Entanglement and teleportation

[vanesch]

The thing about photon detections is that there's
no way to tell whether all or some portion of the
light incident on a polarizer has been transmitted
by the polarizer when a detection occurs.

I suspect that you and I might have somewhat different
conceptions of what the word "photon" might refer to,
aside from it's existence as a theoretical entity and
a recorded detection.

Well, there is of course one true concept of a photon, and that's the theory that defines it, namely QED. But if you insist on classical optics (which is Maxwell's equations), then a way to try to explain photo-electric clicking is by assuming that the EM wave amplitude is strongly pulsed: you don't have the intro textbook sine wave, but you have essentially most of the time, very low amplitudes and then you have sudden pulses (wave packets). When you look at the monochromaticity required (the delta lambda / lambda) and the time scale of detection (a few ns) versus the period of EM field oscillation (order fs), then there is all the room in the world to make these wave packets which are peaked in amplitude on the ns scale and appear still essentially monochromatic. Adding a semiclassical model of the source (where atoms radiate pulses of light during short time intervals) you have a natural setting for claiming that the EM wave is pulsed that way.
So *IF YOU INSIST ON THIS SEMICLASSICAL MODEL* (which, I recall, can explain quite a lot of optical phenomena), with individual light pulses which are EM wave trains according to Maxwell, then I don't see how you can arrive at any other prediction for the correlations than what I calculated, namely eps^2/8 (2 - cos 2(a-b) ).

Mind you that the workings of a beam splitter, a polarizing filter and a photodetector, in this semi-classical model do not have many liberties. Especially the beam splitter: if you ever hope to get interference using this pulsed light, a beam splitter has to send HALF of the EM energy (1/sqrt(2) of the E-field amplitude) very accurately to both sides. If it sends a whole pulse to the left, and then a whole pulse to the right, upon recombination, you wouldn't have any interference. Now, beamsplitters do give rise to interference. So that limits strongly how they can handle the classical EM wave.
In the same way, a photodetector can be checked against bolometric energy flux measurements: there is a very strict relation between the total number of counts during a certain time, and the total incident EM radiation. If you assume that the photodetector doesn't have any memory mechanism beyond the few ns scale then the probability of detection can only depend upon the incident EM energy (the flux of the Pointing vector). You can then also check its dependence, or not, of any polarization state.

Again, interference experiments with light getting through two polarizers show, in a similar way as done with a beam splitter, that classical EM wave pulses do not sometimes get through entirely, and sometimes don't get through, but that their intensities are lowered according to Malus's law, per pulse.

All this in the hypothesis of *classical EM radiation*.

You can think of many experiments that way, people have done them for more than a century, the classical behaviour of these components is completely constrained, and allows one to make precise predictions, based upon classical optics.

And for certain experiments, these predictions are in contradiction:
a) with QED predictions
b) with experimental results
but this only happens in the case of non-classical states of light (according to QED), such as 1-photon and 2-photon states in superposition (entangled photons).

Regarding anticoincidence experiments using
beamsplitters -- it's the same problem. There's
no way to tell if the light incident on a beamsplitter
and subsequently producing a photon detection at
one detector or the other (but never both)
was unevenly split or traveled only one path or
the other.

There is a way: interference of the resulting beams. If they interfere, they have to be present at the same time, and not one after the other.
You have to be able to do E1(t) + E2(t) at the screen. If at one time, you have a full E1 but no E2, and at another time, you have a full E2 but no E1, then you won't see interference.

cheers,
Patrick.

 

[Sherlock]

Well, there is of course one true concept of a photon, and that's the theory that defines it, namely QED. But if you insist on classical optics (which is Maxwell's equations), then a way to try to explain photo-electric clicking is by assuming that the EM wave amplitude is strongly pulsed: you don't have the intro textbook sine wave, but you have essentially most of the time, very low amplitudes and then you have sudden pulses (wave packets). When you look at the monochromaticity required (the delta lambda / lambda) and the time scale of detection (a few ns) versus the period of EM field oscillation (order fs), then there is all the room in the world to make these wave packets which are peaked in amplitude on the ns scale and appear still essentially monochromatic. Adding a semiclassical model of the source (where atoms radiate pulses of light during short time intervals) you have a natural setting for claiming that the EM wave is pulsed that way.
So *IF YOU INSIST ON THIS SEMICLASSICAL MODEL* (which, I recall, can explain quite a lot of optical phenomena), with individual light pulses which are EM wave trains according to Maxwell, then I don't see how you can arrive at any other prediction for the correlations than what I calculated, namely eps^2/8 (2 - cos 2(a-b) ).

Mind you that the workings of a beam splitter, a polarizing filter and a photodetector, in this semi-classical model do not have many liberties. Especially the beam splitter: if you ever hope to get interference using this pulsed light, a beam splitter has to send HALF of the EM energy (1/sqrt(2) of the E-field amplitude) very accurately to both sides. If it sends a whole pulse to the left, and then a whole pulse to the right, upon recombination, you wouldn't have any interference. Now, beamsplitters do give rise to interference. So that limits strongly how they can handle the classical EM wave.
In the same way, a photodetector can be checked against bolometric energy flux measurements: there is a very strict relation between the total number of counts during a certain time, and the total incident EM radiation. If you assume that the photodetector doesn't have any memory mechanism beyond the few ns scale then the probability of detection can only depend upon the incident EM energy (the flux of the Pointing vector). You can then also check its dependence, or not, of any polarization state.

Again, interference experiments with light getting through two polarizers show, in a similar way as done with a beam splitter, that classical EM wave pulses do not sometimes get through entirely, and sometimes don't get through, but that their intensities are lowered according to Malus's law, per pulse.

All this in the hypothesis of *classical EM radiation*.

You can think of many experiments that way, people have done them for more than a century, the classical behaviour of these components is completely constrained, and allows one to make precise predictions, based upon classical optics.

And for certain experiments, these predictions are in contradiction:
a) with QED predictions
b) with experimental results
but this only happens in the case of non-classical states of light (according to QED), such as 1-photon and 2-photon states in superposition (entangled photons).

There is a way: interference of the resulting beams. If they interfere, they have to be present at the same time, and not one after the other.
You have to be able to do E1(t) + E2(t) at the screen. If at one time, you have a full E1 but no E2, and at another time, you have a full E2 but no E1, then you won't see interference.

So, my assessment of what entanglement *is* (offered many
messages ago) would seem to be incomplete. I can't argue with
the fact that the idea that it's due to common emission polarization
results in mathematical representations that are contradicted
by experiments. Yet, the common emission polarization would
seem to be a necessary condition for producing entangled results.

I suppose I should look at the details of the MWI stuff that you
seem to like. :) Thanks for the thoughtful comments from you and
DrChinese, et al.

There's a paperclip symbol by this thread -- what does that
mean? Also, what do the "warnings" mean? I couldn't find
an explanation of this in the faq.

 

[vanesch]

So, my assessment of what entanglement *is* (offered many
messages ago) would seem to be incomplete. I can't argue with
the fact that the idea that it's due to common emission polarization
results in mathematical representations that are contradicted
by experiments. Yet, the common emission polarization would
seem to be a necessary condition for producing entangled results.

Yes, entanglement is "more" than common emission polarization.

You can have, say, 4 different "polarization relations" between two photons.

One is: identical polarization, all the time the same. That's represented in QM by, say, |theta> |theta> (a pure product state), and classically by two beams with identical, fixed polarization theta.

The second is: identical polarization, but randomly distributed from event to event. That is represented in QM by a mixture: half |0>|0> and half |90>|90> (a density matrix). This is the "correlated polarization" situation. In classical EM, it is represented by two identical beams with polarization theta, but this time theta is drawn from a population.
THIS is the situation that can be described by the semiclassical model I talked about.

