you always end up with the equivalence of a single-photon repeated experiment, the coherent state experiment, and the classical <E-(r1,t1) x E+(r2,t2> intensity cross correlation.

vanesch

Oct8-04, 03:32 AM

I still cannot see naively how you can have synchronized clicks with classical fields...

You can't get them and you don't get them with the raw data, which will always have either too much uncorrelated background or too much pair losses. You can always lower the sensitivity to lower the background noise in order to have smaller explicit subtractions, but then you will be discarding too many unpaired singles (events which don't have a matching event on the other side).

How about this:

http://scotty.quantum.physik.uni-muenchen.de/publ/pra_64_023802.pdf

look at figure 4

I don't see how you can explain these (raw, I think) coincidence rates unless you assume (and I'm beginning to understand what you're pointing at) that the classical intensities are "bunched" in synchronized intensity peaks.
However, if that is the case, a SECOND split of one of the beams towards 2 detectors should show a similar correlation, while the quantum prediction will of course be that they are anti-correlated.

2-photon beam === Pol. Beam splitter === beam splitter -- D3
...................................|.............. ................|
................................. D1............................D2

Quantum prediction: D1 is correlated with (D2+D3) in the same way as in the paper ; D2 and D3 are Poisson distributed, so at low intensities anti-correlated.

Your prediction: D1 is correlated with D2 and with D3 in the same way, and D2 is correlated with D3 in the same way.

Is that correct ?

cheers,
Patrick.

nightlight

Oct8-04, 04:19 AM

vanesch After all, these Wigner functions describe - if I understand well - the Fock states that correspond closely to classical EM waves.

No, the Wigner (or Husimi) joint distributions and their differential equations are a formalism fully equivalent to the Fock space formulation. The so-called "deformation quantization" (an alternative form of quantization) is based on this equivalence.

It is the (Glauber's) "coherent states" which correspond to the classical EM theory. Laser light is a template for coherent states. For them the Wigner functions are always positive, thus there is no non-classical prediction for these states.

So how can you 1) use the statistics derived from second quantization (admitted, for cases that correspond to classical waves) to 2) argue that you don't need a second quantization ??

The Marshall-Santos PDC paper you cited uses standard Quantum Optics (in Wigner formalism) and a detection model to show that there is no non-classical correlation predicted by Quantum Optics for the PDC sources. They're not adding or modifying PDC treatment, merely rederiving it in Wingner function formalism.

The key is in analyzing with more precision and finesse (than usual engineering style QO) operational mapping rules between the theoretical distributions (computed under the normal operator ordering convention which correspond to Wigner's functions) and the detection and counting procedures. (You may need to check also few of their other preprints on detection for more details and specific models and calculations.) Their point is that the conventional detection & counting procedures (with the background subtractions and tuning to [almost] no-vacuum detection) amount to the full subtraction needed to produce the negative probability regions (conventionally claimed as non-classicality) of the Wigner distributions, thus the standard QO predictions, for the PDC correlations.

The point of these papers is to show that, at least for the cases analyzed, Quantum Optics doesn't predict anything non-classical, even though PDC, sub-Poissonian distributions, anti-bunching,... are a soft non-classicality (they're only suggestive, e.g. at the superficial engineering or pedagogical levels of analysis, but not decisive as the violation of Bell's inequality which absolutely no classical theory, deterministics or stochastic, can violate).

The classical-Quantum Optics equivalence of the thermal (or chaotic) light was known since 1950s (this was clarified during the Hanbury Brown and Twiss effect controversy). Similar equivalence was established in 1963 for the coherent states, making all the laser light effects (plus linear optical elements and any number of detectors) fully equivalent to a classical description. Marshall and Santos (and their students) have extended this equivalence to the PDC sources.

Note also that 2nd quantization is in these approaches (Marshall-Santos SED, Barut self-field ED, Jaynes neoclassical ED) viewed as a mathematical linearization procedure of the uderlying non-linear system, and not something that adds any new physics. After all the same 2nd quantization techniques are used in solid state physics and other areas for entirely different underlying physics. The 1st quantization is seen as a replacement of point particles by matter fields, thus there is no point in "quantizing" the EM field at all (it is a field already), or the Dirac matter field (again).

As a background to this point, I mentioned (few messages back) some quite interesting results (http://cul.arxiv.org/abs/solv-int/9801018) by a mathematician Krzysztof Kowalski (http://arxiv.org/find/hep-th,grp_nlin/1/au:+kowalski/0/1/0/all/0/1), which show explicitly how a classical non-linear ODE/PDE systems can be linearized in a form that looks just like a bosonic Fock space formalism (with creation/anihilation operators, vacuum state, particle number states, coherent states, bosonic Hamiltonian and standard quantum state evolution). In that case it is perfectly transparent that there is no new physics brought in by the 2nd quantization, it is merely a linear approximation of a non-linear system (it yields iteratively an inifinte number of linear equations from a finite number of non-linear equations). While Kowalski's particular linearization scheme doesn't show that QED is a linearized form of the non-linear equations such as Barut's self-field, it provides an example of this type of relation between the Fock space formalism and the non-linear clasical equations.

You see, the way I understand the message (and maybe I'm wrong) is the following procedure:
-Take a classical EM wave.

No, they don't do that (here). They're using the standard PDC model and are treating it fully within the QO, just in the Wigner function formalism.

nightlight

Oct8-04, 04:55 AM

vanesch I don't see how you can explain these (raw, I think) coincidence rates

Those are not even close to raw counts. Their pairs/singles ratio is 0.286 and their QE is 0.214. Avalanche diodes are very noisy and to reduce background they have used short coincidence window, resulting in quite low (for any non-classicality claim) pair/singles ratio. Thus the combination of the background subtractions and the unpaired singles are much larger than what Marshal-Santos PDC classicality requires (which assumes only the vacuum fluctuation noise subtraction, with everything else granted as optimal). Note that M-S SED (which is largely equivalent in predictions to Wigner distributions with positive probabilities) is not some contrived model made to get around some loophole, but a perfectly natural classical model, a worked out and refined version of the Planck's 2nd Quantum Theory (of 1911, where he added an equivalent of 1/2 hv noise per mode).

Roberth

Oct8-04, 05:28 AM

Hello Nightlight,

I follow your exceptional discussion with Vanesch and a couple of other contributors. It is maybe the best dispute that I have read on this forum so far. In particular, it looks as if you and Vanesch are really getting 'somewhere'. I am looking forward to the final verdict whether or not the reported proof of spooky action at a distance is in fact valid.

Anyway, I consider the Aharanov-Bohm effect as a similar fundamental non-local manifestation of QM as the (here strongly questioned) Bell violation.

To say it a bit more challenging, it also looks like a 'quantum mystery' which you seem to despise.

My question is: Are you familiar with this effect and, if yes, do you believe in it (whatever that means) or do you similarly think that there is a sophisticated semi-classical explanation?

Roberth

nightlight

Oct8-04, 05:59 AM

Roberth Anyway, I consider the Aharanov-Bohm effect as a similar fundamental non-local manifestation of QM as the (here strongly questioned) Bell violation.

Unfortunately, I haven't studied it in any depth beyond a shallow coverage in the undergraduate QM class. I always classified it among the "soft" non-locality phenomena, those which are superficially suggestive of non-locality (after all, both Psi and A still evolve fully locally), but lack decisive criteria (unlike the Bell's inequalities).

vanesch

Oct8-04, 06:04 AM

Their pairs/singles ratio is 0.286 and their QE is 0.214. Avalanche diodes are very noisy and to reduce background they have used short coincidence window, resulting in quite low (for any non-classicality claim) pair/singles ratio.

Aaah, stop with your QE requirements :grumpy: I'm NOT talking about EPR kinds of experiments here, because I have to fight the battle upstream with you :smile: because normally, people accept second quantization, and you don't. So I'm looking at possible differences between what first quantization and second quantization can do. And in the mean time I'm learning a lot of quantum optics :approve: which is one of the reasons why I continue here with this debate. You have 10 lengths of advantage over me there (but hey, I run fast :devil:)

All single-photon situations are indeed fully compatible with classical EM, so I won't be able to find any difference in prediction there. Also, I have to live with low efficiency photon detectors, because otherwise you object about fair sampling, so I'm looking at a possibility of a feasible experiment with today's technology that proves (or refutes ?) second quantization. I'm probably a big naive guy, and this must have been done before, but as nobody is helping here, I have to do all the work myself :bugeye:

What the paper that I showed proves to me is that we can get correlated clicks in detectors way beyond simple Poisson coincidences. I now understand that you picture this as correlated fluctuations in intensity in the two classical beams.
But if the photon picture is correct, I think that after the first split (with the polarizing beam splitter) one photon of the pair goes one way, and the other one goes the other way, giving correlated clicks, superposed on about 3 times more uncorrelated clicks, and with a detection probability of about 20% or so, while you picture that as two intensity peaks in the two beams, giving rise to enhanced detection probabilities (and hence coincidences) at the two detectors (is that right ?).
Ok, up to now, the pictures are indistinguishable.
But I proposed the following extension of the experiment:

In the photon picture, each of the two branches just contains "single photon beams", right ? So if we put a universal beam splitter in one such branch (not polarizing), we should get uncorrelated Poisson streams in each one, so the coincidences between these two detectors (D2 and D3) should be those of two independent Poisson streams. However, D2 PLUS D3 should give a signal which is close to what the old detector gave before we split the branch again. So we will have a similar correlation between (D2+D3) and D1 as we had in the paper, but D2 and D3 shouldn't be particularly correlated.

In your "classical wave" picture, the intensity peak in our split branch splits in two half intensity peaks, which should give rise to a correlation of D2 and D3 which is comparable to half the correlation between D2 and D1 and D3 and D1, no ?

Is this a correct view ? Can this distinguish between the photon picture and the classical wave picture ? I think so, but as I'm not an expert in quantum optics, nor an expert in your views, I need an agreement here.

cheers,
Patrick.

nightlight

Oct8-04, 08:49 AM

In your "classical wave" picture, the intensity peak in our split branch splits in two half intensity peaks, which should give rise to a correlation of D2 and D3 which is comparable to half the correlation between D2 and D1 and D3 and D1, no ?

You're ignoring few additional effects here. One is that the detectors counts are Poissonian (which are significant for the visible range photons). Another is that you don't have a sharp photon number state but a superposition with at least 1/2 photon equivalent spread.

Finally, the "classical" picture with ZPF allows a limited form of sub-Poissonian statistics for the adjusted counts (or the extrapolated counts, e.g. if you tune your detectors to a higher trigger threshold to reduce the explicit background subtractions in which case you raise the unpaired singles counts and have to extrapolate). This is due to the sub-ZPF superpositions (which enter the ZPF averaging for the ensemble statistics) of the signal and the ZPF in one branch after the splitter. Unless you're working in a high-noise, high sensitivity detector mode (which would show you, if you're specifically looking for it, a drop in the noise coinciding with the detection in the other branch), all you would see is an appearance of the sub-Poissonian behavior on the subtracted/extrapolated counts. But this is exactly the level of anticorrelation that the classical ZPF model predicts for the adjusted counts.

The variation you're describing was done for exactly that purpose in 1986 by P. Grangier, G. Roger and A. Aspect ("Experimental evidence for a photon anticorrelation effect on a beam splitter: a new light on a single photon interefernce" Europhys. Lett. Vol 1 (4) pp 173-179, 1986). For the pair source they have used their original Bell test atomic cascade. Of course, the classical model they tested against, to declare the non-classicality, was the non-ZPF classical field which can't reproduce the observed level of anticorrelation on the adjusted data. { I recall seeing another preprint of that experiment (dealing with the setup properties prior to the final experiments) which had more detailed noise data indicating a slight dip in the noise in the 2nd branch, for which they had some aperture/alignment type of explanation. }

Marshall & Santos had several papers following that experiment where their final Stochastic Optics (the SED applied for Quantum Optics) had crystallized, including their idea of "subthreshold" superposition, which was the key for solving the anticorrelation puzzle. A longer very readable overview of their ideas at the time, especially regarding the anticorrelations, was published in Trevor Marshall, Emilio Santos "Stochastic Optics: A Reaffirmation of the Wave Nature of Light" Found. Phys., Vol 18, No 2. 1988, pp 185-223, where they show that a perfectly natural "subthreshold" model is in full quantitative agreeement with the anticorrelation data (they also relate their "subthreshold" idea to its precursors, such as the "empty-wave" by Selleri 1984 and the "latent order" by Greenberger 1987; I tried to convince Trevor to adopt a less accurate but catchier term "antiphoton" but he didn't like it). Some day, when this present QM non-locality spell is broken, these two will be seen as Galileo and Bruno of our own dark ages.

vanesch

Oct8-04, 09:54 AM

You're ignoring few additional effects here. One is that the detectors counts are Poissonian (which are significant for the visible range photons). Another is that you don't have a sharp photon number state but a superposition with at least 1/2 photon equivalent spread.

You repeated that already a few times, but I don't understand this. After all, I can just as well work in the Hamiltonian eigenstates. In quantum theory, if you lower the intensity of the beam enough, you have 0 or 1 photon, and there is no such thing to my knowledge as half a photon spread, because you should then find the same with gammas, which isn't the case (and is closer to my experience, I admit). After all, gamma photons are nothing else but Lorentz-transformed visible photons, so what is true for visible photons is also true for gamma photons, it is sufficient to have the detector speeding at you (ok, there are some practical problems to do that in the lab :-)
Also, if the beam intensity is low enough, (but unfortunately the background scales with the beam intensity), it is a fair assumption that there is only one photon at a time in the field. So I'm pretty sure about what I said about the quantum predictions:

Initial pair -> probability e1 to have a click in D1
probability e2/2 to have a click in D2 and no click in D3
probability e3/2 to have a click in D3 and no click in D3

This is superposed on independent probability b1 to have a click in D1, a probability b2 to have a click in D2 and probability b3 to have a click in D3, independent, but all proportional to some beam power I.

It is possible to have a neglegible background by putting the thresholds high enough and isolating well enough from any lightsource other than the original power source. This can cost some efficiency, but not much.

If I is low enough, we consider that, due to the Poisson nature of the events, no independent events occur together (that is, we neglect probabilities that go in I^2). After all, this is just a matter of spreading the statistics over longer times.

So: rate of coincidences as predicted by quantum theory:
a) D1 D2 D3: none (order I^3)
b) D1 D2 no D3: I x e1 x e2/2 (+ order I^2)
c) D1 no D2 D3: I x e1 x e3/2 (+ order I^2)
d) D1 no D2 no D3: I x (b1 + e1 x (1- e2/2 - e3/2))
e) no D1 D2 D3: none (order I^2)
f) no D1 D2 no D3: I x (b2 + (1-e1)x e2/2)
g) no D1 no D2 D3: I x (b3 + (1-e1)xe3/2)

A longer very readable overview of their ideas at the time, especially regarding the anticorrelations, was published in Trevor Marshall, Emilio Santos "Stochastic Optics: A Reaffirmation of the Wave Nature of Light" Found. Phys., Vol 18, No 2. 1988, pp 185-223,

If you have it, maybe you can make it available here ; I don't have access to Foundations of Physics.

cheers,
Patrick.

nightlight

Oct9-04, 03:39 AM

vanesch After all, I can just as well work in the Hamiltonian eigenstates.

The output of PDC source is not same as picking a state in Fock space freely. That is why they restricted their analysis to PDC sources where they can show that the resulting states will not have the Wigner distribution negative beyond what the detection & counting callibrated to null result for the 'vacuum fluctuations alone' would produce. That source doesn't produce eigenstates of free Hamiltonian (consider also the time resolution of such modes with sharp energy). It also doesn't produce gamma photons.

because you should then find the same with gammas, which isn't the case (and is closer to my experience, I admit).

You're trying to make the argument universal which it is not. It is merely addressing an overlooked effect for the particular non-classicality claim setup (which also includes particular type of source and nearly perfectly efficient polarizer and beam splitters). The interaction constants, cross sections, tunneling rates,... don't scale with the photon energy. You can have a virtually perfect detector for gamma photons. But you won't have a perfect analyzer or a beam splitter. Thus, for gamma you can get nearly perfect particle-like behavior (and very weak wave-like behavior) which is no more puzzling or non-classical than a mirror with holes in the coating scanned by a thin light beam mentioned earlier.

To preempt the loose argument shifts of this kind, I will recall the essence of contention here. We're looking at a setup where a wave packet splits into two equal, coherent parts A and B (packet fragments in orbital space). If brought together to a common area, A and B will produce perfect interference. If any phase shifts are inserted in the paths of A or B, the interference pattern will shift depening on relative phase shift on two paths, implying that in each try the two packet fragments propagate on both paths (this is also the propagation that the dynamical/Maxwell equations describe for the amplitude).

The point of contention is what happens if you insert two detectors DA and DB in paths of A and B. I am saying that the two fragments propagate to respective detectors, interact with the detector and each detectors triggers or doesn't trigger, regardless of what happened on the other detector. The dynamical evolution is never suspended and the triggering is solely a result of the interaction between the local fragment and its detector.

You're saying that, at some undefined stage of triggering process of the detector DA, the dynamical evolution of the fragment B will stop, the fragment B will somehow shrink/vanish even if it is light years away from A and DA. Then, again at some undefined later time, the dynamical evolution of B/DB will be resumed.

The alleged empirical consequence of this conjecture will be the "exclusion" of the trigger B whenever trigger A occurs. The "exclusion" is such that it cannot be explained by the local mechanism of independent detection under the uninterrupted dynamical evolution of each fragment and its detector.

