How Does Counterfactual Computation Work?

[jgraber]

Photons, not puppies

Richard and Kea, well, I do have a subscription to Nature, and the real objects in the actual performed experiment are photons and Pockels cells, of course, not puppies. They even mention "single 670nm photons conditionally prepared by downconversion".They do discuss how to do a similar experiment with trapped ions. They also discuss, but have not performed, or at least do not report, the more advanced experiments of chained, as opposed to single, quantum Zeno effectand of error correction. They do give a diagram of a complex, but apparently feasible, optical setup that would perform the chained quantum Zeno effect with Grovers algorithm.

Careful et al, Quantum experts sometimes say QM is signal-local but not Einstein-local. I interpret this to mean that if you understand locallity as signal-locality, no experiment has or will demonstrate non-locality. If you interpret locality as Einstein-locality, then the EPR-Aspect type experiments have already demonstrated it up to some very quibbly loopholes. (Closing these loopholes will be hard, but I expect it to happen eventually. Proving this impossible would be a big revolution.)

(Understanding the difference between signal-locality and Einstein-locality is sort of a mind blower all by itself, especially that it is really possible to be consistently one without the other.)

Nevertheless, I think signal-locality is closer to what is ordinarily understood by locality than Einstein-locality. Thus you can still say QM is "local". In one variation of this form of language you say EPR-Aspect prove that QM is "contextual" instead of "non-local". Understanding what "contextual" means in this context is another mind-blower. However, it appears that many quantum computer people appear to prefer to say QM is "non-local", but of course they know it is "signal-local". Of course, they use the term "superposition" which can be interpreted to imply non-locality when it is a "simultaneous" superposition of spatially separated states. Take a look at Dave Bacons course and all the mentions of "entanglement and nonlocality".
http://dabacon.org/pontiff/

By the way, I just found Scott Aaronson's blog has a post objecting to the popular press reports. http://www.scottaaronson.com/blog/

At a quick reading, the Nature article never mentions "locality" or "contextuality", but talks a lot about "counterfactual" computing. Of course, they use the term "superposition" which can be interpreted to imply non-locality when it is a "simultaneous" superposition of spatially separated states.

"I'll stop here for now and perhaps post more later about the difference between photons and puppies, and maybe also whether counterfactuality is related to nonlocality.


Jim

 

[rtharbaugh1]

In QFT there is an argument that a measurement at position A cannot
influence a measurement at position B if it's outside the lightcone, see for
instance Peshkin & Schroeder paragraph 2.4 at page 27. Causality requires
every particle to have an anti-particle for the commutator to vanish.

Regards, Hans.

Hi Hans.

So, if we descend the lightcone to the very tip, that is, consider extremely short event times, does it reach a quantum limit in which it resumes the shape of a full sphere? In other words, given the Planck quantum, might there be influence between A and B even if the angle of measurment does not fall within the lightcone, when A and B are extremely close together?

I am trying out the idea that gravity at these short lengths and times is spread out into areas which at slightly longer lengths become inaccessible. I'd like to know what you think about this approach.


Thanks,

Richard

 

[rtharbaugh1]

My god! Generic classical chaotic dynamics in three spatial dimensions is only understood at a fairly elementary level and moreover only in some special cases. Of course everyone knows Newtons laws, knows what torque is, understands to some point GR, but very few deeply understand their consequences. Why do you think that it happens fairly often that a full analysis of a non linear problem reveals surprising, counterintuitive results ? I think my point of view is CRYSTAL clear, as should be obvious from the papers I quoted above.

Cheers,

Careful

Hi Careful

I hope to have time to look at those papers today. You know, it seems to me that the main objection to your posts is that you seem to like to imply that everyone else here is an idiot. That rankles, and makes it difficult to get past the personality thing to the ideas.

I clown around because I want it to be clear that if I offend someone by calling one of their foundational ideas idiotic, it is forgivable because I admit that I am an idiot about many things myself. Whoa, I think I just found another way for someone else to make a million bucks. How about a twelve step program for egotists?

Hello, everyone, my name is Richard and I think very highly of myself, but it is OK because I know from long experience that I am only a human, and humans are very silly creatures.

Thanks for the links.

R.

 

[Hurkyl]

Well, classical explanations are bound to be more involved but are nevertheless possible IMO.

(emphasis mine)

What is your point? It sounds as if you are saying that we don't know absolutely everything, and therefore we should have faith that all will eventually be explained classically. Is this accurate?

 

[Careful]

**
Careful et al, Quantum experts sometimes say QM is signal-local but not Einstein-local. I interpret this to mean that if you understand locallity as signal-locality, no experiment has or will demonstrate non-locality. If you interpret locality as Einstein-locality, then the EPR-Aspect type experiments have already demonstrated it up to some very quibbly loopholes. (Closing these loopholes will be hard, but I expect it to happen eventually. Proving this impossible would be a big revolution. **

Thanks for repeating what I know for around 12 years now: as I said in my reply to Hans, these are just words; quantum mechanics violates local realism (what you associate to Einstein locality - but it is actually not quite the same) in a clear way. Your comment about the loopholes is irrelevant, 25 years have passed by and the lucrative business of EPR experiments has not succeeded in closing them and they have succesfully been exploited in offering realist explanations. At such a point, reasonable doubt is justified, how long do we need to wait : 100 years ?? By the way, local realists do not have to prove that these loopholes are impossible to close at all: local realism is just fine as long as it predicts the unbiased experimental outcome.