The third one is: uncorrelated polarizations. This is represented in QM by a statistical mixture:
1/4 |0>|0> ; 1/4 |0>|90> ; 1/4 |90>|0> and 1/4 |90>|90>.
Classically, we have uncorrelated beams with individual random polarizations.

The final one is entanglement ; a pure state |0>|0> + |90>|90>.
There is no classical equivalent here...
Of course it implies "identical polarization with random distribution" in a certain way, but it is a STRONGER form of correlation than with ONLY this link (which is perfectly well described by the mixture in our second case above).
It has in it, this "magical link at a distance". If you want to describe it "semiclassically" you have to introduce strange things, namely that upon observation of the polarization at one side in direction A+ (which could have been the result of a partial intensity of another polarisation getting through the polarizer), suddenly the polarization at the other side has to jump into exactly that direction ; at which point it can be analysed by another polarizer in another direction, and Malus' law applies then. But that's not how Maxwell tells us that EM waves behave ! They don't "jump" because at a distance, something was detected or not. Hence the puzzling aspects of entangled states when you want to force them into classical concepts.
Again, entanglement has no classical equivalence. It's a new state which exists only within the quantum framework.

cheers,
Patrick.

 

[ZapperZ]

I would like to point out a recent paper in the European Journal of Physics, especially for those who are still trying to grasp what is meant by "entanglement". This is especially true if you think it can be understood without bothering to look into the mathematics.

G.B. Roston et al., "Quantum entanglement, spin 1/2 and the Stern-Gerlach experiment", Eur. J. Phys. v.26, p.657 (2005).

You have no excuse if you say you don't have access to it. As I've pointed out many times on here and in my journals, this is one of IoP journals, and ALL articles appearing on IoP journals are available FREE (via registration) for the first 30 days that paper appears online.

Zz.

 

[DrChinese]

G.B. Roston et al., "Quantum entanglement, spin 1/2 and the Stern-Gerlach experiment", Eur. J. Phys. v.26, p.657 (2005).

You have no excuse if you say you don't have access to it. As I've pointed out many times on here and in my journals, this is one of IoP journals, and ALL articles appearing on IoP journals are available FREE (via registration) for the first 30 days that paper appears online.

Zz.

Here is the link to the page that takes you there (just to make it even easier):

http://www.iop.org/EJ/ejs_extra - Select "This Month's Papers"

The article was put out around May 22 +/- so should be there through much of June. This site is nice, you may want to bookmark this page.

 

[Sherlock]

... entanglement has no classical equivalence. It's a new state which exists only within the quantum framework.

I feel somewhat confident in saying that an eventual qualitative understanding of quantum entanglement will be in terms of concepts developed via our ordinary sensory perception of things (ie., a wave mechanical picture) -- nothing *essentially* new or exotic, but
perhaps a lot more complicated than what's been developed so
far (eg., via quantum or classical or semiclassical descriptions).

The basic idea is that entanglement has to do with
analyzing common physical properties. There are a number
of ways that this can be produced in a universe with a
signal transmission speed limit of c. I don't think that's
been contradicted. The experimental results contradict
some simplistic ways of describing this mathematically,
that's all. If you've got a better idea wrt the essence of
entanglement, then let's hear it. :)

Now I'm going to read the Roston et al. paper referenced by
Zapperz and see if it has anything new in it.

 

[DrChinese]

The basic idea is that entanglement has to do with
analyzing common physical properties. There are a number
of ways that this can be produced in a universe with a
signal transmission speed limit of c. I don't think that's
been contradicted. The experimental results contradict
some simplistic ways of describing this mathematically,
that's all. If you've got a better idea wrt the essence of
entanglement, then let's hear it. :)

You have it backwards, as I see it. The experimental results rule out local reality. If you have a local hidden variable solution - either simplistic OR complicated - that matches experiment, let's hear it. :)

Instead of trying to restore local reality, we should try to understand local non-reality. Or non-local reality. Or non-local non-reality.

 

[Sherlock]

You have it backwards, as I see it. The experimental results rule out local reality.

That's an unwarranted conclusion. The experimental results
rule out quantitative descriptions of a certain form. As yet,
nobody's quite sure what that means as far as nature is
concerned.

If you have a local hidden variable solution - either simplistic OR complicated - that matches experiment, let's hear it. :)

I did provide, some messages back, a sort of semi-classical
approach in terms of local interactions and common source
which even vanesch allowed was ok for the usual EPR-Bell type
setups of an emitter, two polarizers and two detectors, but can't
as yet be extended to eg. beamsplitter setups.
The problem is that details of the physical characteristics of the
emitted light are lacking.

Instead of trying to restore local reality, we should try to
understand local non-reality. Or non-local reality. Or non-local
non-reality.

Local reality is still with us afaik. :) The question is whether we
need to posit superluminal signals to account for experimental
results. Some people don't think so. Some people do think so.
So, these are just two different ways to approach the
problem of explaining the correlations -- which remain
unexplained so far.

 

[vanesch]

I did provide, some messages back, a sort of semi-classical
approach in terms of local interactions and common source
which even vanesch allowed was ok for the usual EPR-Bell type
setups of an emitter, two polarizers and two detectors, but can't
as yet be extended to eg. beamsplitter setups.
The problem is that details of the physical characteristics of the
emitted light are lacking.

I first thought that indeed a semiclassical approach allowed for the reconstruction of Malus' law because that was repeated so many times here. But then I did a calculation and according to me, this semiclassical model gives you eps^2 /8 (2 - cos(2(a-b))) as a correlation function, which is NOT the prediction of QM, nor can explain the experimental results, especially in the case of perpendicular polarizers.

So could you specify again your semiclassical model ? Give us, for each "measurement interval" (a few nanoseconds):

a) what common parameters does the light have on both sides (classical polarization ; maybe also something else) which went with it thanks to a common creation ; and how these parameters are statistically distributed over the entire sample.
b) how, from these parameters, the individual detection probabilities at Alice and Bob are given if their angles of polarizers are a and b respectively
c) how you calculate from this the joint probability of detection assuming statistical independence of the probabilities cited in b).

Local reality is still with us afaik. :) The question is whether we
need to posit superluminal signals to account for experimental
results.

?

Locality implies of course the absense of superluminal signals by definition! Well, unless you are willing to sacrifice causality or special relativity...

cheers,
Patrick.

 

[DrChinese]

That's an unwarranted conclusion. The experimental results rule out quantitative descriptions of a certain form. As yet,
nobody's quite sure what that means as far as nature is
concerned.

The form that is ruled out is the one in which the photon polarization has definite values for any other angles other than the ones actually observed. If you do not choose to call that the local realistic position, that is your choice. However, that is definitely what EPR envisioned and this is what everyone else calls it.

I did provide, some messages back, a sort of semi-classical
approach in terms of local interactions and common source
which even vanesch allowed was ok for the usual EPR-Bell type
setups of an emitter, two polarizers and two detectors, but can't
as yet be extended to eg. beamsplitter setups.
The problem is that details of the physical characteristics of the
emitted light are lacking.

I don't think Vanesch said that you advanced a local realistic position he agreed with. (Of course, he can speak for himself on the matter - edit: he does in the post above.)

However, the quantum mechanical description is as physical as any theory. How about F=ma? Is that a physical description? Why would that make more sense than the HUP, for example? Just because QM uses a different mathematical language doesn't make it less of a description.

Local reality is still with us afaik. :) The question is whether we need to posit superluminal signals to account for experimental
results. Some people don't think so. Some people do think so.
So, these are just two different ways to approach the
problem of explaining the correlations -- which remain
unexplained so far.

Local reality is generally ruled out (unless you think of MWI as local reality). I agree with your question, though. Which is: are superluminal effects present?