Your subsequent attempt to illustrate this "exclusion" unfortunately mixes up the entirely trivial forms of exclusions, which are perfectly consistent with the model of uninterrupted local dynamics. To clarify the main mixup (and assuming no mixups regarding the entirely classical correlation aspect due to any amplitude modulation), lets look at the Poissonian square law detectors (which apply to the energies of photons relevant here, i.e. those for which there are nearly perfect coherent splitters).

Suppose we have a PDC source and we use "photon 1" of the pair as a reference to define our "try" so that whenever detector D1 triggers we have a time window T in which we enable detection of "photon 2." Keep also in mind that the laser pump which feeds the non-linear crystal is Poissonian source (produces coherent states which superpose all photon number states using for coefficient magnutudes the square-roots of Poissonian probabilities), thus neither the input nor the output states are sharp photon number states (pedagogical toy derivations might use as the input the sharp number state, thus they'll show a sharp number state in output).

To avoid the issues of detector dead time or multiphoton capabilities, imagine we use a perfect coherent splitter, split the beam, then we add in each path another perfect splitter, and so on, for L levels of splitting, and place ND=2^L detectors in the final layer of subpaths. The probability of k detectors (Poissonian, square law detectors relevant here) triggering in a given try is P(n,k)=n^k exp(-n)/k! where n is the average number of triggers. A single multiphoton capable detector with no dead time would show this same distribution of k for a given average rate n.

Let's say we tune down the input power (or sensitivity of the detectors) to get an average number of "photon 2" detectors triggering as n=1. Thus the probability of exactly 1 among the ND detectors triggering is P(n=1,k=1)=1/e=37%. Probability of no ND trigger is P(n=1,k=0)=1/e=37%. Thus, the probability of more than 1 detector triggering is 26%, which doesn't look very "exclusive".

Your suggestion was to lower (e.g. via adjustments of detectors thresholds or by lowering the input intensity) the average n to a value much smaller than 1. So, let's look at n=0.1, i.e. on average we get .1 ND triggers for each trigger on the reference "photon 1" detector. The probability of a single ND trigger is P(n=0.1,k=1)=9% and of no trigger P(n=0.1,k=0)=90%.

Thus the probability of multiple ND triggers is now only 1%, i.e. we have 9 times more single triggers than the multiple triggers, while before, for n=1, we had only 37/26=1.4 times more single triggers than multiple triggers. It appears we had greatly improved the "exclusivity". By lowering n further we can make this ratio as large as we wish, thus the counts will appear as "exclusive" as we wish. But does this kind of low intensity exclusivity, which is what your argument keeps returning to, indicate in any way a collapse of the wave packet fragments on all ND-1 detectors as soon as the 1 detector triggers?

Of course not. Lets look what happens under assumption that each of ND detectors triggers via its own Poissonian entirely independently of others. Since the "photon 2" beam splits its intensity into ND equal parts, the Poissonian for each of ND detectors will be P(m,k), where m=n/ND is the average trigger rate of each of ND detectors. Let's denote p0=P(m,k=0) the probability that one (specific) detector will not trigger. Thus p0=exp(-m). The probability that this particular detector will trigger at all (indicating 1 or more "photons") is then p1=1-p0=1-exp(-m). In your high "exclusivity" (i.e. low intensity) limit n->0, we will have m<<1 and p0~1-m, p1~m.

The probability that none of ND's will trigger, call it D(0), is thus D(0)=p0^ND=exp(-m*ND)=exp(-n), which is, as expected, the same as no-trigger probability of the single perfect multiphoton (square law Poissonian) detector capturing all of the "photon 2". Since we can select k detectors in C[ND,k] ways (C[] is a binomial coefficient), the probability of exactly k detectors triggering is D(k)=p1^k*p0^(ND-k)*C[ND,k], which is a binomial distribution with average number of triggers p1*ND. In the low intensity limit (n->0) and for large ND (corresponding to a perfect multiphoton resolution), D(k) becomes (using Stirling approximation and using p1*ND~m*ND=n) precisely the Poisson distribution P(n,k). Therefore, this low intensity exclusivity which you keep bringing up is trivial since it is precisely what the independent triggers of each detector predict no matter how you divide and combine the detectors (it is, after all, the basic property of the Poissonian distribution).

The real question is how to deal with the apparent sub-Poissonian cases as in PDC. That is where these kinds of trivial arguments don't help. One has to, as Marshall & Santos ( http://arxiv.org/find/quant-ph/1/OR+au:+Santos_E+au:+Marshall_T/0/1/0/all/0/1) do, look at the specific output states and find the precise degree of the non-classicality (which they express for convenience in the Wigner function formalism). Their ZPF ("vacuum fluctuations" in conventional treatment) based detection and coincidence counting model (http://cul.arxiv.org/abs/quant-ph/0207073) allows for a limited degree of non-classicality in the adjusted counts. Their PDC series of papers shows that for PDC sources all non-classicality is of this apparent type (the same holds for laser/coherent/Poissonian sources and chaotic/super-Poissonian sources).

Without the universal locality principle, you can only refute specific overlooked effects of a particular claimed non-classicality setup. This does not mean that the nature somehow conspires to thwart non-locality through some obscure loopholes. It simply means that a particular experimental design has overlooked some effect and that it is more likely that the experiment designer will overlook more obscure effects.

In a fully objective scientific system one wouldn't have to bother refuting anything about any of these flawed experiments since their data hasn't objectively shown anything non-local. But in the present nature-is-non-local zeitgeist, a mere wishful excuse by an experimenter that the failure is a minor technical glitch which will be remedied by future technology, becomes, by the time it trickles down to the popular and pedagogical levels, an experimentally established non-locality.

nightlight

Oct9-04, 03:41 AM

If you have it, maybe you can make it available here ; I don't have access to Foundations of Physics.

I have only a paper preprint but no scanner handy which could make a usable electronic copy of it. The Los Alamos archive has their more recent preprints (http://arxiv.org/find/quant-ph/1/OR+au:+Santos_E+au:+Marshall_T/0/1/0/all/0/1). Their preprint "The myth of the Photon" (http://cul.arxiv.org/abs/quant-ph/9711046) also reviews the basic ideas and contains a citation to a Phys.Rev. version of that Found.Phys. paper. For intro on Wigner functions (and the related pseudo-distributions, the Husimi and the Glauber-Sudarshan functions) you can check these lectures (http://web.utk.edu/~pasi/davidovich.pdf) and a longer paper (http://www.fi.muni.cz/usr/buzek/mypapers/96annals0037.pdf) with more on their operational aspects.

vanesch

Oct9-04, 09:07 AM

You're trying to make the argument universal which it is not. It is merely addressing an overlooked effect for the particular non-classicality claim setup (which also includes particular type of source and nearly perfectly efficient polarizer and beam splitters).

I'm looking more into Santos and Co's articles. It's a slow read, but I'm working up my way... so patience :-) BTW, thanks for the lecture notes, they look great !

You're saying that, at some undefined stage of triggering process of the detector DA, the dynamical evolution of the fragment B will stop, the fragment B will somehow shrink/vanish even if it is light years away from A and DA. Then, again at some undefined later time, the dynamical evolution of B/DB will be resumed.

Not at all. My view (which I have expressed here already a few times in other threads) is quite different and I don't really think you need a "collapse at a distance" at all - I'm in fact quite a fan of the decoherence program. You just get interference of measurement results when they are compared by the single observer who gets a hold on both measurements in order to calculate the correlation. This means that macroscopic systems can be in a superposition, but that's no problem, just continuing the unitary evolution (this is th essence of the decoherence program). But the point was not MY view :-)

Your subsequent attempt to illustrate this "exclusion" unfortunately mixes up the entirely trivial forms of exclusions, which are perfectly consistent with the model of uninterrupted local dynamics. To clarify the main mixup (and assuming no mixups regarding the entirely classical correlation aspect due to any amplitude modulation), lets look at the Poissonian square law detectors (which apply to the energies of photons relevant here, i.e. those for which there are nearly perfect coherent splitters).

Suppose we have a PDC source and we use "photon 1" of the pair as a reference to define our "try" so that whenever detector D1 triggers we have a time window T in which we enable detection of "photon 2." Keep also in mind that the laser pump which feeds the non-linear crystal is Poissonian source (produces coherent states which superpose all photon number states using for coefficient magnutudes the square-roots of Poissonian probabilities), thus neither the input nor the output states are sharp photon number states (pedagogical toy derivations might use as the input the sharp number state, thus they'll show a sharp number state in output).

To avoid the issues of detector dead time or multiphoton capabilities, imagine we use a perfect coherent splitter, split the beam, then we add in each path another perfect splitter, and so on, for L levels of splitting, and place ND=2^L detectors in the final layer of subpaths. The probability of k detectors (Poissonian, square law detectors relevant here) triggering in a given try is P(n,k)=n^k exp(-n)/k! where n is the average number of triggers. A single multiphoton capable detector with no dead time would show this same distribution of k for a given average rate n.

Let's say we tune down the input power (or sensitivity of the detectors) to get an average number of "photon 2" detectors triggering as n=1. Thus the probability of exactly 1 among the ND detectors triggering is P(n=1,k=1)=1/e=37%. Probability of no ND trigger is P(n=1,k=0)=1/e=37%. Thus, the probability of more than 1 detector triggering is 26%, which doesn't look very "exclusive".

Your suggestion was to lower (e.g. via adjustments of detectors thresholds or by lowering the input intensity) the average n to a value much smaller than 1. So, let's look at n=0.1, i.e. on average we get .1 ND triggers for each trigger on the reference "photon 1" detector. The probability of a single ND trigger is P(n=0.1,k=1)=9% and of no trigger P(n=0.1,k=0)=90%.

Thus the probability of multiple ND triggers is now only 1%, i.e. we have 9 times more single triggers than the multiple triggers, while before, for n=1, we had only 37/26=1.4 times more single triggers than multiple triggers. It appears we had greatly improved the "exclusivity". By lowering n further we can make this ratio as large as we wish, thus the counts will appear as "exclusive" as we wish. But does this kind of low intensity exclusivity, which is what your argument keeps returning to, indicate in any way a collapse of the wave packet fragments on all ND-1 detectors as soon as the 1 detector triggers?

Of course not. Lets look what happens under assumption that each of ND detectors triggers via its own Poissonian entirely independently of others. Since the "photon 2" beam splits its intensity into ND equal parts, the Poissonian for each of ND detectors will be P(m,k), where m=n/ND is the average trigger rate of each of ND detectors. Let's denote p0=P(m,k=0) the probability that one (specific) detector will not trigger. Thus p0=exp(-m). The probability that this particular detector will trigger at all (indicating 1 or more "photons") is then p1=1-p0=1-exp(-m). In your high "exclusivity" (i.e. low intensity) limit n->0, we will have m<<1 and p0~1-m, p1~m.

The probability that none of ND's will trigger, call it D(0), is thus D(0)=p0^ND=exp(-m*ND)=exp(-n), which is, as expected, the same as no-trigger probability of the single perfect multiphoton (square law Poissonian) detector capturing all of the "photon 2". Since we can select k detectors in C[ND,k] ways (C[] is a binomial coefficient), the probability of exactly k detectors triggering is D(k)=p1^k*p0^(ND-k)*C[ND,k], which is a binomial distribution with average number of triggers p1*ND. In the low intensity limit (n->0) and for large ND (corresponding to a perfect multiphoton resolution), D(k) becomes (using Stirling approximation and using p1*ND~m*ND=n) precisely the Poisson distribution P(n,k). Therefore, this low intensity exclusivity which you keep bringing up is trivial since it is precisely what the independent triggers of each detector predict no matter how you divide and combine the detectors (it is, after all, the basic property of the Poissonian distribution).

You're perfectly right, and I acknowledged that already a while ago when I said that there's indeed no way to distinguish "single photon" events that way. What I said was that such a single-photon event (which is one of a pair of photons), GIVEN A TRIGGER WITH ITS CORRELATED TWIN, will give you an indication of such an exclusivity in the limit of low intensities. It doesn't indicate any non-locality or whatever, but indicates the particle-like nature of photons, which is a first step, in that the marble can only be in one place at a time, and with perfect detectors WILL be in one place at a time. It would correspond to the 2 511KeV photons in positron annihilation, for example. I admit that my views are maybe a bit naive for opticians: my background is in particle physics, and currently I work with thermal neutrons, which come nicely in low-intensity Poissonian streams after interference all the way down the detection spot. So clicks are marbles :-)) There are of course differences with optics: First of all, out of a reactor rarely come correlated neutron pairs :-), but on the other hand, I have all the interference stuff (you can have amazing correlation lengths with neutrons!), and the one-click-one-particle detection (with 98% efficiency or more if you want), background ~ 1 click per hour.

This does not mean that the nature somehow conspires to thwart non-locality through some obscure loopholes. It simply means that a particular experimental design has overlooked some effect and that it is more likely that the experiment designer will overlook more obscure effects.

In a fully objective scientific system one wouldn't have to bother refuting anything about any of these flawed experiments since their data hasn't objectively shown anything non-local. But in the present nature-is-non-local zeitgeist, a mere wishful excuse by an experimenter that the failure is a minor technical glitch which will be remedied by future technology, becomes, by the time it trickles down to the popular and pedagogical levels, an experimentally established non-locality.

I agree with you here concerning the scientific attitude to adopt, and apart from a stimulus for learning more quantum optics, it is the main motivation to continue this discussion :-) To me, these experiments don't exclude anything, but they confirm beautifully the quantum predictions. So it is very well possible that completely other theories will have similar predictions, it is "sufficient" to work them out. However, if I were to advise a student (but I won't cuz it is not my job) on whether to take that path or not, I'd strongly advise against it, because there's so much work to do first: you have to show agreement on SUCH A HUGE AMOUNT OF DATA that the work is enormous, and the probability of failure rather great. On the other hand, we have a beautifully working theory which explains most if not all of it. So it is probably more fruitful to go further in the successfull path than to err "where no man has gone before". On the other hand, for a retired professor, why not play with these things :-) I myself wouldn't dare, for the moment: I hope to make more "standard" contributions and I'm perfectly happy with quantum theory as it stands now - even though I think it isn't the last word, and we will have another theory, 500 years from now. But I can make sense of it, it works great, and that's what matters. Which doesn't mean that I don't like challenges like you're proposing :-)

cheers,
Patrick.

vanesch

Oct9-04, 01:55 PM

I might have misunderstood an argument you gave. After reading your text twice, I think we're not agreeing on something.

Your subsequent attempt to illustrate this "exclusion" unfortunately mixes up the entirely trivial forms of exclusions, which are perfectly consistent with the model of uninterrupted local dynamics. To clarify the main mixup (and assuming no mixups regarding the entirely classical correlation aspect due to any amplitude modulation), lets look at the Poissonian square law detectors (which apply to the energies of photons relevant here, i.e. those for which there are nearly perfect coherent splitters).

Nope, I am assuming 100% efficient detectors. I don't really know what you mean with "Poissonian square law detectors" (I guess you mean some kind of Bolometers which give a Poissonian click rate as a function of incident energy). I'm within the framework of standard quantum theory and I assume "quantum theory" detectors. You can claim they don't exist, but that doesn't matter, I'm talking about a QUANTUM THEORY prediction. This prediction can be adapted with finite quantum efficiency, and assumes fair sampling. Again, I'm not talking about what really happens or not, I'm talking about standard quantum theory predictions, whether correct or not.

Suppose we have a PDC source and we use "photon 1" of the pair as a reference to define our "try" so that whenever detector D1 triggers we have a time window T in which we enable detection of "photon 2."

Well, the quantum prediction with 100% efficient detectors is 100% correlation, because there are EXACTLY as many photons, at the same moment (at least on the time scale of the window) in both beams. The photons can really be seen as marbles, in the same way as the two 511KeV photons from a positron desintegration can be seen, pairwise, in a tracking detector, or the tritium and proton desintegration components can be seen when a He3 nucleus interacts with a neutron.

Keep also in mind that the laser pump which feeds the non-linear crystal is Poissonian source (produces coherent states which superpose all photon number states using for coefficient magnutudes the square-roots of Poissonian probabilities), thus neither the input nor the output states are sharp photon number states (pedagogical toy derivations might use as the input the sharp number state, thus they'll show a sharp number state in output).

Yes, but this is the only Poissonian source, so if we turn down the production rate of couples (which will be a Poissonian source with much lower rate than the incident beam, which has to be rather intense). So the 2-photon states come indeed also in a Poissonian superposition (namely the state |0,0>, the state |1,1>, the state |2,2> ...) where |n,m> indicates n blue and m red photons, but with coefficients which are from a much lower rate Poissonian distribution, which means that essentially only the |0,0> and |1,1> contribute. So one can always, take the low intensity limit and work with a single state.

To avoid the issues of detector dead time or multiphoton capabilities, imagine we use a perfect coherent splitter, split the beam, then we add in each path another perfect splitter, and so on, for L levels of splitting, and place ND=2^L detectors in the final layer of subpaths. The probability of k detectors (Poissonian, square law detectors relevant here) triggering in a given try is P(n,k)=n^k exp(-n)/k! where n is the average number of triggers.

This is correct, for a single-photon coherent beam, if we take A RANDOMLY SELECTED TIME INTERVAL. It is just a dead time calculation, in fact.

Let's say we tune down the input power (or sensitivity of the detectors) to get an average number of "photon 2" detectors triggering as n=1. Thus the probability of exactly 1 among the ND detectors triggering is P(n=1,k=1)=1/e=37%. Probability of no ND trigger is P(n=1,k=0)=1/e=37%.

No, this is not correct, because there is a 100% correlation between the photon-2 trigger and the sum of all the photon-1 clicks. THE TIME INTERVAL IS NOT RANDOM !! You will have AT LEAST 1 click in one of the detectors (and maybe more, if we hit a |2,2> state).
So you have to scale up the above Poissonian probabilities with a factor e.