** (Understanding the difference between signal-locality and Einstein-locality is sort of a mind blower all by itself, especially that it is really possible to be consistently one without the other.) **

It is the kind of pervertedness which you can expect from giving up realism - there is nothing ``deep´´ about it; the rest of your message falls in that category. I would like to remind you that I do not know of any 3+1 dimensional realistic (interacting) QFT in which signal locality is a proven fact (apart from the free theories and the ill defined QFT's in the interaction picture), so please do not attribute desirable features to QFT which are by far not known to be true.

Actually, if one thinks about the measurement problem and the fictition of quantum gravity for long enough then consistently insisting upon local realism seems like most logical strategy to go for. Actually, I could go on for hours about the shortcomings of QM as a physical theory (not as an effective scheme under the appropriate circumstances), but I have experienced my efforts to be in vain.

Cheers,

Careful

 

[Careful]

(emphasis mine)
What is your point? It sounds as if you are saying that we don't know absolutely everything, and therefore we should have faith that all will eventually be explained classically. Is this accurate?

What I want to say boils down to this: in the beginning of th 20'th century, the consequences of Maxwell theory were not well known yet - the famous dirac radiation formula for the electron being ``derived´´ only in 1938 (correction!) for the first time (actually CLASSICAL micromagnetism is an active research area now and reveals many new results still); the known classical phenomena basically being limited to some very special class of solutions to simple (celestial) problems and a whole class of linear problems and first order corrections to suitable asymptotic linearizations of simple non-linear ODE's (or PDE's). It is rather obvious that in such times the phenomena observed at the microscale (double split and black body radiation) came as a shock ! Another example (out of many) is the claim made by Feynman that the gyromagnetic factor of 2 for the electron could only be predicted by QM while actually in 1970 or even before, Wheeler, Carter and others realized that the Kerr solutions in GR gave exactly this figure too (actually it was thought that this could not be because the naive calculation with a circular current in the plane gave the factor of one ).

Now QM really was like an emergency solution, a relatively easy formula which was made to fit observations. It's consequences however, non-locality, the probability interpretation and so on, led its inventers to claim that the scheme would probably be replaced soon (Einstein, Schroedinger, Dirac, de Broglie ...). Of course, it does not lead to any of the following insights: (a) it does not explain why charge is quantized (ii) it does not explain *how* a particle decays... all it did was introducing a new *adaptive* force which allows for equilibrium to settle in (but this could have been achieved by classical means - though involving much more difficult computations !).

My suggestion is that if you really want to understand what is going on at the microlevel then you need to look for a realistic model concerning the structure of elementary particles (actually one of the references I gave above shows that this substructure can significantly influence the motion of the centre of mass coordinate in the radiation back reaction process). So in that sense, QM did not offer any understanding, on the other hand QM did offer the realization that equilibrium can be reached through interactions with a vacuum field - which is the starting point of SED. But many other options are possible...

So, nonlocality so far seems a problem for QM, since I am quite optimistic that (sub) atomic quantum physics can be retrieved without giving up local realism. QM in that sense is like thermodynamics of microscopic phenomena. What I want to tell you, is that this is an exciting time for discovering the next range of phenomena classical physics offers us, this thanks to the computational power of the computer.

Cheers,

Careful

 

[Hans de Vries]

Hi Hans.

So, if we descend the lightcone to the very tip, that is, consider extremely short event times, does it reach a quantum limit in which it resumes the shape of a full sphere?

Actually, The QFT propagator leaks a little bit out of the lightcone,
but only in the range of the Compton radius of the particle and expo-
nentially decreasing further out.

This is not that strange since the Compton Radius is about the smallest
range to which you can confine a particle according to HUP

The measurement statement you quote relies on an argument with
vanishing commutators. Sometimes you see this argument 'attacked'
by proponents of non-locallity, see for instance by Zeh here:

http://www.rzuser.uni-heidelberg.de/~as3/nonlocality.html

(last paragraph)

In other words, given the Planck quantum, might there be influence between A and B even if the angle of measurment does not fall within the lightcone, when A and B are extremely close together?

I am trying out the idea that gravity at these short lengths and times is spread out into areas which at slightly longer lengths become inaccessible. I'd like to know what you think about this approach.

What is happening at Planck's scale is anybody's guess Richard. Regards, Hans

 

[Hans de Vries]

Kwiat Links:

Quantum Zeno Effect:
http://www.physics.uiuc.edu/People/Faculty/profiles/Kwiat/Interaction-Free-Measurements.htm


Grover’s search algorithm : an optical approach:
http://www.physics.uiuc.edu/Research/QI/Photonics/papers/kwiat-jmo-47-257.pdf


Regards, Hans

 

[setAI]

David Deutsch has definitively shown [for me anyway] that quantum computing requires a many-worlds interpretation of QM- non-locality is a perceptual error of trying to interpret entanglement across universes in terms of classical mechanics and getting paradoxes

 

[rtharbaugh1]

Actually, The QFT propagator leaks a little bit out of the lightcone,
but only in the range of the Compton radius of the particle and expo-
nentially decreasing further out.