 

[Sherlock]

I first thought that indeed a semiclassical approach allowed for the reconstruction of Malus' law because that was repeated so many times here. But then I did a calculation and according to me, this semiclassical model gives you eps^2 /8 (2 - cos(2(a-b))) as a correlation function, which is NOT the prediction of QM, nor can explain the experimental results, especially in the case of perpendicular polarizers.

So could you specify again your semiclassical model ? Give us, for each "measurement interval" (a few nanoseconds):

a) what common parameters does the light have on both sides (classical polarization ; maybe also something else) which went with it thanks to a common creation ; and how these parameters are statistically distributed over the entire sample.
b) how, from these parameters, the individual detection probabilities at Alice and Bob are given if their angles of polarizers are a and b respectively
c) how you calculate from this the joint probability of detection assuming statistical independence of the probabilities cited in b).

Locality implies of course the absense of superluminal signals by definition! Well, unless you are willing to sacrifice causality or special relativity...

cheers,
Patrick.

The equation that you set up as a semi-classical model doesn't
describe the approach that I outlined. And it was *just* an
outline. :) I, presently, have no idea how to continue, to
'flesh it out', so to speak. And anyway I don't have time.

In saying that "local reality is still with us, afaik" ... I meant just
that. :) Since I don't think there's any need to posit the
existence of superluminal signals, as far as I'm concerned,
and certainly as far as anyone *knows*, they don't exist.

 

[Sherlock]

The form that is ruled out is the one in which the photon polarization has definite values for any other angles other than the ones actually observed. If you do not choose to call that the local realistic position, that is your choice. However, that is definitely what EPR envisioned and this is what everyone else calls it.

I don't think Vanesch said that you advanced a local realistic position he agreed with. (Of course, he can speak for himself on the matter - edit: he does in the post above.)

However, the quantum mechanical description is as physical as any theory. How about F=ma? Is that a physical description? Why would that make more sense than the HUP, for example? Just because QM uses a different mathematical language doesn't make it less of a description.

Local reality is generally ruled out (unless you think of MWI as local reality). I agree with your question, though. Which is: are superluminal effects present?

We're talking about the essence of entanglement.
Here's what Schroedinger had to say about it:

"If two separated bodies, each by itself known maximally,
enter a situation in which they influence each other,
and separate again, then there occurs regularly that
which I have called entanglement of our knowledge of
the two bodies."

Iow, the subsequent motion of the disturbances as they move
away from a point of interaction (or a common emission source)
contains a property or properties imparted to each as a result of
the interaction (or common origin). These shared properties are what 'entangle' subsequent instrumental records of the
disturbances, as long as it is the shared properties that are
being analysed. (So, you can let the entangled disturbances
move as far away from each other as you want, and as
long as the shared properties are undisturbed, then they'll
remain entangled.)

Now, doesn't this make more sense that positing the existence
of superluminal signals to account for the correlations.
(The lower bound on such signals increases as the entangled
disturbances move away from each other. At some scale of
separation, say opposite ends of the universe, the transmission
would have to be virtually instantaneous. Not a likely
scenario, imo.)

The formal treatment of entanglement by QM is the
embodiment of Schroedinger's original idea, afaik -- and
not some notion of superluminality. The problem is
simply that it can't be qualitatively descriptive enough
(wrt the *details* of the shared physical property or
properties) to dismiss the *possibility* that the entangled
instrumental results are due to superluminal signalling.
(But, as Einstein might say, it's a silly idea anyway :) )

So the program, as I see it, is to get creative and
develop some more descriptive local models that agree
with the experimental results.

 

[DrChinese]

The formal treatment of entanglement by QM is the
embodiment of Schroedinger's original idea, afaik -- and
not some notion of superluminality. The problem is
simply that it can't be qualitatively descriptive enough
(wrt the *details* of the shared physical property or
properties) to dismiss the *possibility* that the entangled
instrumental results are due to superluminal signalling.
(But, as Einstein might say, it's a silly idea anyway :) )

So the program, as I see it, is to get creative and
develop some more descriptive local models that agree
with the experimental results.

You are covering a lot of ground in one post...

1. Schroedinger's quote is not at all the same as the formal treatment by QM, and I don't see why you would think it is. They do NOT share any physical properties until they are observed and this is the essence of any quantum particle's state - which is always limited by the HUP. Certainty about one quantum property (as a result of an observation) creates uncertainty in another.

2. As to the superluminal signal idea... I don't accept that particularly either (maybe it is the case, I don't know) and yet I reject local reality. Bell's Theorem addresses the notion of simultaneous reality of non-commuting observables, and concludes this is incompatible with experiment. It does not REQUIRE superluminal transmission of anything.

3. As already indicated, no local realistic model can agree with experimental results.

 

[Sherlock]

... They do NOT share any physical properties until they are observed ...

If by "they" you mean the opposite-moving disturbances ...
well, nobody knows what they share or don't share. But,
the assumption is that they do share some physical property
or properties. That's what entanglement is all about.
Great care is taken to produce the shared properties
experimentally.

Keep in mind that QM is about the measurement results, not
the opposite-moving disturbances.

... As to the superluminal signal idea... I don't accept that particularly either (maybe it is the case, I don't know) and yet I reject local reality.

This seems like a rather confusing way to talk about it. :)

 

[vanesch]

Iow, the subsequent motion of the disturbances as they move
away from a point of interaction (or a common emission source)
contains a property or properties imparted to each as a result of
the interaction (or common origin). These shared properties are what 'entangle' subsequent instrumental records of the
disturbances, as long as it is the shared properties that are
being analysed. (So, you can let the entangled disturbances
move as far away from each other as you want, and as
long as the shared properties are undisturbed, then they'll
remain entangled.)

I wonder (really no offense intended) if you understood the implications of Bell's theorem, then. Indeed, the above situation is EXACTLY what Einstein thought was "really" happening, and about which Bell wrote his famous theorem. The "shared properties" are simply the "hidden variables". Well, it turns out - that's the entire content of Bell's theorem - that of course these shared properties can give rise to correlations in the observation (that's no surprise), but that correlations obtained that way SATISFY CERTAIN NON-TRIVIAL INEQUALITIES. Guess what ? Quantum theory's predictions violate those inequalities (and seem to be confirmed by experiment - under some *very* reasonable extra assumptions).

The hypothesis Bell started with was the following: correlations between probabilitic events can only have two different causes ; otherwise their randomness is independent. These two causes are: a) direct causal influence (meaning: what happens at A has a direct influence of what happens at B), or b) common origin of causes.
This is in fact a universally accepted idea (which turns out to be false in quantum theory), and most "common sense" judgements take it implicitly for granted. In fact, many people forget about the B option, which leads to a lot of nonsense (especially in politically colored studies), but Bell didn't of course.

Let us consider the following study: carefull investigation has led us to find out a remarkable correlation:there is a correlation between "driving a Jaguar" and "having a Rolex", which means that if P_j is the probability for someone to drive a Jaguar (quite low) and P_r is the probability for someone to have a Rolex (also quite low) and P_rj is the probability for someone to drive a jaguar and to have a rolex, then P_rj is bigger than P_r x P_j (which would be the case if there was no correlation).
You can make the case for the following: this proves that there must be a causal influence! And you find this unfair competition in the watch makers market, because you think that this is proof that the salesman who sells you a Jaguar gives you a Rolex with it for free, which would explain the correlation (there's a causal influence).
However, after your complaint, careful investigation of the records of all Jaguar dealers by the financial police brigade show that no such deals were made.
The other way around then ? People who buy a Rolex also get a Jaguar for free ? Mmmm... probably not, either. A mystery correlation then ?
No of course not. The answer is of course B: the common cause: if you're rich, there's more chance that you drive a Jaguar AND buy a Rolex !