Your suggestion was to lower (e.g. via adjustments of detectors thresholds or by lowering the input intensity) the average n to a value much smaller than 1. So, let's look at n=0.1, i.e. on average we get .1 ND triggers for each trigger on the reference "photon 1" detector. The probability of a single ND trigger is P(n=0.1,k=1)=9% and of no trigger P(n=0.1,k=0)=90%.

Again, because of the trigger on detector 2, we do not have a random time interval, and we have to scale up the probabilities by a factor 10. So the probability of seeing a single ND trigger is 90%, and the probability of having more than 1 is 10%. The case of no triggers is excluded by the perfect correlation.

cheers,
Patrick.

nightlight

Oct9-04, 05:12 PM

vanesch You just get interference of measurement results when they are compared by the single observer who gets a hold on both measurements in order to calculate the correlation.

And how did the world run and pick what to do before there was anyone to measure so they can interfere their results? I don't think universe is being ran by some kind of magnified Stalin, lording over the creation and every now and then erasing fallen comrades from the photos to make a different more consistent history.

This means that macroscopic systems can be in a superposition, but that's no problem, just continuing the unitary evolution (this is the essence of the decoherence program).

Unless you suspend the fully local dynamical evolution (ignoring the non-relativistic approximate non-locality of Coulomb potential and such), you can't reach, at least not coherently, a conclusion of non-locality (a no-go for purely local dynamics).

The formal decoherence schemes have been around since at least early 1960s. Without adding ad hoc, vague (no less so than the collapse) super-selection rules to pick a preferred basis, they still have no way of making a unitary evolution pick a particular result out of a superposition. And without the pick for each instance, it makes no sense to talk of statistics of many such picks. You can't say you will get 30% heads in 1000 flips, while insisting you don't have to get any specific result in the individual flips (which is what these "decoherence" schemes, old and new, claim to be able somehow to achieve).

It is just another try to come up with a new and an improved mind-numbing verbiage, more mesmerising and slippery than the old one which got worn out, to uphold the illusion of being in possession of a coherent theory, for just a bit longer until there is something truly coherent to take its place.

I am ashamed to admit, but I was once taken in, for couple years or so, by one of these "decoherence" verbal shell games, Prigogines' version, and was blabbing senslessly "superoperators" and "subdynamics" and "dissipative systems" and "Friedrichs model" ... to any poor soul I could corner, gave a seminar, then a lecture to undergraduates as their QM TA (I hope it didn't take),...

What I said was that such a single-photon event (which is one of a pair of photons), GIVEN A TRIGGER WITH ITS CORRELATED TWIN, will give you an indication of such an exclusivity in the limit of low intensities. It doesn't indicate any non-locality or whatever, but indicates the particle-like nature of photons, which is a first step, in that the marble can only be in one place at a time,

You seem to be talking about time modulation of Poisson P(n,k), where n=n(t). That does correlate 1 a 2 trigger rates, but that kind of exclusivity is equally representative of fields and particles. In the context of QM/QED, where you already have a complete dynamics for the fields, such informal duality violates the Occam's razor { Classical particles can be simulated in all regards by classical fields (and vice versa). It is the dual QM kind that lacks coherence.}

you have to show agreement on SUCH A HUGE AMOUNT OF DATA that the work is enormous, and the probability of failure rather great.

The explorers don't have to build roads, bridges and cities, they just discover new lands and if these are worthy, the rest will happen without any of their doing.

On the other hand, we have a beautifully working theory which explains most if not all of it.

If you read the Jaynes passage (http://bayes.wustl.edu/etj/articles/scattering.by.free.pdf) quoted few messages back (or his other (http://bayes.wustl.edu/etj/articles/backward.look.pdf) papers (http://bayes.wustl.edu/etj/articles/cmystery.pdf) on the theme, or Barut's views, or Einstein's and Schroedinger's, even Dirac's and some of contemporary greats as well), "beautiful" isn't the attribute that goes anywhere in the vicinity of QED, in any role and under any excuse. Its chief power is in being able to wrap tightly around any experimental numbers which come along, thanks to a rubbery scheme which can as happily "explain" a phenomenon today as it will its exact opposite tomorrow (see Jaynes for the full argument). It is not a kind of power directed forward to the new unseen phenomena, the way Newton's or Maxwell's theories were. Rather, it is more like a scheme for post hoc rationalizations of whatever came along from the experimenters (as Jaynes put it -- the Ptolomean epicycles of our age).

On the other hand, for a retired professor, why not play with these things :-)

I've met few like that, too. There are other ways, though. Many physicists in USA ended up, after graduate school or maybe one postdoc, on the Wall Street or in the computer industry, created their companies (especially in software). They don't live by the publish or perish dictum and don't have to compromise any ideas or research paths to academic fashions and politicking. While they have less time, they have more creative freedom. If I were to bet, I'd say that the future physics will come precisely from these folks (e.g. Wolfram (http://www.wolframscience.com/)).

even though I think it isn't the last word, and we will have another theory, 500 years from now.

I'd say it's around the corner. Who would be going into physics if he believed otherwise. (Isn't there a little Einstein hiding in each of us?)

vanesch

Oct9-04, 10:05 PM

vanesch

Oct9-04, 10:13 PM

You can't say you will get 30% heads in 1000 flips, while insisting you don't have to get any specific result in the individual flips (which is what these "decoherence" schemes, old and new, claim to be able somehow to achieve).

This is not true. If you take a probability of series of 1000 flips together as one observation in a decoherence-like way, then this probability is exactly equal to the probability you would get classically when considering each flip at a time and making up series of 1000, meaning the series with about 30% heads in it will have a relatively high probability as compared to series in which, say, you'll find 45% heads. It depends whether I personally observe each flip or whether I just look at the record of the result of 1000 flips. But the results are indistinguishable.

cheers,
Patrick.

vanesch

Oct9-04, 10:19 PM

I am ashamed to admit, but I was once taken in, for couple years or so, by one of these "decoherence" verbal shell games, Prigogines' version, and was blabbing senslessly "superoperators" and "subdynamics" and "dissipative systems" and "Friedrichs model" ... to any poor soul I could corner, gave a seminar, then a lecture to undergraduates as their QM TA (I hope it didn't take),...
...
I'd say it's around the corner. Who would be going into physics if he believed otherwise. (Isn't there a little Einstein hiding in each of us?)

Like you're now babbling senselessly about Santos and Barut's views ? :tongue2: :tongue2: :tongue2:
Ok, that one was easy, I admit. No, these discussions are really fun, so I should refrain from provoking namecalling games :rolleyes:
As I said, it makes me learn a lot of quantum optics, and you seem to know quite well what you're talking about.

cheers,
Patrick.

vanesch

Oct9-04, 10:32 PM

Its chief power is in being able to wrap tightly around any experimental numbers which come along, thanks to a rubbery scheme which can as happily "explain" a phenomenon today as it will its exact opposite tomorrow (see Jaynes for the full argument).

Yes, I read that, but I can't agree with it. When you read Weinberg, QFT is derived from 3 principles: special relativity, the superposition principle and the cluster decomposition principle. This fixes completely the QFT framework. The only thing you plug in by hand is the representation of the gauge group and that group itself (U(1)xSU(2)xSU(3)), a Higgs potential, and out pops the standard model, completely with all its fields and particles, from classical EM over beta decay, to nuclear structure (true, the QCD calculations in the low energy range are still messy ; but lattice QCD starts giving results).
I have to say that I find this impressive, that from a handful of parameters, you can build up all of known physics (except gravity of course). That doesn't exclude the possibility that other ways exist, but you are quickly in awe for the monumental work such a task will hold.

cheers,
patrick.

vanesch

Oct9-04, 11:04 PM

Again, because of the trigger on detector 2, we do not have a random time interval, and we have to scale up the probabilities by a factor 10. So the probability of seeing a single ND trigger is 90%, and the probability of having more than 1 is 10%. The case of no triggers is excluded by the perfect correlation.

I'd like to point out that a similar reasoning (different from the "Poissonian square law" radiation detectors) holds even for rather low photon detection efficiencies. If the efficiencies are, say, 20% (we take them all equal), then in our above scheme, we will have a probability of exactly one detector triggering equal to 0.2 x 0.9 = 18%, the probability of having exactly two detectors triggering equal to 0.2 x 0.2 x (0.09...) = a bit less than 4% etc...
So indeed, there is some "Poisson-like" distribution due to the finite efficiencies, but it is a FIXED suppression of coincidences by factors of 0.2, 0.04...
At very low intensities, the statistical Poisson coincidences should be much lower than these fixed suppressions (which are the quantum theory way of saying "fair sampling"), so we'd still be able to discriminate the "anticoincidences" due to the fact that each time there's only one marble in the pipe, and the anticoincidences due to lack of efficiency if each detector is generating its Poisson series on its own.

A way to picture this is by using, instead of beam splitters, a setup which causes diffraction of the second photon, and a position-sensitive photomultiplier (which is just an array of independent photomultipliers) looking at the diffraction picture.
You will build up slowly the diffraction picture with the synchronized clicks from detector 1 (which looks at the first photon of the pair) ; of course, each time detector one clicks, you will only have a chance of 0.2 to find a click on the position-sensitive PM. If the beam intensity is low enough, you will NOT find of the order of 0.04 times a second click on that PM. This is something that can only be achieved with a particle and is a prediction of QM.

cheers,
Patrick.

nightlight

Oct10-04, 02:02 AM

vanesch You should look a bit more at recent decohence work by Zeh and Joos for instance. Their work is quite impressive. I think you're mixing up the relative state view (which dates mostly from the sixties) with their work which dates from the nineties.

Zeh has been a QM guru pontificating on QM measurement when my QM professor was a student and still appears to be in a superposition of vews. I looked up some of his & Joos' recent preprints on the theme. Irreversible macroscopic aparatus, 'coherence destroyed very rapidly',... basically the same old stuff. Still the same problem as with the origina Daneri, Loinger and Prosperi macroscopic decoherence scheme of 1962.

It is a simple question. You have |Psi> = a1 |A1> + a2 |A2> = b1 |B1> + b2 |B2>. These are two equivalent orhtogonal exapansions of state Psi, for two observables [A] and [B], of some system (where the system may be a single particle, an aparatus with a particle, rest of the building with the aparatus and the particle,...). On what basis does one declare that we have value A1 of [A] for a given individual instance (you need this to be able to even to talk about statistics of the sequence of such values)?

At some strategically placed point wihin their mind-numbing verbiage these "decoherence" folks will start pretending that it was already established that a1|A1>+a2|A2> is the "true" expansion and A1 is its "true" result, in the sense that allows them talk about statistical poperties of a sequence of outcomes at all i.e. in exactly the same sense that in order to say: word "baloney" has 7 letters, you have (tacitly at least) assumed that the word has the first letter, the second letter,... Yet, these slippery folks will fight tooth an nail such conclusion, or even that they assume there is an individual word at all, yet this word-non-word still somehow manages to have exactly seven letters-non-letters. (The only innovation worthy a note in the "new and improved" version is that they start by telling you right upfront they're not going to do, no sir, not ever, absolutely never, that kind of slippery maneuver.)

No thanks. Can't buy any of it. Considering that the only rationale precluding one from plainly saying that an individual system has the definite properties all along is the Bell's "QM prediction" (which in turn cannot be deduced without assuming the non-dynamical collapse/projection postulate, the collapse postulate which is needed to solve the "measurement" problem, the problem of absence of definite properties in a superposition, thus the problem which still exists solely because of the Bell's QM prediction").

If you drop the non-dynamical collapse postulate, you don't have Bell's "prediction" (you would still have the genuine "predictions" of the kind that actually predict the data obtained, warts and all). There is no other result at that point preventing you from interpeting the wave function as a real matter field, evolving purely, without any interruptions, according to the dynamical equations (which happen to be nonlinear in the general coupled case) and representing thus the local "hidden" variables of the system. The Born rule would be reshuffled from its pedestal of a postulates to a footnote in scattering theory, the way and place it got the into QM. It is an approximate rule of thumb, its precise operational meaning depending ultimately on the aparatus design and measuring and counting rules (as it actually happens in any application, e.g. with the operational interpretations of Glauber P vs Wigner vs Husimi phase space functions), just as it would have beeen if someone had introduced it into the classical EM theory of light scattering in 19th century. The 2nd quantization is then only an approximation scheme for these coupled matter-EM fields, a linearization algorithm (similar to the Kowalski's and virtually identical to the QFT algorithms used in solid state and other branches of physics), adding no more new physics to the coupled nonlinear fields than, say, the Runge-Kutta numeric algorithm adds to the fluid dynamics Navier-Stokes equations.

Interestingly, in one of his superposed eigenviews, master guru Zeh himself insists that the wave function is a regular matter field and definitely not a probability "amplitude" -- see his paper "There is no "first" quantization" (http://cul.arxiv.org/abs/quant-ph/0210098), where he characterizes the "1st quantization" as merely a transition from a particle model to a field model (the way I did several times in this thread; which is of course how Schroedinger, Barut, Jaynes, Marshall & Santos, and others have viewed it). Unfortunately, somewhere down the article, his |Everett> state superposes in, nudging very gently at first, but eventually overtaking his |Schroedinger> state. I hope he makes up his mind in the next fourty years.

vanesch

Oct10-04, 02:20 AM

Unless you suspend the fully local dynamical evolution (ignoring the non-relativistic approximate non-locality of Coulomb potential and such), you can't reach, at least not coherently, a conclusion of non-locality (a no-go for purely local dynamics).

But that is exactly how locality is preserved in my way of viewing things !! I pretend that there is NO collapse at a distance, but that the record of remote measurements remains in a superposition until I look at the result and compare it with the other record (also in a superposition). It is only the power of my mind who forces a LOCAL collapse (beware: it is sufficient that I look at you and you collapse :devil:)

The formal decoherence schemes have been around since at least early 1960s. Without adding ad hoc, vague (no less so than the collapse) super-selection rules to pick a preferred basis, they still have no way of making a unitary evolution pick a particular result out of a superposition.

I know, but that is absolutely not the issue (and often people who do not know exactly what decoherence means make this statement). Zeh himself is very keen on pointing out that decoherence by itself doesn't solve the measurement problem ! It only explains why - after a measurement - everything looks as if it were classical, by showing which is the PREFERRED BASIS to work in. Pure relative-state fans (Many Worlds fans, of which I was one until a few months ago) think that somehow they will, one day, get around this issue. I think it won't happen if you do not add in something else, and the something else I add in is that it is my conciousness that applies the Born rule. In fact this comes very close to the "many minds" interpretation, except that I prefer the single mind interpretation :biggrin: exactly in order to be able to preserve locality. After all, I'm not aware of any other awareness except the one I'm aware of, namely mine :redface:.

And without the pick for each instance, it makes no sense to talk of statistics of many such picks. You can't say you will get 30% heads in 1000 flips, while insisting you don't have to get any specific result in the individual flips (which is what these "decoherence" schemes, old and new, claim to be able somehow to achieve).

I think you're misreading the decoherence program which you seem to confuse with hardline manyworlders. The decoherence program tells you that if you consider the collapse at each individual flip, or you only consider the collapse at the 1000 flips series, the result will be the same, because the non-diagonal terms in the density matrix vanish at a monstruously fast rate for any macroscopic system (UNLESS, of course, WE ARE DEALING WITH EPR LIKE SITUATIONS!!). But in order to be able to even talk about a density matrix, you need to assume the Born rule (in its modern version). So the knowledgeable proponents of decoherence are well aware that they'll never DERIVE the Born rule that way, because they USE it. They just show equivalence between two different ways of using it.

cheers,
Patrick.

vanesch

Oct10-04, 02:58 AM

It is a simple question. You have |Psi> = a1 |A1> + a2 |A2> = b1 |B1> + b2 |B2>. These are two equivalent orhtogonal exapansions of state Psi, for two observables [A] and [B], of some system (where the system may be a single particle, an aparatus with a particle, rest of the building with the aparatus and the particle,...). On what basis does one declare that we have value A1 of [A] for a given individual instance (you need this to be able to even to talk about statistics of the sequence of such values)?

What the decoherence program indicates is that once you're macroscopic enough, certain *coherent* states survive (by factorization) the coupling with their environment, while others get hopelessly mixed up and cannot factorize out. It is the interaction hamiltonian of the system with the environment that determines this set of preferred (sometimes called coherent) states. This is the preferred basis problem which is then solved, and is the essential result of decoherence. But again, a common misconception is that decoherence deduces the Born rule and the projection which is not the case.

A simple example is the position of a charged particle at macroscopic distances. A superposition of macroscopic position states will entangle very quickly (through the Coulomb interaction) with its environment, so states with macroscopically distinguishable positions for a charged particle will not be able to get factorized out. However, a localized position (even though it doesn't have to be a Dirac pulse), will not be affected by this interaction.
So the "position" basis is preferred because it factors out.

There is no other result at that point preventing you from interpeting the wave function as a real matter field, evolving purely, without any interruptions, according to the dynamical equations (which happen to be nonlinear in the general coupled case) and representing thus the local "hidden" variables of the system.

Well, you still have the small problem of how a real matter field (take neutrons) always gives point-like observations. How do you explain the 100% efficient (or close) detection of spot-like neutron interactions from a neutron diffraction pattern that can measure 4 meters across (I'm working right now on such a project) ? And here, the flux is REALLY LOW, we're often at a count rate of a few counts per second, with a time resolution of 1 microsecond, a background of 1 per day, and a detection efficiency of 95%.

The 2nd quantization is then only an approximation scheme for these coupled matter-EM fields, a linearization algorithm (similar to the Kowalski's and virtually identical to the QFT algorithms used in solid state and other branches of physics), adding no more new physics to the coupled nonlinear fields than, say, the Runge-Kutta numeric algorithm adds to the fluid dynamics Navier-Stokes equations.