This is not that strange since the Compton Radius is about the smallest
range to which you can confine a particle according to HUP

The measurement statement you quote relies on an argument with
vanishing commutators. Sometimes you see this argument 'attacked'
by proponents of non-locallity, see for instance by Zeh here:

http://www.rzuser.uni-heidelberg.de/~as3/nonlocality.html

(last paragraph)



What is happening at Planck's scale is anybody's guess Richard.


Regards, Hans

Thanks Hans. I wasn't sure how small the length would need to be, but placing it at the Compton wavelength makes it seem more accessible.

So perhaps a window to the other parts of the multiverse would be available for quantum gravity to leak through, and so the argument that other branches of the multiverse could have no affect on our branch is weakened.

I did scan the Mitchison-Jozsa paper, 9907007, and picked this quote:

"Hence the two worlds or branches will never again interfere in practice - re-interference would require an enormous correlated effort to undo the widspread interaction in eq. 2 and is extremely improbable." (page 5)

I just wonder. Eq. 2 just associates a given ket with a long string of other kets with which it interacts. But each ket is also an action, so takes time. Seems to me that the probablilty of interaction will be very high locally. In other words single actions would likely interfere with each other a lot at first, and interactions would only become rare at some distance from the separation event. At what scale would we expect these interactions to be strong?

Thanks,

R.

 

[rtharbaugh1]

gr-qc/9912045
math-ph/0505042
gr-qc/0508123
gr-qc/0512111
gr-qc/0306052

Careful

Downloaded and had a glance at these. I will have time tomorrow to look at them. Thanks, Careful

monkey

 

[Careful]

** Actually, The QFT propagator leaks a little bit out of the lightcone,
but only in the range of the Compton radius of the particle and expo-
nentially decreasing further out.

This is not that strange since the Compton Radius is about the smallest
range to which you can confine a particle according to HUP

The measurement statement you quote relies on an argument with
vanishing commutators. Sometimes you see this argument 'attacked'
by proponents of non-locallity, see for instance by Zeh here:

**

I am confused now, the REAL propagator (and that is the only one used) in QFT has support within the lightcone. It is true that the COMPLEX propagator coincides with the real one inside the lightcone and becomes purely imaginary outside it, with an exponential decay indeed. Real solutions actually do not allow you to take the complex square root (ie. do not satisfy a Schroedinger type equation - therefore, no ``energy´´ eigenstates, those being all complex) the latter being the textbook reason to conclude that first relativistic quantization does not work and second quantization for HERMITIAN (ie. real) fields is necessary. Of course one could try to come up with alternatives to the KG equation which do satisfy causality without introducing the operational machinery of second quantization (or one could not bother about this in the first place which is what you seem to do).

Cheers,

Careful

ADDENDUM: again, Hans, you do not need to go down to the Planck scale to discover ``new´´ physics or to cure the old deseases... the Compton scale is sufficient for these purposes.

 

[rtharbaugh1]

Hi Careful

I was the one who suggested the Planck scale, actually, and Hans corrected me by pointing out that the Compton scale is deep enough.

Careful, I know you do not like MWI. I am curious about what you think of the idea of virtual particles. You seem to want to be the march warden of things at the classical limit. Are virtual particles just more magic, in your opinion?

Thanks

R.

ps computer problems have kept me from looking at those papers, but I promise to do it today if the keyboard doesn't freeze-up again. Thanks, R

 

[selfAdjoint]

What I want to say boils down to this: in the beginning of th 20'th century, the consequences of Maxwell theory were not well known yet - the famous dirac radiation formula for the electron being ``derived´´ only in 1938 (correction!) for the first time (actually CLASSICAL micromagnetism is an active research area now and reveals many new results still); the known classical phenomena basically being limited to some very special class of solutions to simple (celestial) problems and a whole class of linear problems and first order corrections to suitable asymptotic linearizations of simple non-linear ODE's (or PDE's). It is rather obvious that in such times the phenomena observed at the microscale (double split and black body radiation) came as a shock ! Another example (out of many) is the claim made by Feynman that the gyromagnetic factor of 2 for the electron could only be predicted by QM while actually in 1970 or even before, Wheeler, Carter and others realized that the Kerr solutions in GR gave exactly this figure too (actually it was thought that this could not be because the naive calculation with a circular current in the plane gave the factor of one ).

Now QM really was like an emergency solution, a relatively easy formula which was made to fit observations. It's consequences however, non-locality, the probability interpretation and so on, led its inventers to claim that the scheme would probably be replaced soon (Einstein, Schroedinger, Dirac, de Broglie ...). Of course, it does not lead to any of the following insights: (a) it does not explain why charge is quantized (ii) it does not explain *how* a particle decays... all it did was introducing a new *adaptive* force which allows for equilibrium to settle in (but this could have been achieved by classical means - though involving much more difficult computations !).