So Bell set out to consider what happens if, for one reason or another, A (direct causal influence) is excluded, what happens with correlations by common cause, which you seem to think that explains entanglement. So his hypothesis was that a joint probability P(A,B) can only deviate from P(A) x P(B) if there is a common cause, which he called a "hidden variable" (in our case, it is the bank account of the people having jaguars and rolex watches). But for THE SAME VALUE of the hidden variable (same amount of money $$ on the bank account), you could expect that P_jr($$) = P_j($$) x P_r($$). Maybe it isn't. But then there is maybe yet another hidden variable, say "taste for luxury items T" etc...
So the idea of Bell was: lump ALL of the common causes, specified by values of hidden variables together in a set of parameters L ; if we have all common causes taken into L, then (even if we cannot know L) then
P(A,B ; L) = P(A ; L) x P(B ; L) (B1)

All statistical analysis in, say, medicine and human sciences takes this for granted.

Then, Bell said: over the entire population over which we will do our experiments, L will be distributed according to an (unknown) probability distribution p(L).

Of course, from B1 then follows that the measured joint probability over that population is then given by:

P(A,B) = integral P(A,B ; L) dp(L) = integral P(A;L) P(B;L) dp(L)
and:
P(A) = integral P(A ; L) dp(L)
P(B) = integral P(B ; L) dp(L)

I call these the equations B2.

We can extend them by considering ALL KINDS of correlations:
P(A, not B) = integral P(A ; L) {1 - P(B;L)} dp(L) etc...

As such, for TWO properties (A and B), they put some constraints on the values of P(A,B), P(A) and P(B), the 4 possibilities:
P(A,B) = a
P(A, not B) = b
P(not A, B) = c
P(not A, not B) = 1 - a - b - c
with a,b,c arbitrary numbers between 0 and 1, such that a+b+c <= 1
We have that P(A) = a + b and P(B) = 1 - a - c, which leads us to:

P(A) = P(A,B) + b and P(B) = 1 - P(A,B) - c with b + c <= 1 - P(A,B).

Call this the set of equations B3. For 2 properties A and B, this has nothing spectacular. But if you use that same reasoning for 3 properties A, B and C, you get more stringent conditions on P(A,B), P(A,C) ... ; which are however not very surprising for a statistician.

But now comes the point: if you calculate P(A,B), P(A,C) and P(B,C) from QM for certain properties A, B and C of an entangled state, then you do NOT satify these conditions ! This means that these probabilities cannot be described by something that has a "common cause" (hidden or not) as set out from the beginning. It even means that there is no LOGICAL POSSIBILITY for the properties A, B and C to be associated simultaneously to individual events, because the probabilities then simply don't add up to 1, each being between 0 and 1 !

The only way out is that you cannot measure A, B and C simultaneously. Horray ! That's the case in QM. But that means that you have to CHANGE YOUR MEASUREMENT SETUP to decide whether you measure A,B or A,C or B,C. And THEN there is a possibility: namely that this change in measurement setup CHANGES THE POPULATION p(L), so that when you are calculating P(A,B), you use ANOTHER p(L) than when you are calculating P(A,C). But that needs faster-than-light communication, because it means that, upon EMISSION, the pair will have to know what you are going to measure, to know from what population p(L) it has to be drawn: that can only happen through direct causal influence from the choice of the measurement to the population p(L).

So there is no way out: or there is a common cause L, with distribution p(L) (which is then of course the same, no matter what we are going to measure) and then we satisfy these equations, or there is not such a common cause, in which case there has to be a direct influence of the choice of the measurement on p(L) (or we abandon entirely the model that some L is at the origin of the outcomes). Given QM predictions and experimental results, clearly we are in the second case if we assign a reality to the measurements at spacelike separations.

My explanation (MWI) simply says that the measurement at Bob didn't take place, and only has a meaning when Alice learns about it ; at which point a direct causal influence can be kept local.

cheers,
Patrick.

 

[DrChinese]

If by "they" you mean the opposite-moving disturbances ...
well, nobody knows what they share or don't share. But,
the assumption is that they do share some physical property
or properties. That's what entanglement is all about.
Great care is taken to produce the shared properties
experimentally.

Keep in mind that QM is about the measurement results, not
the opposite-moving disturbances.

As Vanesch states, it sounds as if you don't understand Bell/Aspect (or perhaps deliberately choose to ignore it). We do understand a lot about entanglement, and that is that the entangled particles are in a superposition of states until they are observed. During that time, they do not have well defined physical properties - but they nonetheless share the same wavefunction perfectly. Further, the assumption you describe has been falsified by experiment IF by physical property you mean properties with definite values (hidden variables).

 

[Sherlock]

I wonder (really no offense intended) if you understood the implications of Bell's theorem, then. Indeed, the above situation is EXACTLY what Einstein thought was "really" happening, and about which Bell wrote his famous theorem. The "shared properties" are simply the "hidden variables". Well, it turns out - that's the entire content of Bell's theorem - that of course these shared properties can give rise to correlations in the observation (that's no surprise), but that correlations obtained that way SATISFY CERTAIN NON-TRIVIAL INEQUALITIES. Guess what ? Quantum theory's predictions violate those inequalities (and seem to be confirmed by experiment - under some *very* reasonable extra assumptions).

No offense taken.:) If I'm wrong in how I'm thinking about
this, then I don't mind being wrong sort of in a similar
way to Einstein.:) But, I don't think he was wrong, essentially.
I don't think that experimental violations of Bell inequalities
mean what a lot of people say they mean.

The hypothesis Bell started with was the following: correlations between probabilitic events can only have two different causes ; otherwise their randomness is independent. These two causes are: a) direct causal influence (meaning: what happens at A has a direct influence of what happens at B), or b) common origin of causes.
This is in fact a universally accepted idea (which turns out to be false in quantum theory), and most "common sense" judgements take it implicitly for granted. In fact, many people forget about the B option, which leads to a lot of nonsense (especially in politically colored studies), but Bell didn't of course.

Let us consider the following study: carefull investigation has led us to find out a remarkable correlation:there is a correlation between "driving a Jaguar" and "having a Rolex", which means that if P_j is the probability for someone to drive a Jaguar (quite low) and P_r is the probability for someone to have a Rolex (also quite low) and P_rj is the probability for someone to drive a jaguar and to have a rolex, then P_rj is bigger than P_r x P_j (which would be the case if there was no correlation).

You mean? ... P_j is the probability for someone to drive
a Jaguar and *not also* have a Rolex, and P_r is the probability
for someone to have a Rolex and *not also* drive a Jaguar.
P_rj > (P_r)(P_j), so P_r and P_j are not correlated wrt each
other.

Just like in the EPR-Bell experiments where P(A) and
P(B) aren't correlated wrt each other. :)

(I snipped some stuff)

Ok, the effort is appreciated. :) Here's my
view.

We're analyzing the entanglement. The assumption
is that the entanglement is due to common
properties imparted via common emission event.
In effect, the same light extending from polarizer
to polarizer. We're asking, in effect, to
what degree is it true that the light incident
on the polarizers is the same at A and B for
any set of joint measurements.

You wouldn't write this as,
P(A,B) = (cos^2 |a - L|) (cos^2 |b - L|)

Given our initial assumption, and the
observational context. we wouldn't expect
P(A,B) to be the correlation of P(A) and P(B)
wrt each other. Nor would we expect P(A,B)
to be a function of Lambda. We would expect
P(A,B) to be a function of Theta.

This *isn't* an individual measurement
context. Therefore, the variable, L, isn't
part of the joint formulation. (This doesn't
mean that L doesn't exist. :) )

The 'degree' to which the common property
or properties are shared is what's, in effect,
being analyzed by Theta (and being revealed by
violations of Bell inequalities). We're
assuming that it doesn't vary from pair to
pair.

If the polarizer-incident light is the same at
A and B, then coincidental detection should
vary in proportion to cos^2 Theta ... and it
does.