I already said this a few times, but you ignored it. There is a big difference between 2nd quantization and not. It is given by the Feynman path integral. If you do not consider second quantization, you take the integral only over the *classical* solution (which are the solution of the non-linear field equations you are always talking about). If you do take into account second quantization, you INTEGRATE OVER ALL THE POSSIBLE NON-SOLUTIONS, with a weight factor which is given by exp(i (S-S0)/h-bar), with S the action calculated for a particular non-solution, and S0 the action of your solution (action from the Lagrangian that gives your non-linear coupled EM and Dirac field equations). So this must make a difference.

Interestingly, in one of his superposed eigenviews, master guru Zeh himself insists that the wave function is a regular matter field and definitely not a probability "amplitude" -- see his paper "There is no "first" quantization" (http://cul.arxiv.org/abs/quant-ph/0210098), where he characterizes the "1st quantization" as merely a transition from a particle model to a field model (the way I did several times in this thread; which is of course how Schroedinger, Barut, Jaynes, Marshall & Santos, and others have viewed it).

But OF COURSE. This is the way quantum field theory is done!!! The old quantum fields are replaced by REAL MATTER FIELDS, and then we apply quantization (which is called second quantization, but is in fact the first time we introduce quantum theory). So there's nothing exceptional in Zeh's statements. Any modern quantum field theory book treats the solutions of the Dirac equation on the same footing as the classical EM field. What is called "classical" in a quantum field book, is what you are proposing: namely the solution to the nonlinearly coupled Dirac and EM field equations

But you need then to QUANTIFY those fields in order to extract the appearance of particles. And yes, if you take this in the non-relativistic limit, you find back the Schroedinger picture (also with multiple particle superpositions and all that)... AFTER you introduced "second" quantization.

cheers,
Patrick.

nightlight

Oct10-04, 03:08 AM

vanesch This is not true. If you take a probability of series of 1000 flips together as one observation

And what if you don't take it just so. What happens in one flip. What dynamical equation is valid for that one instance? You can't hold that there is an instance of thousand flips with a definite statistics, or anything definite at all, while insisting there is no single flip within that instance with a definite result.

What if I define a Killoflip to consist of a sequence of thousand regular flips (doing exacly as before), and which I call one intsance of measurement of a variable which can take value 0 to 1000. And then I do 1000 Killoflips to obtain statistics of values. Does each Killoflip have a definite result? Even approximate value, say around 300. Or was that good only before I called what I was doing Killoflip, and now under the name Killoflip, you have to look "a series of 1000 Killoflips" as one observation to be able to say...

It is plain nonsense.

I was simply asking what is the dynamics (on the splitter setup) of wave fragment B in one instance, as it, reaches the detector (viewed as a physical system) and interacts with it. If the joint dynamics proceeds uninterrupted, it yields either to trigger or no trigger based solely on the precise local state of all the fields, regardless of what goes on in the interaction between the physical system Detector-A and the packet fragment A.

To put it even more clearly, imagine we are not "measuring" but simply want to compute dynamical evolution of a combined system, A,B, Splitter, DA, DB, in a manner of a fluid dynamics simulation. We have a system of PDEs and we put in some initial and boundary and run a program to compute what is going on in one instance, under the assumed I&B conditions. In each run, the program follows the combined packet (with whatever time-slicing we set it to do), as it splits to A and B, follows the fragments as they enter detectors, gets the first ionization, then the cascade if it these happen to result in this run for the given I&B conditions (of the full system). As it makes multiple runs, the program also accumulates the statistics of coincidences.

Clearly, the A-B statistics computed this way will always be classical. The sharpest it can be for any given intensity with expectation value n of photo-electrons emitted per try (on DA or DB) is the Poissonian distribution, which will have variance (sigma square) equal n (if the n varies from try to try, you get compound Poissonian). This is also precisely the prediction of both the semiclassical and the QED model of this process.

The point I am making is that if you claim that you are not going to suspend the program at any stage, but let it go through all the steps including counting for any desired number of runs (to collect statistics), you cannot get anything but the classical correlation in the counts.

Explain how you can claim that you will let the program run uninterrupted and that it will show different than classical Poissonian (at best) statistics. We're not talking "measurement" or "postulates" but simply about the computation of the PDE problem, so don't introduce non sequiturs such "perfect detector" or to understand it I now need to imagine 1000 computers together as one computer,....

in a decoherence-like way

Oh, yeah, that's it. Silly me, how come I didn't of so simple solution. I see.

It depends whether I personally observe each flip or whether I just look at the record of the result of 1000 flips. But the results are indistinguishable.

I see, as fallback, if the "decoherence-like way" fails to mesmerize, then we're all constructs of your mind, and your mind has constructed all these constructs to contain a belief construct of every other construct as the just a construct of the last construct's construct of mind.

nightlight

Oct10-04, 07:01 AM

vanesch What the decoherence program indicates is that once you're macroscopic enough, certain *coherent* states survive (by factorization) the coupling with their environment,

The "enviroment" is assumed in |Psi>. A subsystem can trivially follow a non-unitary evolution in the subsystem's factor during the interaction. If our |Psi> includes all that you ever plan to add in, including yourself (whose mind has apparently constructed all of us anyway; do always argue as much with the other constructs of your mind?), you're back exactly where you started -- two different decompositions of |Psi> and you need to specify which is the "true" one and how would a precise postulate be formulated out of such criteria (saying which variables/observables, when and how, gain or lose definitive values, so that you can make sense when talking about a sequence of such values, statistics and such).

It is the interaction hamiltonian of the system with the environment that determines this set of preferred (sometimes called coherent) states. This is the preferred basis problem which is then solved, and is the essential result of decoherence.

The combined hamiltonian basis was claimed as preferred in older approaches (as well as other variants, such as integrals of motion, or Prigogine's "subdynamics" which represents a closed classical-like reduced/effective dynamics of the macroscopic aparatus whose variables can have definite values, a kind of an emergent property). Any basis you claim as preferred will have the same problems with the non-commuting observables if you decide to allow definite values for the preferred basis. It would be as if you declared the Sz observable of particle A and/or B in EPR-Bell model as the "preferred" one that has a definite value and claimed that somehow solves the problem. The problems always re-emerge once you include the stuff you kept outside to help decohere the subsystem. The outer layer never decoheres.

Well, you still have the small problem of how a real matter field (take neutrons) always gives point-like observations. How do you explain the 100% efficient (or close) detection of spot-like neutron interactions from a neutron diffraction pattern that can measure 4 meters across (I'm working right now on such a project) ? And here, the flux is REALLY LOW, we're often at a count rate of a few counts per second, with a time resolution of 1 microsecond, a background of 1 per day, and a detection efficiency of 95%.

The localization problem for matter fields hasn't been solved (even though there are heuristic models indicating some plausible mechanisms, e.g. Jaynes and Barut had toy models of this kind). If your counts are Poissonian (or super-Poissonian) for the buildup of the high visibility 4m large diffraction pattern, there should be no conceptual problem in conceiving a purely local self-focusing or some kind of toplogical/structural unravelling mechanism which could at least superficially replicate such point-like detections with the diffractions. After all, the standard theory doesn't have an explanation here other than saying that is how it is.

There is a big difference between 2nd quantization and not. It is given by the Feynman path integral. If you do not consider second quantization, you take the integral only over the *classical* solution (which are the solution of the non-linear field equations you are always talking about). If you do take into account second quantization, you INTEGRATE OVER ALL THE POSSIBLE NON-SOLUTIONS, with a weight factor which is given by exp(i (S-S0)/h-bar), with S the action calculated for a particular non-solution, and S0 the action of your solution (action from the Lagrangian that gives your non-linear coupled EM and Dirac field equations). So this must make a difference.

You're not using the full system nonlinear dynamics (a la Barut's self-field) for the QED in the path integral representation i.e. the S0 used is not computed for the Barut's full nonlinear solution but for the (iteratively) linearized approximations. The difference is even more transparent in the canonical quantization via Fock space, where it is obvious that you are forming the Fock space from the linear approximations (external fields/current approximation) of the nonlinear fields.

But OF COURSE. This is the way quantum field theory is done!!! The old quantum fields are replaced by REAL MATTER FIELDS, and then we apply quantization (which is called second quantization, but is in fact the first time we introduce quantum theory). So there's nothing exceptional in Zeh's statements.

Well, it is not quite so simple to weasel out. For the QM reasoning, such as Bell's QM prediction, you had used the same matter fields as the probability "amplitides" (be it for Dirac or for it's approximation, Schroedinger-Pauli particle) and insisted they are not local matter fields since they can non-dynamically collapse. How do you transition you logic from the "amplitude" and all that goes with it to just plain matter field right before you go on to quantize it now as plain classical system.

If it were a classical system all along, like the classical EM field, then the issue of collapse when the observer learns the result "in a decoherence-like way" or any other way, is plain nonsense. We never did the same kind of probability "amplitude" talk with the Maxwell field before quantizing it. It was just plain classical field with no mystery, no collapse "decoherence-like way" or jump-like way... There was no question of being able to deduce the no-go for LHVs by just using the dynamics of that field. Yet you somehow claim you can do that for the Dirac field in Stern-Gerlach, without having to stop or suspend its purely local dynamics (Dirac equation). Does it again come back to your mind in a decohernce-like way to have it do the collapse of the superposed amplitudes?

Then suddenly, both fields are declared just plain classical fields (essentially equivalent except for slightly different equations), that we proceed to quantize. There is a dichotomy here (and it has nothing to do with the switch from Schroedinger to Dirac equation).

That is precisely the dichotomy I discussed few messages back (http://www.physicsforums.com/showthread.php?t=44964&page=3&pp=40) when responding to your charge of heresy for failing to show the offcially required level of veneration and befuddlement with the Hilbert product space.

Any modern quantum field theory book treats the solutions of the Dirac equation on the same footing as the classical EM field.

Yes, but my Jackson ED textbook doesn't treat EM fields as my Messiah QM textbook treats Dirac or Schroedinger matter field. The difference in treatment is hugely disproportionate to just the difference implied by the different form of equations.

Note also that, so far there is no experimental data showing that the local dynamics of these fields has to be replaced by a non-local one. There is such data for the "fair sampling" type of local theories, but neither Dirac nor Maxwell fields are of that "fair sampling" type.

What is called "classical" in a quantum field book, is what you are proposing: namely the solution to the nonlinearly coupled Dirac and EM field equations

Not at all. What is called classical in a QED book is the Dirac field in the external EM field approximation and the EM field in the external current approximation. These are linear approximations of the non-linear fields. It is these linear approximations which are being (second) quantized (be it canonically or via path integrals), not the full non-linear equations. Only then, with Fock space defined, the interaction is iteratively phased in via perturbative expansion which is defined in terms of the quantized linear fields. The whole perturbative expansion phasing in the interaction, with all the rest of the (empirically tuned ad hoc) rules on how to do everything just so in order to come out right, is what really defines the QED, not the initial creation of the Fock space from linearized "classical" fields.

That is exactly how the Kowalski's explicit linearization via the Fock space formalism appears. In that case the Fock space formalism was a mere linear approximation (an infinite set of linear equations) to the original nonlinear system, no new effect could exists in the quantized formalism than what was already present in the classical nonlinear system. In particular, one would have no non-locality even for sharp boson number states of the quantized formalism (the usual trump card for the QM/QED non-locality advocates). Any contradiction or a Bell-like no-go theorem for the classical model, should one somehow deduce any such for the Kowalski's Fock space bosons, would simply mean a faulty approximation. (Not that anyone has ever deduced Bell's QM "prediction" without instantaneous and interaction-free collapse of the remote state, but just using the QED dynamics and any polarizer and detector properties & interactions with the quantized EM field.)

And yes, if you take this in the non-relativistic limit, you find back the Schroedinger picture (also with multiple particle superpositions and all that)... AFTER you introduced "second" quantization.

The non-relativistic limit, i.e. the Dirac equation to Schroedinger-Pauli equation limit is irrelevant. The Bell EPR setup and conclusion for spin 1/2 particle was exactly same for Dirac particle or for its Schroedinger-Pauli approximation.

vanesch

Oct10-04, 01:36 PM

The "enviroment" is assumed in |Psi>. A subsystem can trivially follow a non-unitary evolution in the subsystem's factor during the interaction. If our |Psi> includes all that you ever plan to add in, including yourself

It is the "including yourself" part that distinguishes the decoherence part from hardline Many Worlds and at that point, in the decoherence program, the projection postulate has to be applied. At that point, you have included so many many degrees of freedom that you WILL NOT OBSERVE, that you restrict your attention to the reduced density matrix, which has become essentially diagonal in the "preferred basis of the environment".

It would be as if you declared the Sz observable of particle A and/or B in EPR-Bell model as the "preferred" one that has a definite value and claimed that somehow solves the problem. The problems always re-emerge once you include the stuff you kept outside to help decohere the subsystem. The outer layer never decoheres.

Exactly. That's why the outer layer has to apply the projection postulate. And that outer layer is the conscious observer. Again, the decoherence program doesn't solve the measurement problem in replacing the projection postulate. It only indicates which are the observables of the subsystem which are going to be observable during a while (factor out from all the rest which is not observed).

The localization problem for matter fields hasn't been solved (even though there are heuristic models indicating some plausible mechanisms, e.g. Jaynes and Barut had toy models of this kind). If your counts are Poissonian (or super-Poissonian) for the buildup of the high visibility 4m large diffraction pattern, there should be no conceptual problem in conceiving a purely local self-focusing or some kind of toplogical/structural unravelling mechanism which could at least superficially replicate such point-like detections with the diffractions. After all, the standard theory doesn't have an explanation here other than saying that is how it is.

I would be VERY SURPRISED that you can construct such a thing, because it is the main reason of existence of quantum theory. Of course, once this is done, I'd be glad to consider it, but let us not forget that it is the principal reason to quantify fields in the first place!

You're not using the full system nonlinear dynamics (a la Barut's self-field) for the QED in the path integral representation i.e. the S0 used is not computed for the Barut's full nonlinear solution but for the (iteratively) linearized approximations.

No, in PERTURBATIVE quantum field theory, both the nonlinear "classical dynamics" and the quantum effects (from the path integral) are approximated in a series devellopment, simply because we don't know how to do otherwise in all generality, except for some toy models. But in non-perturbative approaches, the full non-linear dynamics is included (for example solitons are a non-linear solution to the classical field problem).

The difference is even more transparent in the canonical quantization via Fock space, where it is obvious that you are forming the Fock space from the linear approximations (external fields/current approximation) of the nonlinear fields.

No, it is a series devellopment. If you consider external fields, that's a semiclassical approach, and not full QFT.

Well, it is not quite so simple to weasel out. For the QM reasoning, such as Bell's QM prediction, you had used the same matter fields as the probability "amplitides" (be it for Dirac or for it's approximation, Schroedinger-Pauli particle) and insisted they are not local matter fields since they can non-dynamically collapse. How do you transition you logic from the "amplitude" and all that goes with it to just plain matter field right before you go on to quantize it now as plain classical system.

Because there is an equivalence between the linear and non-relativistic part of the classical field equation as a quantum wave equation of a single particle and the single-particle states of the second quantized field. It only works if you are sure you work with one or a fixed number of particles. This is a subtle issue of which others know more than I here. I will have to look it up again in more detail.

If it were a classical system all along, like the classical EM field, then the issue of collapse when the observer learns the result "in a decoherence-like way" or any other way, is plain nonsense. We never did the same kind of probability "amplitude" talk with the Maxwell field before quantizing it. It was just plain classical field with no mystery, no collapse "decoherence-like way" or jump-like way... There was no question of being able to deduce the no-go for LHVs by just using the dynamics of that field.

No, you need a multiparticle wave function (because we're working with a 2-particle system) which is essentially non-local, OR you need a classical field which is second-quantized. The second approach is more general, but the first one was sufficient for the case at hand. If there's only ONE particle in the game, there is an equivalence between the classical field and the one-particle wave function: the maxwell equations describe the one-photon situation (but not the two-photon situation).

Then suddenly, both fields are declared just plain classical fields (essentially equivalent except for slightly different equations), that we proceed to quantize.

It is because of the above-mentioned equivalence.

Yes, but my Jackson ED textbook doesn't treat EM fields as my Messiah QM textbook treats Dirac or Schroedinger matter field.

Messiah still works with "relativistic quantum mechanics" which is a confusing issue at best. In fact there exists no such thing. You can work with non-relativistic fixed-particle situations, non-relativistic quantum field situations or relativistic quantum field situations, but there's no such thing as relativistic fixed-particle quantum mechanics.

The difference in treatment is hugely disproportionate to just the difference implied by the different form of equations.

No, Jackson treats the classical field situation, and QFT (the modern approach) quantizes that classical field. The difference comes from the quantization, not from the field equation itself.

Not at all. What is called classical in a QED book is the Dirac field in the external EM field approximation and the EM field in the external current approximation. These are linear approximations of the non-linear fields.
It is these linear approximations which are being (second) quantized (be it canonically or via path integrals), not the full non-linear equations. Only then, with Fock space defined, the interaction is iteratively phased in via perturbative expansion which is defined in terms of the quantized linear fields. The whole perturbative expansion phasing in the interaction, with all the rest of the (empirically tuned ad hoc) rules on how to do everything just so in order to come out right, is what really defines the QED, not the initial creation of the Fock space from linearized "classical" fields.