My suggestion is that if you really want to understand what is going on at the microlevel then you need to look for a realistic model concerning the structure of elementary particles (actually one of the references I gave above shows that this substructure can significantly influence the motion of the centre of mass coordinate in the radiation back reaction process). So in that sense, QM did not offer any understanding, on the other hand QM did offer the realization that equilibrium can be reached through interactions with a vacuum field - which is the starting point of SED. But many other options are possible...

So, nonlocality so far seems a problem for QM, since I am quite optimistic that (sub) atomic quantum physics can be retrieved without giving up local realism. QM in that sense is like thermodynamics of microscopic phenomena. What I want to tell you, is that this is an exciting time for discovering the next range of phenomena classical physics offers us, this thanks to the computational power of the computer.

Cheers,

Careful

This seems rather a hand-waving argument since a quick scan of the papers you linked to supports your point about active research in microlevel classical EM, but none of them provides any account that I could see of double slit, or any other characteristic quantum phenomena.

All this resarch has had nearly 70 years (since your date of 1938) to give at least a glimpse of these things, and what is there to show? If we criticize string physics for 35 years without a testible prediction, shouldn't we also back off micro-EM as a QM substitute for nearly twice as long coming up empty?

My take is that solving the measurement problem will take more quantum, not less. But maybe we should take this discussion to another thread, if not another board.

 

[Careful]

Hi Careful

I was the one who suggested the Planck scale, actually, and Hans corrected me by pointing out that the Compton scale is deep enough.

Careful, I know you do not like MWI. I am curious about what you think of the idea of virtual particles. You seem to want to be the march warden of things at the classical limit. Are virtual particles just more magic, in your opinion?

Thanks

R.

ps computer problems have kept me from looking at those papers, but I promise to do it today if the keyboard doesn't freeze-up again. Thanks, R

Virtual particles are just a way to diagramatically bookkeep the Feynman series and have no direct physical significance at all, so why should I be against that? Moreover, they correspond to unnormalizable plane waves (eigenstates of the momentum operator), so...

Cheers,

Careful

 

[Careful]

**This seems rather a hand-waving argument since a quick scan of the papers you linked to supports your point about active research in microlevel classical EM, but none of them provides any account that I could see of double slit, or any other characteristic quantum phenomena.**

Let me just tell you that interference patters for particles moving in an eather background have even been calculated by Antoon Lorentz as far as I remember. Now, I presume it is feasible to show that a (radiating) electron moving in a suitable microscopic background radiation field is going to resonate with the Fourier component determined by the Compton frequency of the particle, hence resulting in your double slit. I guess this idea must have been worked out already somewhere, but I do not know of any references...


**All this resarch has had nearly 70 years (since your date of 1938) to give at least a glimpse of these things, and what is there to show? If we criticize string physics for 35 years without a testible prediction, shouldn't we also back off micro-EM as a QM substitute for nearly twice as long coming up empty? **

You are funny, the point I wanted to make is that the first reasonable equation for a radiating electron (there existed the lorentz equation before but that one had serious limitations - very slowly varying fields) was developed 20 years after the majority of the physics community was convinced that classical mechanics would predict it to fall on the nucleus Actually, one of the other papers about the Elizer theorem - which came a decade later - shows that this is not necessarily the case for reasonable types of Coulomb fields (even without a background radiation field! ). Then, the other papers show that if you take into account internal structure, then subtantial corrections on the centre of mass motion could be expected. These latest papers nota bene date from 2005 (!) so the topic being very old is far from well understood.

** My take is that solving the measurement problem will take more quantum, not less. But maybe we should take this discussion to another thread, if not another board. **

Oh, if you are prepared to violate Occam's razor by going over excentric constructions such as MWI zombies and alike, go ahead you know.

The point I made is that we better be a bit more humble and try to understand more basic problems: how can one make a definite statement about the radiation behaviour of an electron when we do not even know what the reasonable backreaction *equation* is (let along what an electron is ! ) ? It is for sure not the Lorentz - Dirac equation because of preacceleration and running away phenomena.

And yes, if the same investment would have been made in this kind of reasoning as has been given to string theory, then very likely we would not speak about QM anymore - successes have actually been reached in similar programs as was discussed already at the QM forum.

Cheers,

Careful

 

[Hurkyl]

The point I made is that we better be a bit more humble and try to understand more basic problems: how can one make a definite statement about the radiation behaviour of an electron when we do not even know what the reasonable backreaction *equation* is (let along what an electron is ! ) ?

By using an argument that doesn't require use of the backreaction equation, nor knowledge of the precise nature of an electron.

Oh, if you are prepared to violate Occam's razor by going over excentric constructions such as MWI zombies and alike, go ahead you know.

A violation of your sensibilities does not constitute a violation of Occam's razor.

 

[Careful]

**By using an argument that doesn't require use of the backreaction equation, nor knowledge of the precise nature of an electron. **

Funny: you also have to take into account backreaction effects in QM (of course this is not mentioned in textbooks) for the double slit as well as for the atomic structure (I mentioned that recently in another thread - you know the existence of atoms in QM is not an old RESULT - and for heavy nuclei it is still open in the relativistic case AFAIK ). In both cases, you are obliged to make the full computation in QED which as you know is not renormalizable (it is perturbatively) - so you have to make a cutoff, break Lorentz invariance and so on... So, the same problems come back to you over there. What do you think, that QM allows you to forget about radiation ? By the way, it seems you have what it takes to become an expert in quantum mechanics: you are only remotely interested in the precise nature of things... blurr it up and it will be ok and certainly affirm that we cannot do any better.