My explanation (MWI) simply says that the measurement at Bob didn't take place, and only has a meaning when Alice learns about it ; at which point a direct causal influence can be kept local.

The problem with this is that we can ascertain that
Bob's measurement did take place (in a meaningful way
via the permanent, irreversible, time-stamped data
records) before Alice learned about it.

And that's ok because we don't need causal
influences traveling between Alice and Bob to
account for the coincidence curve.

 

[Sherlock]

We do understand a lot about entanglement...

There's apparently a lot being done with it. Here's a cool
article in case you might not have seen it.

http://physicsweb.org/articles/news/5/9/12/1

... and that is that the entangled particles are in a superposition of states until they are observed.

Right, well that just relates the measurement possibilities wrt
the observational context.

During that time, they do not have well defined physical properties - but they nonetheless share the same wavefunction perfectly.

The wavefunction is about the measurement probabilities.
The deep physical properties of the disturbances that are
presumably causing the instrumental changes are not well
known.

Further, the assumption you describe has been falsified by experiment IF by physical property you mean properties with definite values (hidden variables).

A photon associated with a detector registration doesn't
exist (except symbolically) until it's produced by the
detector. It is assumed that there is some light associated
with the photon detection, and that this light exists before
the detection event. If the light physically exists prior to
detection , then it has some physical characteristics. But,
the photon detection event doesn't tell us enough about the
light to give a very detailed picture. So, the properties
of the light prior to detection are, in effect, more or less,
hidden. If these properties are varying from emission to
emission (and it's a pretty good bet that they are vis the
individual data streams), then these properties of the light
that is producing the instrumental changes are both
somewhat hidden and variable.

So, I guess something else is meant by hidden variable ...
and I consider that to be a rather confusing way to use the
language. :)

As for the assumption of common properties imparted
at emission. This is not Lambda. It doesn't vary from
pair to pair. It's just the assumption that for any and
all pairs, the light incident on polarizer A is, in effect,
the same as the light incident on polarizer B.

There are no hidden variables *relevant* to coincidental
detection. The relevant variable is Theta. The global
property, the entanglement, of the light incident on
A and B that's being analyzed by Theta is a constant.
At least that's the assumption.

 

[DrChinese]

There's apparently a lot being done with it. Here's a cool
article in case you might not have seen it.

http://physicsweb.org/articles/news/5/9/12/1

That is incredibly cool! Thanks!

 

[vanesch]

You mean? ... P_j is the probability for someone to drive
a Jaguar and *not also* have a Rolex, and P_r is the probability
for someone to have a Rolex and *not also* drive a Jaguar.
P_rj > (P_r)(P_j), so P_r and P_j are not correlated wrt each
other.

No, I mean with P_j, the probability for someone to drive a Jaguar REGARDLESS whether he has a rolex or not !

Just like in the EPR-Bell experiments where P(A) and
P(B) aren't correlated wrt each other. :)

And what is the joint probability for uncorrelated events ? If P1 is the probability to throw heads (usually taken 1/2) of a coin, and P2 is the probability to throw 6 on a dice (usually taken 1/6) what is the JOINT PROBABILITY to throw heads with the coin and a 6 on the dice, assuming that the coin and the dice are giving us uncorrelated probabilities ?
Isn't this P1 x P2 ?

We're analyzing the entanglement. The assumption
is that the entanglement is due to common
properties imparted via common emission event.
In effect, the same light extending from polarizer
to polarizer. We're asking, in effect, to
what degree is it true that the light incident
on the polarizers is the same at A and B for
any set of joint measurements.

You wouldn't write this as,
P(A,B) = (cos^2 |a - L|) (cos^2 |b - L|)

Small correction: this is P(A,B ; L): only for a fixed value of L.

Well, you surely would. L is the polarization angle of the light which is emitted both to A and to B, right ? Now you told me that the probability of being detected by a polarizer under angle a is then (Malus' law) cos^2(a-L). But there is such a detection at A (with incident light under angle L), and there is SUCH AN INDEPENDENT detection at B, this time with angle b.
That's of course the whole point: these detection events are, in a semiclassical model, independent, because there are classically only 2 ways to NOT have statistical independence, which is 1) direct causal influence (which is excluded here because of the spacelike separation) 2) common cause not taken into account. But we DID take the common cause into account with variable L. So FOR A GIVEN VALUE OF L, the events have no EXTRA common cause anymore, and their probabilities are hence independent.

Given our initial assumption, and the
observational context. we wouldn't expect
P(A,B) to be the correlation of P(A) and P(B)
wrt each other. Nor would we expect P(A,B)
to be a function of Lambda. We would expect
P(A,B) to be a function of Theta.

Well, P(A,B) IS of courrse a function of theta, because we don't observe L. So the probabilities given above, depending on L, still have to be weighted over the population of L. But from symmetry it is easy to find out that that population is uniform: p(L) dL = 1/2Pi dL.
After integration of P(A,B ; L) over p(L), you find the OBSERVABLE P(A,B), which is of course NOT equal to P(A) (equal to 1/2) x P(B) (also equal to 1/2). That's because we took into account the "common cause" which was the fact that the polarization L was identical.

This *isn't* an individual measurement
context. Therefore, the variable, L, isn't
part of the joint formulation. (This doesn't
mean that L doesn't exist. :) )

I don't know what you mean. L is determining the probability of detection for an incident beam of polarization L, and, this being the only parameter that determines these probabilities, they are independent at spacelike separated intervals. So of course they are part of it !

The 'degree' to which the common property
or properties are shared is what's, in effect,
being analyzed by Theta (and being revealed by
violations of Bell inequalities). We're
assuming that it doesn't vary from pair to
pair.

I agree with what you say, and I don't vary THETA, I vary L (the incident, common, polarization of the light).

If the polarizer-incident light is the same at
A and B, then coincidental detection should
vary in proportion to cos^2 Theta ... and it
does.

Apart from stating this, how do you obtain it, from the individual detection probabilities ?? You pull this out of nowhere.
You still have to provide me with the probabilities, for an incident beam with polarization L, of:
P(A, ~B ; L) (the probability of A clicking, and B not clicking with incident L)
P(A,B ; L)
P(~A,B ; L)
P(~A,~B ; L)

given that A has its polarizer at angle a and B has its polarizer at angle b, and the probability distribution of L (which should be 1/2Pi given by symmetry, but you are free to specify it).

The problem with this is that we can ascertain that
Bob's measurement did take place (in a meaningful way
via the permanent, irreversible, time-stamped data
records) before Alice learned about it.

Those "irreversible time stamped records" are supposed to be in a superposition of different states (a sheet of paper is in a superposition of having 0 on it, and 1 on it), and Alice chooses which of these branches she will actually observe.
But let us not treat two problems at the same time.

cheers,
patrick.

 

[Sherlock]

But we DID take the common cause into account with variable L. So FOR A GIVEN VALUE OF L, the events have no EXTRA common cause anymore, and their probabilities are hence independent.

Detection at either end is random and
independent of what happens at the other end.
But you didn't take the common cause(s) of the
correlations into account. Lambda (the *variable*,
from pair to pair, shared properties of the
emitted light) is a factor in determining individual
results, but the combined context isn't analyzing
Lambda.

The combined context is analyzing the, assumed,
*unchanging* relationship between the properties
of the light incident on A and the properties
of the light incident on B for any given
emission/coincidence interval. That is, whatever
the value of Lambda is, it's always the same
at A as it is at B, and vice versa.

The common cause of the shared properties of the
light incident on the polarizers is the emission
event(s) that produced the light.

The common cause of variations in the
rate of coincidental detection is variations
in Theta, the angular difference between the
polarizers.

The variable Lambda determines the rate of
individual detection. Lambda's value has no
effect on the rate of coincidental detection.