We must be reading different books on quantum field theory :-)
Look at the general formulation of the path integral (a recent exposition is by Zee, but any modern book such as Peskin and Schroeder, or Hatfield will do).
The integral clearly contains the FULL nonlinear dynamics of the classical fields.

cheers,
patrick.

vanesch

Oct10-04, 10:54 PM

I would like to add something here, because the discussion is taking a turn that is in my opinion wrongheaded. You're trying to attack "my view" of quantum theory (which is 90% standard and 10% personal: the "standard" part being the decoherence program, and the personal part the "single mind" part). But honestly that's not very interesting because I don't take that view very seriously myself. To me it is a way, at the moment, with the current theories, to have an unambiguous view on things. Although it is very strange because no ontological view is presented - everything is epistemology (and you qualify it as nonsense), it is a consistent view that gives me "peace of mind" with the actual state of things. If one day another theory takes over, I'll think up of something else. At the time of Poisson, there was a lot of philosophy on the mechanistic workings of the universe, an effort that was futile. In the same way, our current theories shouldn't give us such a fundamental view that gives a ground to do philosophy with, because they aren't the final word. After all, what counts is the agreement with experiment, and that's all there is to it. If we have two different theories with the same experimental success, of course the temptation is to go for the one that fits nicest with our mental preferences. In fact, the best choice is dictated by what allows us to expand the theory more easily (and correctly).
That's why I was interested in what you are telling, in that I wasn't aware that you could build a classical field theory that gives you equivalent results with quantum field theory for all experimentally verified results. Honestly I have a hard time believing it, but I can accept that you can go way further than what is usually said with such a model.

What is called second quantization (but which is in fact a first quantisation of classical fields) has as main aim to explain the wave-particle duality when you can have particle creation and annihilation. You are right that the Fock space is build up on the linear part of the classical field equations ; however, that's not a linearization of the dynamics, but almost the DEFINITION of what are the associated particles with the matter field. Indeed, particles only have a well-defined meaning when they are propagating freely through space, without interaction (or where the interaction has been renormalized away). The fact that these states are used to span the Fock space should simply be seen as the classical analogon to do, say, a Fourier transform on the fields you're working with. You simply assume that your solutions are going to be written in terms of sine and cosines, not that the solutions ARE sines and cosines. So that, by itself, is not a "linearisation of the dynamics", it is just a choice of basis, in a way. But we're not that free in the choice: at the end of the day we observe particles, so we observe in that basis.

The only way that is known to find particles associated with fields (at least to me, which doesn't exclude others of course) is the trick with the creator-anticreator operators of a harmonic oscillator. That's why I said that I would be VERY SURPRISED INDEED if you can crank out a non-linear classical field theory (even including ZPF noise or whatever) that gives us nice particle-like solutions with the correct mass and energy momentum relationship which then propagate nicely throughout space, but which act for the rest like what quantum theory predicts (at least in those cases where it has been tested).

That's why I talked about gammas and then about neutrons. Indeed, once you consider that in one way or another you're only going to observe lumps of fields when you've integrated enough "field" locally, and that you're then going to generate a Poisson series of clicks, you can do a lot with a "classical field", and it will be indistinguishable from any quantum prediction as long as you have independent single-particle situations. The classical field then looks a lot like a single-particle wave function. But to explain WHY you integrate "neutron-ness" until you have a full neutron, and then you will click Poisson-like looks to me quite a challenging task if no mechanism is build into the theory that makes you have steps of neutrons in the first place. And as I said, the only way I know how to do that is through the method of "second quantization" ; and that supposes linear superposition of particle states (such as EPR like states).

cheers,
patrick.

nightlight

Oct11-04, 01:39 AM

vanesch Nope, I am assuming 100% efficient detectors.

If you recall that 85% QE detector cooled to 6K (http://cul.arxiv.org/abs/quant-ph/0308054), check the QE calculation -- it subtracts the dark current, which was exactly at 20,000 triggers/sec as the incident photon count. Thus your 100% efficient detector is no good for anticorrelations if half the triggers might be vacuum noise. You can look their curves, see if you get more suitable QE to noise deal (they were looking only to max out on the QE).

Unfortunately, you comments in this message show you are off again on an unrelated tangent, ignoring the context you're disputing, and I expect gamma photons to be trotted out any moment now.

The context was -- I am trying to pinpoint exactly the place you depart from the dynamical evolution in the PDC beam splitter case in order to arrive at the non-classical anticorrelation. Especially since you're claiming that the dynamical evolution is not being suspended at any point. My aim was to show that this position is self-contradictory -- you cannot obtain different result from the classical one without suspending the dynamics and declaring collapse.

In order to analyse this, the monotonous mantras of "strict QM", "perfect 100% detectors"... are much too shallow and vacuous to yield anything. We need to look at the "detectors" DA and DB as physical systems, subject to QM/QED (as anything else) in order to see whether they could do what you say they could without violating logic or any agreed upon facts (theoretical or empirical) and without bringing in your mind/consciousness into the equations, the decoherence-like way or otherwise.

To this end we are following a wave packet (in coordinate representation) of PDC "photon 2" and we are using "photon 1" as as an indicator that there is a "photon 1" heading to our splitter. This part of the correlation between 1 and 2 is purely classical amplitude based correlation i.e. a trigger of D1 at time t1 indicates that the incident intensity of "photon 2", I2(t) will be sharply increased within some time window T at starting at t1 (with an offset from t1, depending on path lengths).

The only implication of this amplitude correlation used is that we can have a time window defined via the "photon 1" trigger as [t1,t1+T] and DB. During this window the incident intensity of "photon 2" can be considered some constant I, or in terms of the average photon counts on DA/DB denoted as n. The constancy assumption within the window simplifies discussion and it is favorable to the stronger anticorrelation anyway (since the variable rate would result in the compound Poissonian which has greater variance for any given expectation value). This is again just a minor point.

I don't really know what you mean with "Poissonian square law detectors".

I mean the photon detectors for the type of photons we're discussing (PDC, atomic cascades, laser,...). The "square law" refers to the trigger probability in a given time window [t,t+T] being proportional to the incident EM energy in that time window. The Poissonian means that the ejected photo-electron count has a Poissonian distribution i.e. probability of k electrons being ejected in a given time interval is P(n,k)=n^k exp(-n)/k! where n=average numbers of photoelectrons ejected in that time interval. In our case, the time window is the short coincidence window (defined via the PDC "photon 1" trigger) and we assume n=constant in this window. As indicated earlier, the n(t) varies with time t, it is low generally except for the sharp peaks within the windows defined by the triggers of "photon 1" detector.

Note that we might assume an idealized multiphoton detector which amplifies optimally all photo-electrons, thus we would then have for the case of k electron ejection exactly k triggers. Alternatively, as suggested earlier, we can divide the "photon 2" beam via the L level binary tree of beam splitters obtaining ND=2^L reduced beams on which we place simpler "1-photon" detectors (which only indicate yes/no). These simple 1-photon detectors would receive intensity I1=I/ND and thus have the photo-electron Poissonian with n1=n/ND. But since they don't differentiate in their output k=1 from k=2,3,... we would have to count 1 when they trigger at all, 0 if they don't trigger. For "large" enough ND (see earlier msg for discussion) the single ideal multiphoton detector is equivalent to the array of ND 1-photon detectors.

For brevity, I'll assume the multiphoton detector (optimal amplification and photon number resolution). The rest of your comments indicate some confusion on what precisely this P(n,k) means, what does it depend on and how does it apply to our case. Let's try clearing that a bit.

There are two primary references which analyze photodetection from the ground up, [1] is semiclassical and [2] is full QED derivation. Mandel & Wolf's textbook [3] has one chapter for each approach with more readable coverage and nearly full detail of derivations. Papers [4] and [5] discuss in more depth the relation between the two approaches, especially the operational meaning of the normal ordering convention and of the resulting Glauber's correlation functions (the usual Qunatum Optics correlations).

Both approaches yield exactly the same conclusion, the square law property of photo-ionization and the Poisson distribution (super-Poisson for mixed or varying fields within the detection window) of the ejected photo-electrons. They all also derive detector counts (proportional to electron counts/currents) for single and multiple detectors in arbitrary fields and any positions and time windows (for correlations).

The essential aspect of the derivations relevant here is that the general time dependent photo-electron count distribution (photo-current) of each detector depends exclusively on the local field incident on that detector. There is absolutely no interruption of the purely local continuous dynamics and the photo ejections depend solely on the local fields/QED amplitudes which also never collapse or deviate in any way from the local interaction dynamics. (Note: the count variance is due to averaging over the detector states => the identical incident field in multiple tries repats at best up to a Poissonian distribution.)

The QED derivations also show explicitly how the vacuum contribution to the count yields 0 for the normal operator ordering convention. That immediately provides operational meaning of the quantum correlations as vacuum-normalized counts, i.e. to match the Glauber "correlation" function, all background effects need to be subtracted from the obtained counts.

The complete content of the multi-point correlations is entirely contained in the purely classical correlations of the instantaneous local intensities, which throughout follow purely local evolution. There are two main "quantum mysteries" often brought up here:

a) The "mysterious" quantum amplitude superposition (which the popular/pedagogical accounts make a huge ballyhoo out of) for the multiple sources is a simple local EM field superposition (even in QED treatment) which yields local intensity (which is naturally, not a sum of non-superposed intensities). The "mystery" here is simply due to "explaining" to student that he must imagine particles (for which the counts would add up) instead of fields which superpose into the net amplitude which then gets squared to get the count (resulting in the "mysterious" interference, the non-additivity of counts for separate fields, duh).

b) Negative probabilities, anti-correlations, sub-Poissonian light -- The multi-detector coincidence counts are computed (in QED and semiclassical derivations) by constructing a product of individual instantaneous counts -- a perfectly classical expression (same kind as Bell's LHV). These positive counts are then expressed via local intensities (operators in QED), which are still fully positive definite. It is at this point that QED treatment introduces the normal ordering convention (which simplifes integrals by canceling out the vacuum sourced terms in each detector's count integrals; see [4],[5]), redefining thus the observable whose expectation value is being computed, while retaining the classical coincidence terminology they started with, resulting in much confusion and bewilderment (in popular and "pedagogical" retelling, where to harmonize their "understanding" with the facts they had to invent "ideal" detectors endowed with magical power of reproducing G via plain counts correlations).

The resulting Glauber "correlation" function G(X1,X2...), (the standard QO "correlation" functions), is not the correlation of the counts at X1,X2,... but a correlation-like expression extracted (though the vacuum terms removal via [a+],[a] operator reordering) from the expectation value of the observable corresponding to the counts correlations (which, naturally, shows no negative counts or non-classical statistics).

-----
1. L. Mandel, E.C.G. Sudarshan, E. Wolf "Theory of Photoelectric Detection of Light Fluctuations" Proc. Phys. Soc. V84, 1964, pp. 435-444 (reproduced also in P.L. Knight's 'Concepts of Quantum Optics' )

2. P.L. Kelly, W.H. Kleiner "Theory of Electromagnetic Field Measurement and Photoelectron Counting" Phys. Rev. 136 (1964) pp. A316-A334.

3. L. Mandel, E. Wolf "Optical Coherence and Quantum Optics" Cambridge Univ. Press 1995.

4. L. Mandel "Physical Significance of Operators in Quantum Optics" Phys. Rev. 136 (1964), pp B1221-B1224.

5. C.L. Mehta, E.C.G Sudarshan "Relation between Quantum and Semiclassical Description of Optical Coherence" Phys. Rev. 138 (1965) pp B274-B280.

nightlight

Oct11-04, 02:42 AM

vanesch I would like to add something here, because the discussion is taking a turn that is in my opinion wrongheaded. You're trying to attack "my view" of quantum theory (which is 90% standard and 10% personal: the "standard" part being the decoherence program, and the personal part the "single mind" part). But honestly that's not very interesting because I don't take that view very seriously myself.

Agree on this, that's a waste of time. I would also hate to have to defend the standard QM interpretation. Even arguing from this side, against its slippery language is like mud-wrestling a lawyer. It never goes anywhere.

vanesch

Oct11-04, 03:19 AM

To this end we are following a wave packet (in coordinate representation) of PDC "photon 2" and we are using "photon 1" as as an indicator that there is a "photon 1" heading to our splitter. This part of the correlation between 1 and 2 is purely classical amplitude based correlation i.e. a trigger of D1 at time t1 indicates that the incident intensity of "photon 2", I2(t) will be sharply increased within some time window T at starting at t1 (with an offset from t1, depending on path lengths).

I know that that is how YOU picture things. But it is not the case of the quantum description, where the two photons are genuine particles.

I don't really know what you mean with "Poissonian square law detectors".

I mean the photon detectors for the type of photons we're discussing (PDC, atomic cascades, laser,...). The "square law" refers to the trigger probability in a given time window [t,t+T] being proportional to the incident EM energy in that time window.

Again, that's your view of a photon detector, and it is not the view of quantum theory proper. So I used that distinction to point out a potential difference in predictions. A quantum photon detector detects a marble, or not. A finite quantum efficiency photon detector has QE chance of seeing the marble when it hits, and (1-QE) chance of not seeing it. But if the marble isn't there, it doesn't see it. This was exactly what I tried to point out in the anti-coincidence series. If the detectors are "square law" then they have a different behaviour than if they are "marble or no marble", so such an experiment can discriminate between both.

The Poissonian means that the ejected photo-electron count has a Poissonian distribution i.e. probability of k electrons being ejected in a given time interval is P(n,k)=n^k exp(-n)/k! where n=average numbers of photoelectrons ejected in that time interval. In our case, the time window is the short coincidence window (defined via the PDC "photon 1" trigger) and we assume n=constant in this window. As indicated earlier, the n(t) varies with time t, it is low generally except for the sharp peaks within the windows defined by the triggers of "photon 1" detector. For simplicity you can assume n(t)=0 outside the window and n(t)=n within the window (we're not putting numbers in yet, so hold on your |1,1>, |2,2>...).

Exactly, that's a "square law" detector. And not a quantum photon detector. But statistically you cannot distinguish both if you have no trigger, so the semiclassical description works in that case for both. However, this is NOT the case for a 2-photon state, because then, BEFORE TAKING INTO ACCOUNT THE PHOTOELECTRON distribution, you have somehow to decide whether the first photon was there or not. If it is not there, nothing will happen, and if it is there, you draw from the photoelectron distribution, which will generate you a finite probability of having detected the photon or not.

Both approaches yield exactly the same conclusion, the square law property of photo-ionization and the Poisson distribution (super-Poisson for mixed or varying fields within the detection window) of the ejected photo-electrons. They all also derive detector counts (proportional to electron counts/currents) for single and multiple detectors in arbitrary fields and any positions and time windows (for correlations).

I don't disagree with the Poissonian distribution of the photoelectrons of course, IN THE CASE A PHOTON DID HIT. The big difference is that you consider streams of 1/N photons (intensity peaks which are 1/N of the original, pre-split peak) which give rise to INDEPENDENT detection probabilities at each detector, while I claim that pure quantum theory predicts you individually the same rates, with the same distributions, but MOREOVER ANTICORRELATED in that the click (the undivisible) photon can be only at one place at a time. This discriminates both approaches, and is perfectly realizable with finite-efficiency detectors.

The essential aspect of the derivations relevant here is that the general time dependent photo-electron count (photo-current) of each detector depends exclusively on the local field incident on that detector.

Not in 2-photon states. They are not independent, in quantum theory. I'm pretty sure about that, but I'll try to back up my statements with other people's opinions in how QUANTUM THEORY works (how nature works is a different issue which can only be decided by experiment).

cheers,
Patrick.

nightlight

Oct11-04, 05:39 AM

vanesch I know that that is how YOU picture things. But it is not the case of the quantum description, where the two photons are genuine particles.

One photon state spans infinite space and time and would require inifinite detector and infinite time to detect. Any finite time, finite space field is necessarily a superposition of multiple photon number states (also called Fock states). The "photon" is not what photo detectors count, despite suggestive name and the pedagocial/popular literature mixups. That's just a jargon, a shorthand. They count photo-electrons. The theory of detectors shows what these counts are and how the QED (or classical) field amplitudes relate to the photodetector counts. Of course, the integrated absolute squares of field amplitudes are proportional to the expectation value of the "photon number operator" [n], so one can loosely relate the average "photon number" <[n]> to the photo detector counts, but this is a relation between an average of an observable [n] and a (Poisson) distribution P(ne,k), which is a much too soft connection for the kind of tight enumerative reasoning required in the analysis of the anti-correlations or of the Bell's inequality tests.

There is nothing corresponding operationally to the "photon detector". And to speak of coincidence correlations of |1,1> at places X1,X2 at times t1 and t2 is vacuous to the square.

What photodetector counts are, is quite relevant if you wish to interpret what the Quantum Optics experiments are showing or even to state what the QED predictions are, at all.

Ignoring the toy "prediction" based on simple reasoning with |1,1>, |2,2> and such, the QED prediction for coincidences is given precisely by the Glauber's correlation functions (which includes their operational interpretation, the usual QO vacuum effects subtractions).

You can't predict any coincidences with |1,1> since |1,1> represents plane waves of infinite duration and infinite extent (they are expansion basis sensitive, too). All you can "predict" with such mnemonic devices is what the real coincidence prediction given via G() might roughly look like. Coincidence count is meaningless for |1,1>, it is operationally empty.

You did manage to miss the main point (which in retrospect appears a bit too fine a point), though, which is that what is shown in the papers cited (and explicitly stated in [4]), is that the "Quantum Optics correlation" G(X1,X2,..) is not the (expectation value of) observable representing the correlation of coincidence counts. The observable which does correspond to the correlation of coincidence counts (the pre-normal ordered correlation function) yields prefectly local (Bell's LHV type) predictions, no negative counts, no sub-Poissonian statistics, no anti-correlations. That is the result of both QED and semiclassical treatment of multi-detector coincidences.

Debating whether there is a "photon" and whether it is hiding inside the amplitude somehow (since the formalism doesn't have a counterpart for it), is like debating the count of dancing angels on a head of a pin. All you can say is that fields have such and such amplitudes (which are measurable for any given setup, e.g. via tomographic methods based on Wigner functions). The theory of detection then tells you how such amplitudes relate to counts (of photo-electrons) produced by the photo-detector.