**
A violation of your sensibilities does not constitute a violation of Occam's razor. [/QUOTE] **

You should open a restaurant with interfering steaks bien cuit and a point ... , so that the costumers can project it down to their favorite taste without being asked a priori.

Cheers,

Careful

 

[Hurkyl]

Funny: you also have to take into account backreaction effects in QM ...

So what? This is irrelevant to whatever arguments we might be making about classical EM.

The classical textbook proof that you can't have a stable atom doesn't involve at all the forces acting on the electron, nor its true nature. Accelerating charge radiates electromagnetic waves which carries energy. A stable atom is therefore a source of free energy.

All of your arguments that we don't know everything about the classical stuff is irrelevant -- we knew enough that there is a serious problem. In order to reconcile a stable atom with classical EM, you have to tweak something in the theory so that the textbook argument is invalid. Arguments that we don't have complete knowledge, and progress in finding the forces acting on and in an electron does not do that.

I reject your arguments because they continually have the form "We don't know everything. Look, we're still learning new stuff. Have faith and all will be explained", and you don't seem to make any attempt to address the traditional questions that are considered to be killing blows.

(P.S. as I understand it, QM "smears" the electron throughout the entire orbital, and as a result, the system has stationary charge and current distributions -- a configuration that does not radiate, thus resolving the problems with a stable atom)

 

[Careful]

**So what? This is irrelevant to whatever arguments we might be making about classical EM. **

No, it is not, that is the whole point.

** The classical textbook proof that you can't have a stable atom doesn't involve at all the forces acting on the electron, nor its true nature. Accelerating charge radiates electromagnetic waves which carries energy. A stable atom is therefore a source of free energy. **

Nothing says that this energy is free for the taken... [Actually, if you calculate the EM field at large distances from the slow moving source, you get an outward directed Poynting vector (in lowest order) for the radiation - however close to the source, the Poynting vector is ZERO (in first order)...] If you would take the effort to look at the recent papers of Cole (who builds further on the work of Boyer and Marshall) I quoted before (on another thread), you will actually see that an equilibrium between radiation and matter could be formed (provided the existence of zero point radiation) - there are pleanty of papers about this (starting from the 1960'ties) which are all published in Phys. Rev. which is not so easy for realist papers.

**
All of your arguments that we don't know everything about the classical stuff is irrelevant -- we knew enough that there is a serious problem. **

Difficult problems are there to be solved rationally.

** In order to reconcile a stable atom with classical EM, you have to tweak something in the theory so that the textbook argument is invalid. Arguments that we don't have complete knowledge, and progress in finding the forces acting on and in an electron does not do that. **

But a zero point radiation field seemingly does that.

** I reject your arguments because they continually have the form "We don't know everything. Look, we're still learning new stuff. Have faith and all will be explained", and you don't seem to make any attempt to address the traditional questions that are considered to be killing blows. **

But people (and I) do that (Marshall, Santos, Barut...), it takes a while you know


**
(P.S. as I understand it, QM "smears" the electron throughout the entire orbital, and as a result, the system has stationary charge and current distributions -- a configuration that does not radiate, thus resolving the problems with a stable atom)[/QUOTE] **

The static spherical ground state does not radiate (classically), but the orbitals with angular momentum do.

 

[rtharbaugh1]

Let me just tell you that interference patters for particles moving in an eather background have even been calculated by Antoon Lorentz as far as I remember. Now, I presume it is feasible to show that a (radiating) electron moving in a suitable microscopic background radiation field is going to resonate with the Fourier component determined by the Compton frequency of the particle, hence resulting in your double slit. I guess this idea must have been worked out already somewhere, but I do not know of any references...

Careful, I am surprised to see that you are ressurrecting the aether...I thought Michealson-Morley had effectively shown (classically!) that the aether cannot exist. Maybe I misremember my modern physics?

R

 

[Careful]

Careful, I am surprised to see that you are ressurrecting the aether...I thought Michealson-Morley had effectively shown (classically!) that the aether cannot exist. Maybe I misremember my modern physics?

R

Two answers :
(a) there exist *modern* contrived eather theories which break Lorentz invariance only at very high energies so no contradiction with experiment there. By the way, the modern deformed special relativity theories - associated to quantum gravity effects - do the same no ? (look into a magazine about Galileian mechanics)
(b) I was merely using this analogy to mention the ``interference´´ result, the issue of Lorentz invariance is not substantial in this reasoning.

Cheers,

Careful

 

[rtharbaugh1]

The puppy thing could be translated into a more mathematical depiction, if that's what you'd like to see. I will still use the suggestive labels from the story though -- of course they could be replaced with whatever you want.


Suppose we have an unknown particle whose state space has the following basis:
|no>
|asleep>
|awake>

And, for whatever reason, we know that it is in one of the first two basis states.