P(A) and P(B) are not *correlated* wrt Lambda.

P(A) and P(B) *correlated* wrt Theta.

We're analyzing the shared rotational, and perhaps
other, properties of the light incident on the
polarizers. These properties are assumed to be the
same at A and B for paired (A,B) measurements.
This global parameter (assumed to be produced via
common emission event(s) for photon_1 and photon_2
of any and all pairs) is assumed to be *unchanging*
from pair to pair. (In effect, A and B are, jointly,
always analyzing the same light.)

There's no way to have P(A,B) in the
form of the product of individual probabilities.
P(A) and P(B) *are* causally independent,
but because they're correlated wrt Theta,
then Theta has to be in the formulation
for P(A,B). But there is no Theta (angular
difference between the polarizers) in the
individual contexts, so it obviously
doesn't determine individual results, and
there's obviously no way to express
individual probabilities in terms of Theta.

There *is* a Lambda, in the combined measurement
context. But, it's value is irrelevant wrt
coincidental detection, so it doesn't figure
into the formulation. We're not analyzing
the variable Lambda. We're analyzing the
degree to which the assumed emission-produced
entanglement of the light incident on the
polarizers has been instrumentally produced.

Given the foregoing assumptions, you would
*expect* the rate of coincidental detection to
vary as cos^2 Theta, wouldn't you? I didn't
pull this out of nowhere.:) This is, classically,
the formula that relates the amplitudes of the light
waves that are between the crossed linear polarizers
and their respective detectors (given that
the light incident on (ie., *between*)
the polarizers is the same for any given
coincidence interval.

The entanglement is the common rotational or
other properties imparted via common emission
events -- the commonality of which is assumed
to be constant from pair to pair. It's this
presumably unchanging commonality which is
being analyzed. The only variable in the
joint observational context is Theta.

You can't see the correlations from the
perspective of a combination of the individual
probabilities. But if you envision the process
in terms of variations in Theta and the same
light between the polarizers, then it becomes
clear how rate of coincidental detection must
vary, nonlineary, in proportion to changes in
Theta.

Bell asked if supplementary variable
such as Lambda would be compatible with
QM formulation. The answer is no.
Just not for the reasons that most people
give.

The degree to which Bell inequalities
are violated can tell us something about
the degree to which entanglement has
been instrumentally produced and preserved.
But, it doesn't tell us anything, necessarily,
about exactly where the entanglement is or isn't
produced, or whether nature is local or
nonlocal.

 

[vanesch]

The common cause of the shared properties of the
light incident on the polarizers is the emission
event(s) that produced the light.

The common cause of variations in the
rate of coincidental detection is variations
in Theta, the angular difference between the
polarizers.

How can one polarizer "know" what is the value of theta (and hence the angle of the "other" polarizer, in order to adapt its local detection rate to it ??

The variable Lambda determines the rate of
individual detection. Lambda's value has no
effect on the rate of coincidental detection.

P(A) and P(B) are not *correlated* wrt Lambda.

P(A) and P(B) *correlated* wrt Theta.

Ah, so you mean that for polarized light with a FIXED lambda (say, we use a source which always sends out light with a known polarization direction, for instance because there is a polarizer in the source), the probability of detecting an event at A (that's P(A)) is INDEPENDENT of the angle of polarization of the source ?? So whether the source is at 90 degrees or parallel, that will always result in the same detection rate at A ?
On the other hand, it IS dependent of the angle at B ? That's funny. I thought that light at 90 degrees with respect to a polarizer didn't get through, and light which is parallel got through. But you say that the detection probability is INDEPENDENT of the relative angle between the polarization of the light (Lambda) and the angle of the analyzer at A. It only depends on the angle between the analyzer at A and the angle of the analyser at B. Independent of whether the source is linearly polarized.

There's no way to have P(A,B) in the
form of the product of individual probabilities.
P(A) and P(B) *are* causally independent,
but because they're correlated wrt Theta,
then Theta has to be in the formulation
for P(A,B).

What do you mean by "causally independent" then, if they are not a product ? That's the very definition of statistical independence !
Again, for a source with FIXED, linear polarization under angle Lambda, what do you think that the following probabilities are ?

P(A) (probability of detection at A, with angle a)
P(B) (probability of detection at B, with angle b)
P(A,B) (joint probability of detection at A and B)
P(A, ~B) (joint probability of detection at A and no detection at B).
P(~A,B) (joint probability of detection at B and no detection at A).
P(~A,~B) (joint probability of no detection at A and at B).

Note that, with polarizing beam splitters, P(~A,B) simply means that on the A side, we've got a detection at the OTHER photodetector, and not at the photodetector at angle a. There are two photodetectors on each side, one corresponding to the "correct" angle, and one corresponding to the "perpendicular" angle.

But there is no Theta (angular
difference between the polarizers) in the
individual contexts, so it obviously
doesn't determine individual results, and
there's obviously no way to express
individual probabilities in terms of Theta.

Well, I'm sorry, but P(A) = P(A,B) + P(A,~B) and P(B) = P(A,B) + P(~A,B), so there IS a relationship between P(A), P(B) and P(A,B). By definition, the individual events are statistically independent if P(A,B) = P(A) x P(B). If you can determine (as a function of Theta) what is P(A,B) (and also P(A,~B) etc..), then you have of course fixed P(A) and P(B). So it *does* determine individual results.

Given the foregoing assumptions, you would
*expect* the rate of coincidental detection to
vary as cos^2 Theta, wouldn't you?

No, not at all. Malus' law tells me what I'm supposed to get as a detection probability as a function of THE DIFFERENCE OF THE POLARIZATION ANGLE OF THE LIGHT AND THE DIRECTION OF THE ANALYZER. Malus' law doesn't say anything about two analyzers being correlated or not. So I don't know where you get your cos^2 theta from. Again, do you expect cos^2 theta to be the joint detection probability P(A,B) IRRESPECTIVE of the incident polarization ?

This is, classically,
the formula that relates the amplitudes of the light
waves that are between the crossed linear polarizers
and their respective detectors (given that
the light incident on (ie., *between*)
the polarizers is the same for any given
coincidence interval.

No, it is the formula that gives you the RELATIONSHIP between the light intensity between the two polarizers on one hand, and after the two polarizers on the other (the first polarizer fixes the polarization direction of the light in between, and the second one analyzes this light). But the setup here is different. The light doesn't go through two polarizers in succession. One beam goes to one polarizer, and another beam goes to another.
Imagine one polarizer broken, so that it let's through all light. If we apply you reasoning, we first have a polarizer and next we have a glass plate (broken polarizer). "Malus' law" for this setup is simply 1 (ratio of intensity behind the glass plate to the intensity between glass plate and first polarizer). Do you still maintain that in that case, the joint probability of detection equals 1, irrespectively what is the polarization of the incident light ?
What happens, then, if the incident light is perpendicularly polarized to the one and only polarizer we have ? I'd think that we would have joint probability 0, because the detector behind the polarizer will never click.

cheers,
Patrick.

 

[seratend]

How can one polarizer "know" what is the value of theta (and hence the angle of the "other" polarizer, in order to adapt its local detection rate to it ??

This is the eternal problem of contextuality in QM . The probability law of the 2 random variables is given by (a.A, b.B, |psi>). For every (a,b) we have a couple of different random variables that give the probability law of the QM outcomes.

(Note, I have not read the rest of the post. Sorry if it is completely out of the context).

(just to add more confusion to this thread )

Seratend.

 

[Sherlock]

How can one polarizer "know" what is the value of theta (and hence the angle of the "other" polarizer, in order to adapt its local detection rate to it ??