While it is perfectly fine to imagine "photon" somewhere inside the amplitude (if such mnemonics helps you) you can't call the counts produced by the photodetectors the counts of your mnemonic devices (without risking a major confusion). That simply is not what those counts are, as the references cited show clearly and in great detail. After you clear up this bit, you're not done since there is the next layer of confusion to get through, which is the common mixup between the Glauber's G() "correlation" function and the detector counts correlations, for which [4] and [5] should help clear it up. And after that, you will come to still finer layers of mixups which Marshall and Santos address in their PDC papers.

vanesch

Oct11-04, 06:52 AM

The observable which does correspond to the correlation of coincidence counts (the pre-normal ordered correlation function) yields prefectly local (Bell's LHV type) predictions, no negative counts, no sub-Poissonian statistics, no anti-correlations. That is the result of both QED and semiclassical treatment of multi-detector coincidences.

My Mandel and Wolf is in the mail, but I checked the copy in our library. You are quite wrong concerning the standard quantum predictions. On p706, section 14.5, it is indicated that the anticoincidence in a 1-photon state is perfect, as calculated from the full quantum formalism.
On p 1079, section 22.4.3, it is indicated that PDC, using one photon of the pair as a trigger, gives you a state which is an extremely close approximation to a 1-photon state. So stop saying that what I told you are not the predictions of standard quantum theory.

I know YOUR predictions are different, but standard quantum mechanical predictions indicate a perfect anticorrelation in the hits. You should be happy about that because it indicates an experimentally verifiable claim of your approach, and not an unverifiable claim such as "you will never be able to build a photon detector with 92% efficiency and neglegible dark current".

cheers,
Patrick.

PS: I can see the confusion if you apply equation 14.3-5 in all generality. It has been deduced in the case of COHERENT states only, which have a classical description.

nightlight

Oct11-04, 07:28 AM

while I claim that pure quantum theory predicts you individually the same rates, with the same distributions, but MOREOVER ANTICORRELATED in that the click (the undivisible) photon can be only at one place at a time. This discriminates both approaches, and is perfectly realizable with finite-efficiency detectors.

That is not a QED prediction, but a shorthand for the prediction which needs a grain of salt before use. If you check the detector foundations in the references given, you will find out that even preparing the absolutely identical field amplitudes in each try, you will still get (at best) the the Poisson distribution of photoelectrons in each try, thus the Poissonian for the detector's count (equivalent to the tree-split count of activated detectors). The reason for the non-repeatability of the exact count is the averaging over the states of the detector. The only thing which remains the same for the absolutely identical preparation in each try is the Poissonian average n=<k>.

Therefore the beam splitter, which can only approximate the absolutely identical packets in the two paths, will also yield in each try the independent Poissonian counts on each side, with only the Poissonian average n=<k> being the same on the two sides.

The finer effect that PDC (and some anticorrelation experiments) specifically add in this context is the apparent excess of the anti-correlation, the apparent sub-Poissonian behavior on the coincidence data processed by the usual Quantum Optics prescription (the Glauber's prescription of vacuum effects removal, corresponding to the normal ordering). Here you need to recheck Marshall & Santos PDC and detector papers for full details and derivations, I will only sketch the answer here.

First one needs to recall that the Glauber's correlation (mapped to the experimental counts via usual vacuum-effects subtractions) is not the (expected value of) observable corresponding to the counts correlation. It is only obtained by modifying the observable for the count corrrelations through normal ordering of operators (to in effect remove the vacuum generated photons, the vacuum fluctuations).

As pointed out in [4] these vacuum terms subtractions from the true count correlation observable, do not merely make G(X1,X2,..) depart from the true correlation observable, but if one were to rewrite G() in a form of a regular correlation function of some abstract "G counts" one would need to use negative numbers for these abstract "G counts" for some conceivable density operators [rho] (G is the expectation value of Glaubers observable [G] over density operator [rho] i.e. G=Tr([rho] [G])). There is never question, of course, of the regular correlation observable [C] requiring negative counts for any [rho] -- it is defined as a proper correlation function observable of the photo-electron counts (as predicted in the detection theory), which are always non-negative.

These abstract "G counts" lead to the exactly same kind "paradoxes" (if confused with the counts) that the superposition mystery presents (item (a) couple messages back) . Namely in the "superposition mystery", your counts are always (proportional to) C=|A|^2, where A is the total EM field amplitude. When you have two sources yielding in separate experiments amplitudes A1 and A2 and the corresponding counts C1=|A1|^2 and C2=|A2|^2, then if you have both sources turned on, the net amplitude is: A=A1+A2 and the net count is C=|A1+A2|^2, which is generally different from C1+C2=|A1|^2+|A2|^2.

If one wants to rewrite formally C as a sum of two abstract counts G1 and G2, one can say C=G1+G2, but one should not confuse C1 and C2 with the abstract counts G1 and G2. In the case of negative interference you could have A1=-A2, so that C=0. If one knows C1 and also misattributes G1=C1, G2=C2, then one would need to set G2=-G1, a negative abstract count. Indeed, the negative interference is precisely the aspect the students will be the most puzzled with.

It turns out, the PDC generates [rho] states which require <[G]> to use negative "abstract G counts" if one were to write it as a proper correlation function correlating these abstract "G counts". The physical reason (in Marshal-Santos jargon) it does so is because the PDC generation uses two vacuum modes (to turn them into down-converted photons on phase matching conditions), thus the vacuum fluctuation noise alone (without these down-converted photons) is actually smaller in the PDC photons detection region. Therefore the conventional QO vacuum effects subtractions from the observed counts, aiming to reconstruct Glauber's <[G]> and implicitly its abstract "G counts", oversubtract here since the remaining vacuum fluctuations effects are smaller in the space region travelling with the PDC photons (they are modified vacuum modes, where the modification is done by the nonlinear crystal via absorption and re-emission of the matching vacuum modes).

nightlight

Oct11-04, 08:39 AM

vanesch My Mandel and Wolf is in the mail, but I checked the copy in our library. You are quite wrong concerning the standard quantum predictions. On p706, section 14.5, it is indicated that the anticoincidence in a 1-photon state is perfect, as calculated from the full quantum formalism.

The textbook doesn't dwell on the fine points of distinction between the Glauber's pseudo-correlation function <[G]> and the true count coincidence correlation observable <[C]> but uses the conventional Quantum Optics shorthand (which tacitly includes vacuum effects subtractons by standard QO procedures, to reconstruct <[G]> from the obtained counts correlation <[C]>).

This same Mandel, of course, wrote about these finer distinctions in ref [4].

Although Mandel-Wolf textbook is better than most, it is still a textbook, for students just learning the material and it has used there a didactic toy "prediction", not a scientific prediction one would find in a paper as predicting something experimenters ought to test against. Find me a real paper in QO which predicts (seriously) such anticorrelation for the plane wave, then goes to measure coincidences on them with infinite detector in infinite time. It is a toy derivation, for students, not a scientifc prediction that you can go out and measure and hope to get what you "predicted".

On p 1079, section 22.4.3, it is indicated that PDC, using one photon of the pair as a trigger, gives you a state which is an extremely close approximation to a 1-photon state. So stop saying that what I told you are not the predictions of standard quantum theory.

Well, the "extremely close" could be, say, about half a photon short of a single photon (generally it will be at best as close as the Poissonian distribution allows, which has a variance <[n]>).

Again, you're taking didactic material toy models without sufficient grain of salt. I cited Mandel & Wolf as a more readable overview of the photodectection theory than the master references in the original papers. It is not a scientific paper, though (not that those are The Word from Above, either). You can't take all it says at the face value and in the most literal way. It is a very nice and useful book (much nicer for a physicist than Yariv's QO textbook), if one reads it maturely and factors out the unavoidable didactic presentation effects.

I know YOUR predictions are different, but standard quantum mechanical predictions indicate a perfect anticorrelation in the hits. You should be happy about that because it indicates an experimentally verifiable claim of your approach, and not an unverifiable claim such as "you will never be able to build a photon detector with 92% efficiency and neglegible dark current".

I was describing what the standard detection theory says, what are the counts and what is the difference between <[G]> and <[C]>. You keep bringing up same didactic toy models and claims, taken in the most literal way.

The shorthand "correlation" function for <[G]> in Quantum Optics is just that. You need a grain of salt to translate what it means in terms of detector counts (it is standard QO reconstruction of <[G]> from the measurement of the count correlation observable <[C]>). It is not a correlation function of any counts -- [G] is not an observable which measures correlations in photo-electron counts. It is an observable which is measured by reconstruction of such observable [C], the count correlation observable (see [4] for distinctions).

The [G] is defined by taking [C] and commuting all field amplitude operators A+ to the left and all A to the right. The two, [C] and [G] are different observables. <[C]> is measured directly as the correlation among the counts (the measured photocurrents approximate the "ideal" photo-electron counts assumed in [C]). Then the <[G]> is reconstructed from <[C]> through the standard QO subtractions procedures.

As a rough shorthand one can think of <[G]> as a correlation function. But [G] is not a correlation observable of anything that can be counted (that observable is [C]). So one has to watch how far one goes, with such rough shorthand, otherwise one may end up wondering why the "counts" which correlate as <[G]> says they ought to, come out negative. They don't. There are no such "G counts" since [G] isn't a genuine correlation observable, thus <[G]> is not a genuine correlation function. You can, of course, rewrite it purely formally as a correlation of some abstract G_counts, but there is no direct operational mapping of these abstract G_counts to anything that can be counted. In contrast, for the observable [C] which is defined as a proper correlation observable of the photo-electron counts, the kind of counts you can assign operational meaning to (i.e. map to something which can be counted -- the photo-electrons, or approximately their amplified currents) the correlation function <[C]> has no such problems as the puzzling non-classical correlations or the mysterious negative counts.

nightlight

Oct11-04, 10:49 AM

vanesch Look at the general formulation of the path integral (a recent exposition is by Zee, but any modern book such as Peskin and Schroeder, or Hatfield will do).
The integral clearly contains the FULL nonlinear dynamics of the classical fields.

You may be overinterpreting the formal path integral "solutions" here. The path integral computes the Green functions of the regular QFT (the linear evolution model in Fock space with its basis from the linearized classical theory), and not (explicitly) the nonlinear classical fields solution. The multipoint Green function is a solution only in the sense of approximating the nonlinear solution via the multipoint collisions (of quasiparticles; or what you call particles such as "photons", "phonons" etc) while the propagation between the collisions is still via the linear approximations of the nonlinear fields, the free field propagators. The collisions merely re-attach the approximate free (linearized) propagators back to the nonlinear template, or as I labeled it earlier, it is a piecewise linear approximation (for a funny tidbit on this, check L.S. Schulman "Techniques and applications of Path Integration" Wiley 1981; pp 39-41, the Appendix for the WKB chapter, where a bit too explicit re-attachment to the classical solution is labeled "an embarrassment to the purist"). If you already have the exact solutions of the classical nonlinear fields problem, you don't need the QFT propagators of any order at all.

For example, the Barut's replication of QED radiative corrections in his nonlinear fields model purely as the classical solution effects, makes redundant the computation of these same effects via the QED expansion and propagators (to say nothing of making a whole lot more sense). You can compute the QFT propagators if you absolutely want to do so (e.g. to check the error behavior of the perturbative linearized approximation). But you don't need them to find out any new physics that is missing in the exact solutions of the nonlinear classical fields that you already have.

Note also that path integrals and the Feynman diagrams with their 'quasiparticle' heuristic/mnemonic imagery are pretty standard approximation tool for many nonlinear PDE systems outside of the QFT, and even outside of physics (cf. R.D. Mattuck "A Guide to Feynman Diagrams in the Many-Body Problem" Dover 1976; or various math books on nonlinear PDE systems; Kowalski's is just one general treatment of that kind where he emphasized the linearization angle and the connection to the Backlund transformation and inverse scattering methods (http://cul.arxiv.org/abs/hep-th/9212031), which is why I brought him up earlier).

vanesch

Oct11-04, 01:15 PM

As a rough shorthand one can think of <[G]> as a correlation function. But [G] is not a correlation observable of anything that can be counted (that observable is [C]). So one has to watch how far one goes, with such rough shorthand, otherwise one may end up wondering why the "counts" which correlate as <[G]> says they ought to, come out negative.

My opinion is that you make an intrinsically simple situation hopelessly complicated. BTW, |<psi2| O | psi1>|^2 and |<psi2| :O: |psi1>|^2 are both absolute values squared of complex numbers, so are both positive definite. Hence the normal ordering cannot render G negative.

Nevertheless, this stimulated me to have another look at quantum field theory, which I thought was locked up in particle physics. But I think I'll bail out of this discussion for a while until I'm better armed to tear your arguments to pieces :devil: :devil:

cheers,
Patrick.

vanesch

Oct11-04, 01:28 PM

The multipoint Green function is a solution only in the sense of approximating the nonlinear solution via the multipoint collisions (of quasiparticles; or what you call particles such as "photons", "phonons" etc) while the propagation between the collisions is still via the linear approximations of the nonlinear fields, the free field propagators.

No, the multipoint green function IS the path integral with the full nonlinear solution and all the neighboring non-solutions. It is its series development in the interaction constants (the Feynman graphs) what you seem to be talking about, not the path integral itself.

But I will tell you a little secret which will make you famous if you listen carefully. You know, in QCD, the difficulty is that the series development in the coupling constant doesn't work well at "low" energies (however, it works quite well in the high energy limit). Now, the stupid lot of second quantization physicists are doing extremely complicated things in order to try to get a glimpse of what might happen at low energies. They don't realise that it is sufficient to solve a classical non-linear problem. If they would realise this, they would be able to simplify enormously the calculations, because you could then apply finite-element techniques. That would then allow them to calculate nuclear structure without any difficulty ; compared to what they try to do right away, it would be easy. So, hint hint, solve the classical non-linear problem of the fields, say, for a 3 up quarks and 3 down quarks and you'll find... deuterium !! :rofl:

cheers,
Patrick.

nightlight

Oct11-04, 03:33 PM

vanesch No, the multipoint green function IS the path integral with the full nonlinear solution and all the neighboring non-solutions. It is its series development in the interaction constants (the Feynman graphs) what you seem to be talking about, not the path integral itself.

Formally the path integral with full S contains implicitly the full solution of the nonlinear PDE system, just as the symbolic sum from 0 to infinity of Taylor series is formally the exact function. But each specific multipoint G is only a scattering matrix type piecewise linearization of the exact nonlinear problem. The multipoint Green function approximates the propagation between the collisions using the free field propagators (which are only the solutions of the linearized approximation of the nonlinear equation, but they're not the solutions of the exact nonlinear equation) while the interaction part, the full nonlinear system, is "turned on" only for the finite number of points (and in their infinitesimal vicinity), as in the scattering theory (this is all explicit in the S matrix formulations of QED).

That is roughly analogous to each x^n term of Taylor series approximating some function f(x) with the next higher polynomial, where the full function f(x) is "turned on" only in the point x=0 and its "infintesimal" vicinity to obtain the needed derivatives.

So, hint hint, solve the classical non-linear problem of the fields, say, for a 3 up quarks and 3 down quarks and you'll find... deuterium !!

Before deciding that solving a general equations of interacting nonlinear QCD fields exactly is a trivial matter, why don't you try a toy problem of 3 simple point particles with simple Newtonian gravitational interaction and given masses m1, m2, m3 and positions r1, r2, r3. It is an infinitely simpler problem than the QCD nonlinear fields problem, so maybe, say in ten minutes, you could come back and give us the exact three body problem solution in closed form in the parameters as given? Try it, it ought to be trivial. I'll check back to see the solution.

Note also that even the solutions to the much simpler nonlinear coupled Maxwell-Dirac equations in 3+1 or even reduced dimensions hasn't budged an inch (in terms of getting exact solutions) for decades of pretty good mathematicians banging their heads against it. That's why physicists invented the QED expansion, to at least get some numbers out of it. Compare Barut's QED calculations to the conventional QED calculations of the same numbers and see which is easier and why it wasn't done via the nonlinear equations. The nonlinear field approach is only a conceptual simplification, not a computational one. The computational simplification was the QED.

nightlight

Oct11-04, 03:35 PM

vanesch My opinion is that you make an intrinsically simple situation hopelessly complicated. BTW, |<psi2| O | psi1>|^2 and |<psi2| :O: |psi1>|^2 are both absolute values squared of complex numbers, so are both positive definite. Hence the normal ordering cannot render G negative.

It is not <[G]> that is being made negative (just as in the superposition example (a), it wasn't C that was made negative). What I said is that if you take <[G]> and re-express it formally as if it were an actual correlation function of some fictitious/abstract "G_counts" (i.e. re-express it in the form of a sum or an integral of the products GN1*GN2... over the sequence of time intervals/coincidence windows), it is these fictitious G_Counts, the GN's, that may have to become negative if they were to reproduce <[G]> (which in turn is reconstructed from measured <[C]>, the real correlation function) for some density operators (such as PDC). This is not an inherent problem of definition of <[G]> or its practical use (since nothing is counted as GN's, they're merely formal variables without any operational meaning), but it is a common mixup in the operational interpretation of Glauber/QO correlations (which mixes up the genuine correlation observable [C] with the Glauber's pseudo-correlation observable [G]).

This is the same type of negative probability on abstract counts as in the interference (a) example where, if you were to express the combined source count formally as a sum of fictitious counts ie. C=G1+G2, then some of these fictitious counts may have to be negative (see the earlier msg) to reproduce the measured C. The C is itself is not negative, though.

But I think I'll bail out of this discussion for a while ...