We have a particle under our control whose state space has the following basis:
|no>
|salad>
|steak>

And we have a device that implements the following transformation:

|steak, no> --> |steak, no>
|steak, asleep> --> |no, awake>
|steak, awake> --> |no, awake>
|salad, x> --> |salad, x>
|no, x> --> |no, x>


We also will be applying the rotation:
|salad> --> (1/sqrt(2)) [ |salad> + |steak> ]
|steak> --> (1/sqrt(2)) [ -|salad> + |steak> ]
|no> --> |no>

So our experiment is as follows:
1. Prepare our particle in the |salad> state.
2. Rotate it.
3. Apply the measuring device.
4. Rotate it.
5. Observe our particle.


Observe what happens to the |no> state of the hidden particle:
1:: |salad, no>
2:: (1/sqrt(2)) [ |salad, no> + |steak, no> ]
3:: (1/sqrt(2)) [ |salad, no> + |steak, no> ]
4:: |steak, no>
5:: 100% chance of observing steak.

Now, observe what happens to the |asleep> state of the hidden particle:
1:: |salad, asleep>
2:: (1/sqrt(2)) [ |salad, asleep> + |steak, asleep> ]
3:: (1/sqrt(2)) [ |salad, asleep> + |no, awake> ]
4:: (1/2) [ |salad, asleep> + |steak, asleep> ] + (1/sqrt(2)) |no, awake>
5::
25% chance of observing salad, and leaving hidden particle unchanged.
25% chance of observing steak, and leaving hidden particle unchanged.
50% chance of observing no, and having altered the hidden particle.



So, we have given ourselves some ability to distingush between the |no> and |asleep> states without disturbing the particle. And with a more clever approach, you can arbitrarily improve this method.

I haven't yet worked out how to map this into the quantum computer case, but I think this at least conveys the idea about what's going on.

Hi Hurkyl

This is my first progress in using the ket notation, so I would like to take some space to expand the notation and expose my understanding to

corrections.

You said "The puppy thing could be translated into a more mathematical depiction, if that's what you'd like to see. I will still use the

suggestive labels from the story though -- of course they could be replaced with whatever you want."

I want to replace the puppy with the actual conditions reported in the experiment. So I will take the liberty of adding to your post some

explanations of the notation from my own understanding, which I hope you will either verify or offer corrections. I put my additions in

parenthesis brackets, ().

Suppose we have an unknown particle whose state space has the following basis:
|no>(==>the box is empty)
|asleep>(==>there is a particle in the box, but it does not interact with our probe)
|awake>(==>there is a particle in the box and it does interact with our probe)

And, for whatever reason, we know that it is in one of the first two basis states.(So, either the box is empty or the particle in the box will

not interact with our probe.)

We have a particle under our control (the probe) whose state space has the following basis:
|no>(==>the probe does not get close enough to interact with the particle in the box)
|salad>(==>the probe gets close enough but the particle in the box does not interact)
|steak>(==>the probe gets close enough and the particle does interact)

And we have a device that implements the following transformation:(this is the part where an interaction is attempted)

|steak, no> --> |steak, no>(==>we begin with a probe which would interact, but there is no particle in the box, so after the attempt, we still

have the probe which would react, and we know that the box is empty)
|steak, asleep> --> |no, awake>(==>we begin with a probe which would interact, and a box containing an unreacted particle, and after the attempt

we find that the probe has been consumed in the reaction and the particle in the box has reacted)
|steak, awake> --> |no, awake>(==>we begin with a probe which would interact, and a box containing a particle which will react, and after the

attempt we find the probe consumed and the particle reacted)
|salad, x> --> |salad, x>(we begin with a probe that is not in a state to interact, and any condition in the box, and we end with an unreacted

probe and the condition in the box unchanged)
|no, x> --> |no, x>(we begin with no probe, and a box in any condition, and we end with no probe and the box unchanged.

If you have time maybe you could review my attempt to interpret and tell me where I lack understanding. I find that at my current level I am

not able to continue the above analysis any further in your post. It would be lots of help to me, but I realize you are busy, so I will be

happy to wait.

Thanks,

R

 

[selfAdjoint]

Careful, I am surprised to see that you are ressurrecting the aether...I thought Michealson-Morley had effectively shown (classically!) that the aether cannot exist. Maybe I misremember my modern physics?

R

Richard there are many qubblers who have this or that argument against the M-M experiment. This thread is recapitulating many inconclusive threads on quantum physics (measurement problem) and on Relativity (ether).

But Careful should stick to the point. Lorentz's derivation is irrelevant to his argument; that modern micro-EM, back-reaction, and so on can account for the things that the physics community (minus "a set of measure zero") thinks only a quantum hypothesis can address. Not only two-slit, but the cascaded spin measurements and yes, quantum eraser, delayed choice, and quantum Zeno effect experiments.

Far as I can see all he has offered so far is hand waving and distaste for the elements of quantum mechanics.

 

[rtharbaugh1]

Two answers :
(a) there exist *modern* contrived eather theories which break Lorentz invariance only at very high energies so no contradiction with experiment there. By the way, the modern deformed special relativity theories - associated to quantum gravity effects - do the same no ? (look into a magazine about Galileian mechanics)
(b) I was merely using this analogy to mention the ``interference´´ result, the issue of Lorentz invariance is not substantial in this reasoning.