Well, *one* polarizer can't know the value of Theta.
But, Theta is the observational context that produces the
correlations (predictable *joint* results). So, Theta
is analyzing something which isn't varying randomly. It's
analyzing how *alike* the wavepackets incident on
polarizer_a and polarizer_b are. Theta is analyzing
the degree of sameness of the emitted, paired wavepackets.
Theta is analyzing the entanglement, which is assumed
to not vary from pair to pair. Theta is not analyzing
some/any specific value for Lambda.

If Theta is analyzing the same thing, then if Theta
is 0 we would expect the amplitudes of the wavepackets
transmitted by polarizer_a and polarizer_b to be
the same.

The variable Lambda determines the rate of
individual detection. Lambda's value has no
effect on the rate of coincidental detection.

P(A) and P(B) are not *correlated* wrt Lambda.

P(A) and P(B) are *correlated* wrt Theta.

Ah, so you mean that for polarized light with a FIXED lambda (say, we use a source which always sends out light with a known polarization direction, for instance because there is a polarizer in the source), the probability of detecting an event at A (that's P(A)) is INDEPENDENT of the angle of polarization of the source ?? So whether the source is at 90 degrees or parallel, that will always result in the same detection rate at A?

I mean that in the experiments jointly analyzing
paired wavepackets assumed to be entangled via
emission, the correlation P(A,B;L) doesn't describe
the observational context.

The observational context is the joint settings
of polarizer_a and polarizer_b (Theta) analyzing
the emission-produced entanglement. The entanglement
is not represented by the variable, Lambda.

What do you mean by "causally independent" then, if they are
not a product ? That's the very definition of statistical
independence!

I mean that P(A) and P(B) are not *causally* related
*to-each-other*. Nor is P(A,B) causally related to
changes in Lambda. P(A,B) is causally related to
changes in Theta, because Theta is analyzing,
simultaneously, the strength of the entanglement
of the wavepackets incident on polarizer_a and
polarizer_b during any given emission/coincidence
interval.

Wrt Theta, the results at A and B, P(A,B), are
not statistically independent.

... there IS a relationship between P(A), P(B) and P(A,B). By definition, the individual events are statistically independent if P(A,B) = P(A) x P(B). If you can determine (as a function of Theta) what is P(A,B) (and also P(A,~B) etc..), then you have of course fixed P(A) and P(B). So it *does* determine individual results.

I don't think so. Because then you'd be saying that the
*entanglement*, per se, determines individual results. But it
doesn't. The entanglement only (via Theta) determines
joint results. You can't observe the entanglement in the
individual context. You can, sort of, observe Lambda
(the randomly varying wavepacket properties) in the individual
context.

Malus' law tells me what I'm supposed to get as a detection probability as a function of THE DIFFERENCE OF THE POLARIZATION ANGLE OF THE LIGHT AND THE DIRECTION OF THE ANALYZER. Malus' law doesn't say anything about two analyzers being correlated or not. So I don't know where you get your cos^2 theta from. Again, do you expect cos^2 theta to be the joint detection probability P(A,B) IRRESPECTIVE of the incident polarization?

Cos^2 Theta relates the amplitudes of the wavepackets
produced by the polarizers. These amplitudes (and other,
eg., rotational, properties) are subsets, maybe proper
subsets, of the wavepackets incident on the
polarizers. If a detection is recorded, then the
amplitude of the wavepacket that produced it (the amplitude
of the wavepacket transmitted by the polarizer), whether
the same or different from the emission amplitude and
whether the same or different wrt any other properties
of the emitted wavepacket, can be taken as extending
between the polarizers (ie., contained in the wavepacket
incident on the other polarizer for the same interval).
So, if Theta = 0 then we expect identical results, and
as Theta increases we expect the incidence of indentical
results to decrease as cos^2 Theta.

No, it is the formula that gives you the RELATIONSHIP between the light intensity between the two polarizers on one hand, and after the two polarizers on the other (the first polarizer fixes the polarization direction of the light in between, and the second one analyzes this light).

It's the formula that gives the relationship between the
amplitude (and therefore the intensity) of the light
produced by the second polarizer wrt the amplitude (intensity)
of the light produced by the first polarizer.

But the setup here is different.

Yes, somewhat. But, I'm asking you to see the similarities.:)

 

[DrChinese]

Well, *one* polarizer can't know the value of Theta.
But, Theta is the observational context that produces the
correlations (predictable *joint* results). So, Theta
is analyzing something which isn't varying randomly. It's
analyzing how *alike* the wavepackets incident on
polarizer_a and polarizer_b are. Theta is analyzing
the degree of sameness of the emitted, paired wavepackets.
Theta is analyzing the entanglement, which is assumed
to not vary from pair to pair. Theta is not analyzing
some/any specific value for Lambda.

If Theta is analyzing the same thing, then if Theta
is 0 we would expect the amplitudes of the wavepackets
transmitted by polarizer_a and polarizer_b to be
the same.

The problem with this entire argument is that it is exactly what Bell's Theorem was intended to demonstrate could NOT be the case. You cannot advance this argument without addressing Bell first. Period. Vanesch has tried to make this clear. You can say all day long that you MUST be right but that is what makes Bell so special... it forces us to throw out something we would otherwise defend strongly.

 

[vanesch]

So, Theta
is analyzing something which isn't varying randomly. It's
analyzing how *alike* the wavepackets incident on
polarizer_a and polarizer_b are. Theta is analyzing
the degree of sameness of the emitted, paired wavepackets.
Theta is analyzing the entanglement, which is assumed
to not vary from pair to pair. Theta is not analyzing
some/any specific value for Lambda.

If Theta is analyzing the same thing, then if Theta
is 0 we would expect the amplitudes of the wavepackets
transmitted by polarizer_a and polarizer_b to be
the same.

I agree with you about 2 points:
1) P(A,B) will be a function of theta. But it will of course also be a function of the polarization of the incident light.
2) if theta = 0, then the amplitudes of the wavepackets transmitted by polarizer_a and polarizer_b are to be the same.

But remember that that doesn't mean that P(A,B) is equal to 1. Let us suppose for a moment that a = b. If the incident light is perpendicular to a and b, then P(A,B) = 0. If the incident light is parallel to a and b, then P(A,B) = 1. I could think you agree with that ? So this proves already that P(A,B), in the case of a = b, is not only a function of theta (= 0), because we obtain two different values for the same theta !

You still didn't give me P(A,B ; a, b, L) and the complementary functions P(~A,B ; a,b,L) etc... If you think that L doesn't play a role, then just write a function that doesn't depend on L.

cheers,
Patrick.

 

[Sherlock]

Well, *one* polarizer can't know the value of Theta.
But, Theta is the observational context that produces the
correlations (predictable *joint* results). So, Theta
is analyzing something which isn't varying randomly. It's
analyzing how *alike* the wavepackets incident on
polarizer_a and polarizer_b are. Theta is analyzing
the degree of sameness of the emitted, paired wavepackets.
Theta is analyzing the entanglement, which is assumed
to not vary from pair to pair. Theta is not analyzing
some/any specific value for Lambda.

If Theta is analyzing the same thing, then if Theta
is 0 we would expect the amplitudes of the wavepackets
transmitted by polarizer_a and polarizer_b to be
the same.

The problem with this entire argument is that it is exactly what Bell's Theorem was intended to demonstrate could NOT be the case. You cannot advance this argument without addressing Bell first. Period. Vanesch has tried to make this clear. You can say all day long that you MUST be right but that is what makes Bell so special... it forces us to throw out something we would otherwise defend strongly.

I'm not saying that I must be right. I'm just presenting a way of
looking at these sorts of experiments that seems to me to make
sense.

Bell showed that the correlations can't be due to Lambda -- unless
some sort of superluminal causal influence or signal is involved.
I agree with that. The correlations aren't due to Lambda.

The correlations are due to the analysis of a global property
(the entanglement of the light incident on the polarizers) that
is revealed in the context of joint polarizer settings (Theta),
but not in the context of individual measurement.