I am hitting a busy patch in my day job, too. It was fun and it helped me clear up few bits for myself. Thanks for the lively discussion, and to all the other participants as well.

nightlight

Oct12-04, 03:39 AM

MiGUi

Oct12-04, 06:03 AM

How we can be sure that we send only one electron, and then the diffraction makes the interference pattern?

vanesch

Oct12-04, 06:05 AM

vanesch
Your mixup here may be between the "full nonlinear solution" of the Langrangian in the S of the path integral (which is a single classical particle dynamics problem, a nonlinear ODE) and the full nonlinear solution of the classical fields (nonlinear PDE).

And I was not going to respond... But I can't let this one pass :tongue:

The QED path integral is given by:
(there might be small errors, I'm typing this without any reference, from the top of my head)

Lagrangian density:

L = -1/4 F_uv F^uv + psi-bar (D_mu gamma^mu + m) psi

(I don't remember if it is m or m^2 in this way of writing...)

with D_m the covariant derivative: D_mu = d_mu - q A_mu

Clearly, this is the lagrangian density which gives you the coupled Maxwell-Dirac equations if you work out the Euler-Lagrange equations. Note that these are the non-linear PDE you are talking about, no ?
(indeed, the coupling is present through the term A in D_m)

the action is defined:

S[A_mu,psi] = Integral over spacetime (4 coordinates) of L, given a solution (or non-solution) of fields A_mu and psi.

S is extremal if A_mu and psi are the solutions to your non-linear PDE.

Path integral for an n-point correlation function (I take an example: a 4-point function, which is taken to be a positron-anti positron field and two photon fields, for instance corresponding to the pair annihilation ; but also Compton scattering - however, it doesn't matter what it represents in QED ; it is just the quantum amplitude corresponding to a product of 4 fields)

<0| psibar[x1] psi[x2] A[x3] A[x4] |0> = Path integral over all possible field configurations of A_m and psi of {Exp[ i / hbar S] psibar[x1] psi[x2] A[x3] A[x4]}

For the classical solution, the path integral reduces to one single field configuration, namely the classical solution psi_cl[x] and A_cl[x], and we find of course that the 4-point correlation function is then nothing else but
psi_cl[x1] psi_cl[x2] A_cl[x3] A_cl[x4] (times a phase factor exp(iS0) with S0 the action when you fill in the classical solution). This classical solution is the one that makes S extremal, and hence for which the psi_cl and A_cl obey the non-linear PDE which I think you propose.
But the path integral also includes all the non-solutions to the classical problem, with their phase weight, and it is THAT PROBLEM which is so terribly hard to solve and for which not much is known except series devellopment, given by Feynman diagrams. If it were only to find the classical solution to the non-linear PDE, it would be peanuts to solve :biggrin:.

Now, there is one thing I didn't mention, and that is that because of the fermionic nature of the dirac field, their field values aren't taken to be 4-tuples of complex numbers at each spacetime point, but taken to be anticommuting Grassman variables ; as such indeed, the PDE is different from the PDE where the dirac equation takes its solutions as complex fields. You can do away with that, and then you'd have some kind of bosonic QED (for which the quantum case falls on its face due to the spin-statistics theorem, but for which you can always find classical solutions).

But it should now be clear that the non-linear PDE that you are always talking about IS FULLY TAKEN INTO ACCOUNT as a special case in the path integral.

cheers,
patrick.

PS: I could also include nasty remarks such as not to confuse pedagogical introductions to the path integral with the professional use by particle physicists, but I won't :devil: :rofl:

EDIT: there were some errors in my formulas above. The most important one is that the correlation is not given by the path integral alone, but that we also have to devide by the path integral of exp(iS) without extra factors (that takes out the factor exp(iS0) I talked about.
The second one is that one has a path integral over psi, and an independent one over psi-bar as if it were an independent variable. Of course, for the classical solution it doesn't change anything.
Finally, x1, x2, x3 and x4 have to be in time order. Otherwise, we can say that we are taking the correlation of the time-ordered product.

Ian

Oct12-04, 09:14 AM

ZapperZ

Oct12-04, 09:32 AM

Wouldn't it be easier to think of the electron in Young's experiment as a 'speedboat' passing through the vacuum, but that also generates a wave in the same way as a boat does on water.
What would the result be if you used a ripple tank and water to recreate Young's experiment? And how would we interpret it?

We know what happens when an electron (or any charge particles) generates a wake. The double-slit result is NOT due to a wake.

Zz.

vanesch

Oct12-04, 10:33 PM

But it should now be clear that the non-linear PDE that you are always talking about IS FULLY TAKEN INTO ACCOUNT as a special case in the path integral.

I would like to add that the classical solution has often the main contribution to the path integral, because the classical solution makes S stationary, which means that up to second order, all the neighboring field configurations (which are non-solutions, but are "almost" solutions) have almost the same S value and hence the same phase factor exp(iS). They add up constructively in the pathintegral as such. If the fields are far from the classical solution, their neighbours will have S values which change in first order and hence they have different phase factors, and tend to cancel out.
So for certain cases, it can be that the classical solution gives you a very good approximation (or even the exact result, I don't know) to the full quantum problem, especially if you limit yourself to a series devellopment in the coupling constant. It can then be that the first few terms give you identical results. It is in that light that I see Barut's results.

cheers,
Patrick.

vanesch

Oct12-04, 10:57 PM

nightlight

Oct13-04, 02:41 AM

vanesch
<0| psibar[x1] psi[x2] A[x3] A[x4] |0> = Path integral over all possible field configurations of A_m and psi of {Exp[ i / hbar S] psibar[x1] psi[x2] A[x3] A[x4]}

Thanks for clearing up what you meant. I use term "path integral" when the sum is over paths and "functional integral" when it is over the field configurations. The Feynman's original QED formulation was in terms of the "path integrals" and no new physics is being added to it by re-expressing it in an alternative formalism, such as the "functional integrals" (just as the path integral formulation doesn't add any new physics to the canonically quantized QED or to S matrix formalism).

Therefore the state evolution in Fock space generated by the obtained multipoint Green functions is still piecewise linearized evolution (the linear sections are generated by the Fock space H) with the full interaction being turned on only within the infinitesimal scattering regions. If you a nice physical picture, though, of what goes on here in terms your favorite formalism, I wouldn't mind learning something new.

It is important to distinguish here that even though the 2nd quantization by itself doesn't add any new physics (being a general purpose linearization algorithm used in various forms in many other areas, an empty mathematical shell like Kowalski's Hilbert space linearization (http://cul.arxiv.org/abs/solv-int/9801018) or, as Jaynes (http://bayes.wustl.edu/etj/age.14mo.html) put it, like Ptolomean epicycles (http://bayes.wustl.edu/etj/articles/scattering.by.free.pdf)) that wasn't already present in the nonlinear fields, the new physics can be (and is likely being) added that wasn't present in the initial nonlinear fields model within the techniques working out the details of the scattering (in S matrix imagery), since in QED these techniques were tweaked over the years to fit the experimental data. Obviously, this new physics distilled from the experiments and absorbed into the computational rules of QED, is by necessity in a form given to it by the 2nd quantization formalism they were fitted into. The mathematical unsoundness and logical incoherence of the overall scheme as it evolved only aided its flexibility, to better wrap around whatever experimental data that turned up.

That is why it is likely that Barut's self-fields are not the whole story, the most notable missing pieces being the charge quantization and the electron localization (not that QED has an answer other than 'that's how it is and the infinities hocus-pocus go away'). In principle, had the nonlinear classical fields been the starting formalism instead of the 2nd quantization (in fact they were the starting formalism and the most natural way to look at the Maxwell-Schroedinger/Dirac equations, and that's how Schroedinger understood it from day one), all the empirical facts and new physics accumulated over the decades would have been incorporated into it and would have had a form appropriate to that formalism e.g. some additional interaction terms or new fields in the nonlinear equations. But this kind of minor tweaking is not where the physics will go; it's been done and that way can go only so far. My view is that Wolfram's NKS (http://www.wolframscience.com/) points in the direction of the next physics, recalling especially the Toffoli's (http://pm1.bu.edu/~tt/publ.html) cellular automata modelling of physics (note that his archive hyperlink (http://kh.bu.edu/qcl/) is wrong on his home page; see for example how the relativistic time dilatation comes out as a property of the plain random walk (http://kh.bu.edu/qcl/pdf/toffolit199064697e1d.pdf)) and Garnet Ord's interesting models (http://www.scs.ryerson.ca/~gord/) (which reproduce the key Maxwell, Dirac and Schroedinger equations as purely enumerative and combinatorial properties of plain random walks, without using imaginary time/diffusion constant; these can also be re-expressed in the richer modelling medium of cellular automata and the predator-prey eco networks, where they're much more interesting and capable). Or another little curiosity, again from a mathematician, Kevin Brown (http://www.mathpages.com/), showing the relativistic velocities addition formulas as a simple enumerative property of set unions and intersections (http://www.mathpages.com/home/kmath216/kmath216.htm).

But it should now be clear that the non-linear PDE that you are always talking about IS FULLY TAKEN INTO ACCOUNT as a special case in the path integral.

The "fully taken into account" is in the same sense that Taylor or Fourier series cofficients "fully take into account" the function the series is trying to approximate. In either situation, you have to take fully into account, explictly or implicitly, that which you are trying to approximate. How else could the algorithm know it isn't approximating something else. In the functional integrals formulation of QED, this tautological trait is simply more manifest than in the path integrals or the canonical quantization. There is thus nothing nontrivial about this "fully taking into account" tautological phenomenon you keep bringing up.

If there is anything it does for the argument, this more explicit manifestation of the full nonlinear dynamics only emphasizes my view, by pointing more clearly what is it at all that the algorithm is trying to ultimately get at, what is the go of it. And there it is.

But the path integral also includes all the non-solutions to the classical problem, with their phase weight,

If you approximata a parabola with a Fourier series, you will be including (adding) a lot of functions which are not even close to parabola. It doesn't mean that all this inclusion of non-parabolas amounts, after all is said and done, to anything more than what was already contained in the parabola. In other words, the Green functions do not generate in the Fock space the classical nonlinear PDE evolution but only a series of the piecewise linearized approximations of it, none of which is the same as the nonlinear evolution (note also that obtaining a Green function could be generally more useful in various ways than just having one classical solution of the nonlinear system). This kind of overshoot/undershoot busywork is a common trait of approximating.

nightlight

Oct13-04, 03:16 AM

vanesch

Oct13-04, 03:29 AM

Therefore the state evolution in Fock space generated by the obtained multipoint Green functions is still piecewise linearized evolution (the linear sections are generated by the Fock space H) with the full interaction being turned on only within the infinitesimal scattering regions. If you a nice physical picture, though, of what goes on here in terms your favorite formalism, I wouldn't mind learning something new.

You seem to have missed what I pointed out. The "piecewise linearised evolution" is correct when you consider the PERTURBATIVE APPROXIMATION of the functional integral (you know, in particle physics everybody calls it the path integral) using Feynman diagrams. Feynman diagrams (or, for that matter, Wick's theorem) are a technique to express each term in the series expansion of the FULL CORRELATION FUNCTION as combinations of the FREE CORRELATION FUNCTIONS, which are indeed the exact solutions to the linear quantum field parts. But I wasn't talking about that. I was talking about the full correlation function itself. That one doesn't have any "piecewise linear approximations" in it, and contains the FULL DYNAMICS. Only, except in special circumstances, nobody knows how to solve that problem directly, but the quantity itself is no approximation or contains no linearisation at all, and contains, as a very special case, the full nonlinear classical solution - I thought that my previous message made that clear.
There are some attempts (which work out better and better) to tackle the problem differently than by series development, such as lattice field theory, but it requires still enormous amounts of CPU power, as compared to nonlinear classical problems such as fluid dynamics. I don't know much about these techniques myself, but there are some specialists here around. But in all cases, we try to solve the same problem, which is a much more involved problem than the classical non-linear field equations, namely calculate the full correlation functions as I wrote them out.

If you take your opinions and information from the sixties, indeed, you can have the impression that QFT is a shaky enterprise for which you change the rules as data come in. At a certain point, it looked like that. However, by now, it is on much firmer grounds (although problems remain). First of all, the amount of data which is explained by it has exploded ; 30 years of experimental particle physics confirm the techniques. If it were a fitting procedure, that would mean that by now we'd have thousands of different rules to apply to fit the data. It isn't the case. There are serious mathematical problems too, if QFT is taken as a fundamental theory. But not if you suppose that there is a real high energy cutoff determined by what will come next. And all this thanks to second quantization :tongue:

cheers,
Patrick.

vanesch

Oct13-04, 03:31 AM

In physics and mathematics the facts and logic have to stand or fail on their own merits. Give them a link here if you need help, let them read the thread, let them check and pick apart the references, and then 'splain it to me how it really works.

Well, you could start by reading the article of the experiment by Thorn
:tongue2:

cheers,
Patrick.

EDIT: Am. J. Phys. Vol 72, No 9, September 2004.
They did EXACTLY the experiment I proposed - don't forget that it is my mind who can collapse any wavefunction :rofl: :rofl:

The experiment is described in painstaking detail, because it is meant to be a guide for an undergrad lab. There is no data tweaking at all.

They use photodetectors with QE 50% and 250 counts per second dark current.

They find about 100.000 cps triggers of the first photon, and about 8800 cps triggers of coincidences between the first and one of the two others, within time coincidence window of 2.5 nanoseconds.

The coincidences are hardwired logic gates which count.
If the first photon clicks are given by N_G, the two individual coincidences between trigger (first photon and second photon left or right) are N_GT and N_GR and the triple coincidence N_GTR, then they calculate (no subtractions, no efficiency corrections nothing):

g(2)(0) = N_GTR N_G / (N_GT N_GR)

In your model, g(2) has to be bigger than 1.

They find: 0.0177 +/- 0.0026 for a 40 minute run.

Now given the opening window of 2.5 ns and the rates of the different detectors, they also calculate what they expect as "spurious coincidences". They find 0.0164.
Now if that doesn't explain nicely the full anticorrelation as I told you, I don't know what will ever do so.

nightlight

Oct13-04, 03:46 AM

vanesch Ok, I asked the question on sci.physics.research and the answer was clear, not only about the quantum prediction (there IS STRICT ANTICORRELATION), but also about its experimental verification. Look up the thread "photodetector coincidence or anticoincidence" on s.p.r.

I just checked, look the kind of argument he gives:

But for this, look at Davis and Mandel, in _Coherence and Quantum Optics_ (ed. Mandel and Wolf, 1973). This is a very careful observation of ``prompt'' electrons in the photoelectric effect, that is, electrons emitted before there would be time, in a wave model, for enough energy to build up (even over the entire cathode!) to overcome the potential barrier. The experiment shows that the energy is *not* delivered continuously to a photodetector, and that this cannot be explained solely by detector properties unless one is prepared to give up energy conservation.

This is the Old Quantum theory (the Bohr's atom era) argument for Einstein's 'light quantum'. The entire photoeffect is fully within the semiclassical model -- the Schroedinger atoms interacting with the classical EM waves. Any number you can pull out of the QED/Quantum Optics on this, you can get from the semiclassical model (usually much easier, check ref's [1] & [2] on detector theory to see the enormous difference in the efforts to reach the same result). The only thing you won't get is a lively story about a "particle" (but after all the handwaving, there won't be any number out of all that 'photon' particle ballyhoo). And, of course, you won't get to see the real photons, shown clearly as a day in the Feynman diagrams.

What a non-starter. Then he quotes the Grangier, et al, 1986 paper I told you myself to check out.

nightlight

Oct13-04, 06:16 AM

vanesch Well, you could start by reading the article of the experiment by Thorn

Abstract: "We observe a near absence of coincidence counts between the two detectors—a result inconsistent with a classical wave model of light, "

I wonder if they tested against the Marshall-Santos classical model (with ZPF) for the PDC which covers any multipoint coincidence experiment you can do with PDC source, plus any number of mirrors, lenses, splitters, polarizers,... (and any other linear optical elements) with any number of detectors. Or was it just the usual strawman "classical model".

Even if I had AJP access, I doubt it would have been worth the trouble, considering the existence of general results for the thermal, laser and PDC sources, unless they explictly faced head on the no-go result of Marshall-Santos and have shown how their experiment gets around it. It is easy to fight and "win" if you get to pick the opponent (the usual QO/QM "classical" caricature), while knowing that no one will challenge your pick since the gatekeepers is you.

You can't, not even in principle, get any measured count correlation (which approximates the expectation value <[C]>, where [C] is the observable for the correlations in the numbers of photo-electrons ejected on multiple detectors; see ref [1] & [4] in the detector theory message) in Quantum Optics which violates classical statistics. That observable (the photo-electron counts correlations) has all counts strictly non-negative (they're proportional to the EM field intensity in the photo-detection area) and the counts are in the standard correlation form, Sum(N1[i]*N2[i]), same form as Bell's LHVs. Pure classical correlation.

You can only reconstruct the Glauber's pseudo-correlation function from the measured count correlation observable (via the Glauber's prescription for subtractions of vacuum generated modes, the standard QO way of coincidence "counting") -- and it is that recontructed function <[G]>, if you were to express it formally as a correlation function of some imaginary G_Counts, that is write it formally as: <[G]> = Sum(GN1[i]*GN2[i]), which would show that some of these G_Counts (the GN's) would need to be negative (because for the PDC the standard Glauber QO "counting" prescription, equivalent to subtracting the effects of vacuum generated modes, over-subtracts here, since the PDC pair actually uses up the phase-matching vacuum modes). The G_Counts have no direct operational meaning, there is no G_Count detector which counts these. There is not even a design for any such (Glauber's 1963 QO founding papers suggests a single atom might do it, although he stopped short of calling for the experimenters to hurry up and make one like that).