Cheers,

Careful

(a) I don't see how this applies to double slit. High energies are not required. As I have pointed out before, quantum effects are detectable at ordinary energies. You seem to be saying that double slit effect is the result of an aether which should be effective on the bench top. But Michealson-Morley seems to show that there can be no such aether effective in bench top experiments. At very high energies, very short lenghts and times, there may be an aether effect due to four and maybe higher dimensional actions. But of course you have already committed your reputation to the argument that there are no such higher dimensions. It seems to me your stand is , umm, counterfactual.

(b) why not?

 

[rtharbaugh1]

Richard there are many qubblers who have this or that argument against the M-M experiment. This thread is recapitulating many inconclusive threads on quantum physics (measurement problem) and on Relativity (ether).

But Careful should stick to the point. Lorentz's derivation is irrelevant to his argument; that modern micro-EM, back-reaction, and so on can account for the things that the physics community (minus "a set of measure zero") thinks only a quantum hypothesis can address. Not only two-slit, but the cascaded spin measurements and yes, quantum eraser, delayed choice, and quantum Zeno effect experiments.

Far as I can see all he has offered so far is hand waving and distaste for the elements of quantum mechanics.

Hi selfAdjoint

Yes, well, I am just an amature and so Careful's insistance that classical means are sufficient seems to have some value. I agree with him in so far as I think we need to be dem sure that classical rules are violated before we accept the astounding implications of QM. Of course you know that I have embarked on a long and difficult study to understand what I can of the maths so that I have a chance to decide for myself. And really the beauty, elegance, and magic of quantum is tremendously appealing, even if it turns out to be an elaborate and expensive science fiction.

Classical rules seem to tell us that we will never get to the stars, just as medieval rules said that we would never fly. I have faith that we will prove the doubters wrong again.

R.

 

[Hurkyl]

No, it is not, that is the whole point.

How do you figure? The problem with a stable atom is an apparent flaw in CM. Raising issues with QM does not make the problem go away -- it's just a smoke screen. Even if you were able to show that every experiment done since 1905 is actually in disagreement with quantum mechanics, that would only mean that we have two failed theories -- it wouldn't magically fix CM.

The only way to argue that CM is not a flawed theory is to argue that CM is not a flawed theory.

Yes, when one is trying to defend their viewpoint, it is reasonable to also argue against the opposing viewpoints -- but the latter is not a substitute for the former. My problem with your posts is that you almost entirely focus on the latter -- they contain so much QM-bashing and so little defense of CM that it leads me to believe that you really don't have a good defense of CM.

While it would be neat to see the problems with CM rectified, the tone of your posts leads me to believe that I will not find it here. (I had been hoping to elicit more informative responses. )

Difficult problems are there to be solved rationally.

Yes. Keep in mind that "rational" is not synonymous with "having faith that the theory I like will prove to be correct, and the theory I don't like will prove to be flawed" -- in fact, that is essentially the antonym of "rational".

The static spherical ground state does not radiate (classically), but the orbitals with angular momentum do.

I went and checked a textbook derivation on this one again to be sure -- sure enough, all of the orbitals are stationary. So why would one think it radiates?

(Or have I misread you -- that you're making a statement about CM instead?)

 

[Careful]

**
I went and checked a textbook derivation on this one again to be sure -- sure enough, all of the orbitals are stationary. So why would one think it radiates?

(Or have I misread you -- that you're making a statement about CM instead?)[/QUOTE] **

Stationary means that the wave function is an eigenfunction of the quantum Hamiltonian (in which you ignored radiation) - nothing more. In classical mechanics, a spinning ball is also stationary albeit the constituents are clearly accelerating, the same goes for the spinning Kerr solutions in general relativity - which is a vacuum spacetime with tidal effects. ADDENDUM: The spinning Kerr solutions do not radiate, but so far one only succeeded in finding infinitesimally thin (rotating) dust shells to match it with. I am unaware of the existence of a realistic (smooth) charge distribution to which it could be pasted (and I am pretty sure it has not been done yet) - if it woud exist it would be interesting to know about that. So yes, there exist very special (distributional) rotating classical charged matter configurations which do *not* radiate, I am not aware however if this woud apply to the stationary solutions of the Schroedinger equation for an electron in a central Coulomb field - I guess not.

** How do you figure? The problem with a stable atom is an apparent flaw in CM. **

no, that is *not* appearant at all. This radiation cannot leak outside the universe (your boundary conditions at spatial infinity must be zero), therefore it needs to be adsorbed again (by other/and the same charge distributions). Nobody says that the problem of a fully ISOLATED atom is the correct one, on the contrary you would reasonably expect such system to be unstable (as common sense experience in diffusion phenomena teaches us). Really, you should take a look at the Boyer, Marshall, Cole papers, these people are *not* idiots you know...


** Raising issues with QM does not make the problem go away -- it's just a smoke screen. Even if you were able to show that every experiment done since 1905 is actually in disagreement with quantum mechanics, that would only mean that we have two failed theories -- it wouldn't magically fix CM. **

True, but I would certainly have raised the point that we really did not understand what is going on, a conclusion you seem to find so troublesome that you cannot imagine it.