The entanglement isn't a variable. The entanglement isn't
represented by Lambda. The only thing varying in
the joint context that is relevant to coincidental detection
is Theta.

Bell didn't deal with that, and so violations of Bell inequalities
don't contradict the idea that the entanglement is produced
at emission, and therefore coincidental detection varies
nonlinearly as a function of this (presumed) unchanging
global property of the incident light (the entanglement)
being analyzed simultaneously by crossed linear polarizers.

Now, if anyone has any specific objection to the view
I've presented, other than to offer a reiteration of why
Lambda can't be responsible for the correlations (which I
agree with), then I'm glad to hear it.

I'm quite familiar with Bell's analysis. One day the thought
struck me that Bell's Theorem isn't really dealing with
what is happening in the experiments. It isn't dealing
with the actual observational context. We're not analyzing
a variable (Lambda), we're analyzing a constant (the
entanglement). So, of course, the correct correlation
function can't be generated via individual contexts
wrt Lambda.

 

[Sherlock]

I agree with you about 2 points:
1) P(A,B) will be a function of theta. But it will of course also be a function of the polarization of the incident light.

It's only a function of Theta. And, I'll grant you that that *is*
the hardest thing to envision. But, keep in mind that it isn't
Lambda that's being analyzed. Whatever amplitude was transmitted
by one polarizer to produce a detection, it's, a subset of the
light that's incident on the other polarizer for that interval
(via the assumption of emission entanglement).

2) if theta = 0, then the amplitudes of the wavepackets transmitted by polarizer_a and polarizer_b are to be the same.

But remember that that doesn't mean that P(A,B) is equal to 1.

P(A,B) is the probability of coincidental detection, ++ or --. So,
if Theta = 0 then P(A,B) = 1. In the actual experiments, I don't
think there's any way to count coincidental nondetections, since
the coincidence circuitry is only activated upon detection at
either A or B.

Let us suppose for a moment that a = b. If the incident light is perpendicular to a and b, then P(A,B) = 0. If the incident light is parallel to a and b, then P(A,B) = 1. I could think you agree with that ? So this proves already that P(A,B), in the case of a = b, is not only a function of theta (= 0), because we obtain two different values for the same theta!

Another nice demonstration of why trying to explain the
correlations in terms of assumed values for Lambda is
not the right approach. :)

You still didn't give me P(A,B ; a, b, L) and the complementary functions P(~A,B ; a,b,L) etc... If you think that L doesn't play a role, then just write a function that doesn't depend on L.

P(A,B) = cos^2 Theta. :)

This is an empirical law that applies to setups which I
think are quite similar to the archetypal EPR-Bell tests
(eg. Aspect et al.). Afaik, there's no way to get that
function using Lambda.

I could be quite wrong in my analogizing, but so far I
don't think so. In my perusal of several books and
a few dozen papers dealing with Bell stuff, I haven't
seen this line of reasoning used. But you probably
have read more articles than I. Anyway, if it is
a novel approach, then maybe you can develop
it into a paper. Or, maybe you'll demolish the
idea in your next message. One never knows. :)

 

[vanesch]

P(A,B) is the probability of coincidental detection, ++ or --.

No, a priori P(A,B) is the probability of detector A and detector B clicking, in an arbitrary interval of, say, 10 ns.
P(A) is the probability of detector A clicking in an arbitrary interval of 10 ns and P(B) is the probability of detector B clicking in an arbitrary interval of 10 ns.

However, the quantum probabilities are renormalized on 1-photon events, but of course this is not possible in a semiclassical model, which will introduce an overall "attenuation": most of the time, A doesn't click, and B doesn't click.

I would like to point out that we can normalize (in quantum theory) quite easily onto the number of photon events: indeed, we do not use absorbing polarizers, but polarizing beam splitters, with 2 detectors. The transmitted beam is the same as of an absorbing polarizer, but the complementary part which is absorbed in an absorbing polarizer is now sent into the reflected beam, so that there is conservation of intensity. We will call that event An.
If the detectors are perfectly efficient, then always exactly one detector (A or An) triggers ; otherwise sometimes they do not. But they NEVER trigger together (this exclusiveness cannot be explained classically btw).
So we can normalize on a click in ONE OF BOTH detectors. When we do so, P(A) + P(An) = 1, so we can take An to be equivalent to ~A (thanks to the exclusiveness of A and An).
Semiclassically you can then do the same: P(A,B) is then defined as the probability that A and B click together, when at A, one of both detectors (A or An) triggers. Mind you that this is NOT the same than P(B | A). Indeed, B can click when An clicks.
The only serious problem is that semiclassically, there is no way to stop A and An to click BOTH. But this is not empirically observed (Thorn's experiment!) and moreover not allowed for by QED. So use as a normalization P(A or An).

When the light is polarized, and is perpendicular to a and b (theta = 0), then it is ALWAYS An and Bn that trigger, never A or B. So this leads to P(A,B) = 0. When the light is polarized and parallel to a and b, then it is always A and B that trigger, never An or Bn, and we have P(A,B) = 1.

So,
if Theta = 0 then P(A,B) = 1. In the actual experiments, I don't
think there's any way to count coincidental nondetections, since
the coincidence circuitry is only activated upon detection at
either A or B.

There is, using a polarizing beam splitter and two detectors on each side, as was first done by Aspect.

P(A,B) = cos^2 Theta. :)

Clearly this is wrong when the incident light is perpendicular to a and b, in which case P(A,B) = 0. But you were not using the right P(A,B), which is the probability for A and B to click together when A or An click. (or when B or Bn click, which is the same in the case of perfect detectors - which we don't have but correct for finite efficiency).

This is an empirical law that applies to setups which I
think are quite similar to the archetypal EPR-Bell tests
(eg. Aspect et al.). Afaik, there's no way to get that
function using Lambda.

Indeed, there is no way to get that function using lambda, and that's exactly the content of Bell's theorem !

cheers,
Patrick.

 

[DrChinese]

I'm not saying that I must be right. I'm just presenting a way of looking at these sorts of experiments that seems to me to make
sense.

Bell showed that the correlations can't be due to Lambda -- unless
some sort of superluminal causal influence or signal is involved.
I agree with that. The correlations aren't due to Lambda.

The correlations are due to the analysis of a global property
(the entanglement of the light incident on the polarizers) that
is revealed in the context of joint polarizer settings (Theta),
but not in the context of individual measurement.

The entanglement isn't a variable. The entanglement isn't
represented by Lambda. The only thing varying in
the joint context that is relevant to coincidental detection
is Theta.

Bell didn't deal with that, and so violations of Bell inequalities
don't contradict the idea that the entanglement is produced
at emission, and therefore coincidental detection varies
nonlinearly as a function of this (presumed) unchanging
global property of the incident light (the entanglement)
being analyzed simultaneously by crossed linear polarizers.

Now, if anyone has any specific objection to the view
I've presented, other than to offer a reiteration of why
Lambda can't be responsible for the correlations (which I
agree with), then I'm glad to hear it.

I have a specific objection: your idea that the incident light produces a "presumed" function Theta which has a) hidden variables, but no Lambda; and b) the correlations still change according to distant settings prepared while the photons are in flight.

You don't need Lambda anyway to get Bell's Theorem. All you need to believe is that the wave function had a definite value for ANY possible polarizer setting at one of the detectors independent of the setting at the other. That is at the base of your presumption no matter how you try to describe it. Specifically, that results for polarizer settings A, B AND C could all exist simultaneously. If you say there are only A and B, you are describing the QM view.

Vanesch has called for you to present some details of your Theta. The burden is now on you to present something other than a few words if you want to make a convincing argument. It may make "sense" to you, but it doesn't make sense to me. You may as well just say that you assume you are right, and are leaving the details of your argument to someone else.