Note that for a single hypothetical "photon" counter device these G_Counts would be the value of the "pure incident" photon number operator, and as luck would have it, the full quantum field photon number operator, which happens to be a close relative of the one the design calls for, is none other than a Hermitean operator in the Fock space, thus it is an "observable", which means it is observable, which, teacher adds, this means kids that this photo-detector we have right here, in our very own lab, gives us the counts which are the values of this 'pure incident photon number observable' { the "pure incident" photons, interacting with the detector's atoms, are imagined in this "photon counter" concept, as somehow separated out from all the vacuum modes, even from those vacuum modes which are superposed with the incident EM field, not by any physical law or known data, but by the sheer raw willpower of the device designer, Glauber: "they [vacuum modes] have nothing to do with the detection of photons" and presto! the vacuum modes are all gone, even the superposed ones, miracle, Halleluiah, Praise the Almighty.} The G_Counts are a theoretical construct, not something any device actually counts. And it certainly is not what the conventional detectors (of the AJP article experiment) did -- those counted as always, or at least since 1964, just the plain old boring classical [C], the photoelectron counts correlation observable.

The photo-electron counts correlation observable [C], the one their detectors actually report as the count correlation <[C]> (and which is approximately measured as the correlation of the amplified photo-curents; see [1],[2],[4]) is fully 100% classical, no negative counts required, no non-classical statistics required to explain anything they can ever show.

nightlight

Oct13-04, 07:17 AM

vanesch But I wasn't talking about that. I was talking about the full correlation function itself. That one doesn't have any "piecewise linear approximations" in it, and contains the FULL DYNAMICS. Only, except in special circumstances, nobody knows how to solve that problem directly, but the quantity itself is no approximation or contains no linearisation at all, and contains, as a very special case, the full nonlinear classical solution - I thought that my previous message made that clear.

I know what you were saying. The question is, for these few exactly solvable toy models, where you can get the exact propagator (which would have to be a non-linear operator in the Fock space) and compute the exact classical fields evolution -- do the two evolutions differ at all?

This is just a curiosity, but it is not a decisive matter regarding the QED or QCD. Namely, there could be conceivably a toy model where the two evolutions differ, since it is not given from above that any particular formalism (which is always a huge generalization of the empirical data) has to work correctly in all of its farthest reaches. More decisive would be to see whether Barut's type model could replicate QED prediction to at least another order or two, and if not whether the experiment can pick one or the other.

If you take your opinions and information from the sixties,

Wait a minute, that's the lowliest of the lowest lows:)

indeed, you can have the impression that QFT is a shaky enterprise for which you change the rules as data come in.

Jaynes had for his PhD advisor Eugene Wigner and for decades was in the circle and was a close friend of the names the theorems and models and theories were named after in the QED textbooks . Read what he said till well into the 1990s. In comparison, I would be classified as a QED fan.

And all this thanks to second quantization

Or, maybe, despite of it. I have nothing against it as an effective algorithm, unsightly as it is. Unfortunately too much physics has been ensnared into its evolving computational rules, largely implicitly, for anyone to be able to disentangle it out and teach the cleaned up leftover algorithm in the applied math class. But it shouldn't be taken as a sacred oracle, a genuine foundation or a way to go.

nightlight

Oct13-04, 10:51 AM

vanesch The "piecewise linearised evolution" is correct when you consider the PERTURBATIVE APPROXIMATION of the functional integral (you know, in particle physics everybody calls it the path integral) using Feynman diagrams. Feynman diagrams (or, for that matter, Wick's theorem) are a technique to express each term in the series expansion of the FULL CORRELATION FUNCTION as combinations of the FREE CORRELATION FUNCTIONS, which are indeed the exact solutions to the linear quantum field parts.

Re-reading that comment, I think you too ought to pause for a moment and step back a bit and connect the dots you already have in front of you. I will just list them since there are several longer messages in this thread, with an in depth disscussion on each one with a hard fought battle back and forth, where each point took your and other contributors' best shots. And you can read them back, in the light of the totality listed here (and probably as many lesser dots I didn't list), and see what the outcome was.

a) You recognize here that the QED perturbative expansion is a 'piecewise linear approximation'. The QED field amplitude propagation can't be approximating another piecewise linear approximation, or linear fields. And each new order of the perturbation invalidates the previous order approximation as a possible candidate for the last and the exact evolution. Therefore, there must be a limiting nonlinear evolution, not equal to any of the orders of QED, thus an "underlying" (at the bottom) nonlinear evolution (of QED amplitudes in coordinate basis) being approximated by the QED perturbative expansion, which is (since nothing else is left of all the finite orders of QED expansion, each is invalid, thus not the last word) "some" local classical nonlinear field theory (we're not interpreting what this limit-evolution means, but just establishing its plausible existence).

b) You also read within the last ten days at least some of the Barut's results on radiative corrections, including the Lamb shift, the crown jewel of QED. There ought to be no great mystery then, what could it be, what kind of nonlinear field evolution is it that QED amplitudes are actually piecewise linearizing.

c) What is the most natural thing, say a classical mathematician, would have considered if someone had handed him Dirac and Maxwell equations and told him: here are our basic equations, what ought to be done. Would he consider EM field potential A occurring in Dirac equation external, or the Dirac currents in the Maxwell's equations as external? Or would he do exactly what Schroedinger, Einstein, Jaynes, Barut... thought needs to be done and tried to do -- see them as set of coupled nonlinear PDEs to be solved?

d) Oddly that this most natural and conceptually the simplest way to look at these classical field equations, nonlinear PDEs, fully formed in 1920s, already had the high precision result of Lamb shift in it, with nothing that had to be added or changed in them (all it needed was someone to carry out the calculations for a problem already posed along with the equations, the problem of H atom) -- it had the experimental fact which would come twenty years later.

e) In contrast, the Dirac-Jordan-Heisenberg-Pauli Quantum theory of EM fields at the time of the Lamb shift discovery (1947), a vastly more complex edifice, failed the prediction, and had to be reworked thorughly in the years after the result, until Dyson's QED finally had managed to put all the pieces together.

f) The Quantum Optics may not have the magic it shows off with. Even if you haven't got yet to the detector papers, or the Glauber's QO foundation papers, you at least should have the grounds for rational doubt and more questions, what is really being shown by these folks? Especially in view of dots (a)-(e) which imply the Quantum Opticians may be wrong, overly enthusiastic with their claims.

g) The point (f), considering that the plain classical nonlinear fields, the Maxwell-Dirac equations, already had the correct QED radiative corrections right from the start, and these are much closer to the core of QED, they're its crown jewels, couple orders beyond the orders at which the Quantum Optics operates (which is barely at the level of the Old QED).

h) In fact, the toppled Old QED (e), has already all that Quantum Optics needs, including the key of Quantum Magic, the remote state collapse. Yet that Old QED flopped and the Maxwell-Dirac worked. Would it be plausible that for the key pride of QED predictions, the Lamb shift, the one which toppled the Old QED, the Maxwell-Dirac just got lucky. What about (b) & (c), lucky again that QED appears to be approximating it, in the formalism through several orders, and well beyond the Quantum Optics level, as well? All just luck? And that Maxwell-Dirac nonlinear fields are the simplest and the most natural approach (d)?

i) The Glauber's correlations <[G]>, the standard QO "correlations" may not be what they are claimed to be (correlating something being literally and actually counted). Its flat-out vacuum removal procedures are over-subtracting whenever there is a vacuum generated mode. And this is the way the Bell test results are processed.

j) The photo-detectors are not counting "photons" but are counting photo-electrons and the established non-controversial detector theory neither shows nor claims any non-classical photo-electron count results (it is defined as a standard correlation function with non-negative p-e counts). Entire nonclassicality in QO comes from the reconstructed <[G]>, which doesn't correlate anything literally and actually being counted (the <[C]> is what is being counted). Keep also in mind dots (a)-(i)

k) The Bell theorem tests seem to be stalled for over three decades. So far they have managed to exclude only the "fair sampling" type local theories (none of such theories ever existed). The Maxwell-Dirac, the little guy from (a)-(j) which does happen to exist, is not a "fair sampling" theory, and more embarrassingly, it even predicts perfectly well what the actual counting data show and agrees perfectly with the <[C]> correlations, the photo-electron counts correlations, which is what the detectors actually and literally produce (within the photo-current amplification error limits).

l) The Bell's QM prediction is not a genuine prediction, in the sense of giving the range of its own accuracy. It is a toy derivation, a hint for someone to go and do full QO/QED calculation. Indeed such calculations exist, and if one removes <[G]> and simply leaves it at its bare quantitative prediction of detector counts (which would match fairly well the photo-electron counts obtained), the QO/QED predicts the obtained raw counts well and does not predict violation either. There is no prediction of detector counts (the photo-electron counts, the stuff that detectors actually count), not even in principle and not with the most ideal photo-electron counter conceivable, even with 100% QE, which would violate Bell's inequality. No such prediction and it cannot be deduced even in principle for anything that can be actually counted.

m) The Bell's QM "prediction" does require remote non-local projection/collapse. Without it can't be derived.

n) The only reason we need collapse at all is the allegedly verified Bell's QM prediction saying we can't have LHVs. Otherwise variables could have values (such as Maxwell-Dirac fields), just not known, but local and classical. The same lucky Maxwell-Dirac of the other dots.

o) Without the general 'global non-local collapse' postulate, Bell could not get state of particle (2) to become |+> for the sub-ensemble of particle (2) instances, for which the particle (1) gave (-1) result (and he does assume he can get that state, by Gleason's theorem by which the statistics determines the state; he assumes statistics of |+> state on the particle 2 sub-ensemble for which the particle 1 gave -1). Isn't it a bit odd that to deduce non-local QM prediction one needs to use non-local collapse as a premise? How could any other conclusion be reached, but the exclusion of locality, with the starting premise of non-locality?

p) Without collapse postulate, no Bell's QM prediction, thus no measurement problem (the Bell's no-go for LHV), thus no reason to keep collapse at all. The Born rule as an approximate operational rule would suffice (e.g. the way a 19th century physicist might have defined it for the light measurements: the incident energy is proportional to photocurrent, which is correct empirically and theoretically, the square law detection).

q) The Poissonian counts of photo-electrons in all Quantum Optics experiments preclude Bell's inequality violation ever in photon experiments. The simple classical model, the same Maxwell-Dirac from (a)...(p) points, the lucky one, predicts somehow exactly what you actually measure, the detector counts, with no need for untested conjectures or handwaving or euphemisms, all it uses is the established detector theory (QED based or Maxwell-Dirac based) and a model of an unknown but perfectly existent polarization. And it gets lucky again. While the QO needs to appologize and promise yet again, it will get it just as soon as the detectors which count Glauber's <[G]> get constructed, soon, no question about it.

r) Could it be all luck for Maxwell-Dirac? All the points above, just dumb luck? And the non-linear fields actually don't contradict any QED quantitative prediction, in fact agree to an astonishing precision with QED. QED amplitude evolution even converges to Maxwell-Dirac, as far as anyone can see and as precisely as anything that gets measured in this area. The Maxwell-Dirac disagrees only with the collapse postulate (the general non-local projection postulate), for which there is no empirical evidence, and for which there is no theoretical need of any sort, other than the conclusions it creates by itself (such as Bell's QM prediction or various QO non-classicalities based on <[G]> and collapse).

s) Decades of physicists have banged their heads to figure out how can QM work like that. And no good way out, but multiple universes or observers mind when all shots have been fired and all other QM "measurement theory" defense lines have fallen. It can't be defended with a serious face. That means, no way to solve it as long as the collapse postulate is there, otherwise someone would have thought it up. And the only thing that is holding up the whole of the puzzle is the general non-local collapse postulate. Why do we need it? As an approximate operational rule (as Bell himself advocated in his final QM paper) with only local validity it would be perfectly fine, no puzzle. What does it do, other than to uphold the puzzle of its own making, to earn its pricey keeps? What is that secret invaluable function it serves, the purpose so secret and invaluable that no one knows for sure what it is, to be able to explain it as plainly and directly as 2+2, but everyone believes that someone else knows exactly what it is? Perhaps, just maybe, if I were to dare to wildly conjecture here, there is none?

t) No single or even a few dots above may be decisive. But all of it? What are the odds?

PS: I will have to take at least a few weeks break from this forum. Thanks again to you 'vanesch' and all the folks who contributed their challenges to make this a very stimulating discussion.

vanesch

Oct14-04, 03:14 AM

Ok, you posted your summary, I will post mine and I think that after that I'll stop with this discussion too ; it has been interesting but took quite some time, and the subjects are being worn out in that we now seem to camp on our positions. Also it starts to take a lot of time.

a) Concerning the Lamb shift: it is true that you get it out of the Dirac-Maxwell equations, because now I remember that that was how my old professor did it (I don't find my notes from long ago, they must be at my parents home 1000 km from here, but I'm pretty sure he must have done something like Barut). The name of my old professor is Jean Reignier, he's long retired now (but I think he's still alive).

b) The fundamental reason for "second quantization" (meaning, quantizing fields) was not the Lamb shift of course. It's principal prediction is the existence of electrons (and positrons) as particles. As I said, I don't know of any other technique to get particles out of fields. As a bonus, you also get the photon (which you don't like, not my fault). I think that people tried and tried and didn't manage to get multi-particle-like behaviour out of classical fields. There are of course soliton solutions to things like the Korteweg Devries equation. But to my knowledge there has never been a satisfying solution to multiparticle situations in the case of the classical Dirac-Maxwell equation. Second quantization brilliantly solved that problem, but once done, with the huge mathematical difficulties of the complex machinery set up, how to get nice predictions beyond the obvious "tree level" ? It is here that the Lamb shift came in: the fact that you ALSO get it out of QFT ! (historically of course, they were first, but that doesn't matter).

c) I can be wrong, but I don't think that the classical approach you propose can even solve something like the absorption lines of Helium (a 2-electron system) or another low-count multi-electron atom, EVEN if we allow for the existance of a particle-like nucleus (which is another problem you'll have to solve: there's more to this world than electrons and EM radiation, and if everything is classical fields, you'd have to show me where the nucleus comes from and doesn't leak out).
Remember that you do not reduce to 2-particle non-relativistic QM if you take the classical Dirac equation (but that you do in the case of second quantization). You have ONE field, in which you'll have to produce the 2-particle state in a Coulomb field - I suppose with two bumps in the field that whirl around or I don't know what. I'd be pretty sure you cannot get anything reasonable out of it.

d) Concerning the anticoincidence: come on, you said there wouldn't be anticoincidence of clicks, and you even claimed that quantum theory (as used by professionals, not by those who write pedagogical stuff for students) also predicted that. You went off explaining that I confuse lots of quantities I don't even know what they mean in QO and asked me to show you a single paper where 1) the quantum prediction of anticoincidence was made and 2) the experiment was performed. I showed you (thanks to professor Carlip, from s.p.r.) an article of very recent research (September 2004) where the RAW COINCIDENCE g(2,0) (which is expected in classical maxwell theory to be bigger than 1) is something of the order of 0.017 (much and much better than Grangier and this time with no detector coefficients, background subtraction etc...)
Essentially, they find about 100.000 "first photon" triggers per second, about 8800 coincidences per second between first and one of the two others (so these are the identified pairs), and, hold your breath, about 3 or 4 triple coincidences (of which I said there wouldn't be any) per second, which, moreover are explained as Poissonian double pairs within the coincidence window of about 2.5 ns, but that doesn't matter.
If we take it in classical electromagnetism that both intensity profiles are split evenly by the beam splitter and if the detectors were square law devices responding to these intensities, you'd expect about 200 hits per second for these triple coincidences.
Remember: no background subtractions, no efficiency corrections. These are raw clicks. No need for Glauber or whatever functions. Marbles do the trick!
Two marbles in; one triggers, the other one chooses his way on the beam splitter. If it goes left, a click left (or not) but no click right. If it goes right, a click right (or not) but no click left. Never a click left and right. Well, we almost never see a click left and right. And these few clicks can even be explained by the probability of having 2 pairs of marbles in the pipe.
According to you, first we would never find this anticoincidence as a prediction of "professional" quantum theory, and of course never measure it. Now that we measured it, it doesn't mean anything because you expected so.

e) Once you acknowledge the existence of particles from fields, such as proposed by second quantization, the fair-sampling hypothesis becomes much much more natural, because you realise (or not! depends on the openness of mind) that photodetectors are particle detectors with a finite probability of seeing the particle or not. I acknowledge of course that the EPR like experiments today do not exclude local realistic theories. They are only a strong indication that entanglement over spacelike intervals is true.

f) Nobody believes that QFT is ultimately true, and everybody thinks that something else will come after it. Some think that the strict linearity of QM will remain (string theorists, for instance), while others (like Penrose) think that one will have to do something about it and hopes that gravity will. But I think that simplistic proposals such as classical field theory (with added noises borrowed from QFT or whatever you want to add) are deluded approaches who will fail even before they achieve anything. Nevertheless, why don't you guys continue. You still have a lot of work to do, after all, before it turns into a working theory and get you Nobel prizes (or will go down the drain of lost ink and sweat...). Really, try the helium atom and the hydrogen molecule. If that works, try something slightly more ambitious, such as a benzene molecule. If that also works you are really on the way of replacing quantum theory by classical field physics, so then tackle solid state physics, in the beginning, simply with metals. Then try to work out the photoelectric effect to substantiate all the would be's in your descriptions of how photodetectors work.

g) QFT is not just a numerical technique to find classical field solutions in a disguised way, it solves a quite different problem (which is much more involved). In certain circumstances, however, it can produce results which are close to the classical field solution (after all, there is the correspondence principle which states that QFT goes into the classical theory if h -> 0). I know that in QCD the results don't work out, for instance. People tried it.

cheers,
Patrick.