**
The only way to argue that CM is not a flawed theory is to argue that CM is not a flawed theory. **

Sure, but YOU have to show that QM solves them (I mean you cannot just sit and wait you know).

What concerns the informative part of my messages, I think I am informative enough, sure I cannot present a definitive solution yet but I certainly offer good arguments that such thing is conceivable (as well as references where such partial results have been achieved already) - and I certainly hope to be more conclusive in the future.

That someone like Self Adjoint calls my messages speculative is IMO outrageous. This man is dripping each time a *presumed* result about quantum gravity (non testable and by no means mathematically well constructed) or a speculative idea alike, is posted on the web.

Cheers,

Careful

 

[Hurkyl]

Stationary means that the wave function is an eigenfunction of the quantum Hamiltonian (in which you ignored radiation ) - nothing more. In classical mechanics, a spinning ball is also stationary albeit the constituents are clearly accelerating...

Of course -- that's by definition. But, that implies all the things that come with being an eigenfunction of the Hamiltonian -- such as all physical quantities (e.g. charge and current distributions) being time independent.

I would not expect a (continuous) classical spinning charged ball to radiate either. (As for a charged ball made of classical pieces, I don't know. I would guess that it would radiate, but very weakly)

(And since stationary charge/current distributions don't radiate, there's no need to bother with considering radiation in the Hamiltonian)

no, that is *not* appearant at all.

It feels silly that I have to explain the textbook argument to you, but alas...

The atom continuously radiates energy. Due to conservation of energy, in order to remain "stable", it must have an external source that is continuously pumping energy into it. (Does that even qualify as "stable"?)

Really, you should take a look at the Boyer, Marshall, Cole papers, these people are *not* idiots you know...

None of the papers you've "linked" have been by either of them, which makes it difficult.

Sure, but YOU have to show that QM solves them (I mean you cannot just sit and wait you know).

Only if I was trying to argue something to the effect that QM solves them.

But given the assumption that QM maintains the classical property that stationary charge/current distributions do not radiate, the textbook solution of the (Hydrogen) atom clearly solves that problem.

I know enough about QM to see how it ought to be able to solve the problem of wave/particle duality.

And, of course, the EPR experiments are not a problem for QM.

I haven't bothered assembling, in my mind, a further list of problems with CM, because these seem serious enough. These would need to be addressed fairly adequately before I could even begin to consider CM as the fundamental theory here.

Of course, QM as we have it today is not the fundamental theory either: it is strongly believed (known?) to be irreconsilable with gravity. Would it be appropriate to call the quantum gravity research "QM"? I get the impression that it wouldn't.

 

[Careful]

**Of course -- that's by definition. But, that implies all the things that come with being an eigenfunction of the Hamiltonian -- such as all physical quantities (e.g. charge and current distributions) being time independent. And since stationary charge/current distributions don't radiate, there's no need to bother with considering radiation in the Hamiltonian) **

Come on, there is no straigthforward *good* prescription at all for the radiation field determined by the wave function (actually, there exists an obvious candidate, but this one does not seem to give stationary states) ! In the Hamiltonian we are talking about, you just put in BY HAND that there is NO correspondence between the wave function and the radiation vector potential. The Schroedinger equation - as it stands there - does not allow for a dynamical coupling between charge and radiation. It is easy to ``solve´´ the problem like that in classical mechanics too you know

What you say is the following: one should just take any stationary current for an equation of motion which does not contain a radiation vector potential and solve the Maxwell equations with respect this current. But in this way, I can claim that (correction!) a classical atomic model with electrons as rotating strings is stable too !


**
It feels silly that I have to explain the textbook argument to you, but alas...

The atom continuously radiates energy. Due to conservation of energy, in order to remain "stable", it must have an external source that is continuously pumping energy into it. (Does that even qualify as "stable"?) **

The point is that the electron will not only radiate energy, it will also *extract* energy from an an external radiation field. The question being whether this could be a stable process. Again, it probably makes no sense in speaking about a stable atom in vacuum. You should read the textbooks more critically.

**
None of the papers you've "linked" have been by either of them, which makes it difficult. **

True, I gave them in another thread as I mentioned specifically. They can all be found in

* simulation study of aspects of the classical hydrogen atom interacting with electromagnetic radiation : circular orbits, Daniel C Cole and Yi Zou
*Analysis of orbital decay time for the classical hydrogen atom interacting with circulary polarized radiation, Daniel C Cole and Yi Zou
* quantum mechanical ground state of hydrogen obtained from classical electrodynamics, Daniel C Cole and Yi Zou


**Only if I was trying to argue something to the effect that QM solves them.
But given the assumption that QM maintains the classical property that stationary charge/current distributions do not radiate, the textbook solution of the (Hydrogen) atom clearly solves that problem.**

Not really, the textbook treatment does not teach you anything of that kind; the STABILITY of this configurations is a more advanced (partial !) recent result - check out another thread where I have posted the relevant papers.


** And, of course, the EPR experiments are not a problem for QM. **

Neither are they for CM, apart from some restrictions it puts on local realism.

I am trying to be patient with you here, I would appreciate it if you would even just consider to think about what I say.

Cheers,

Careful