Need Understandable Explanation Of Bell's Theorum

[DrChinese]

Regarding my previous post:

So far I could not find an explicit statement which would be more specific and definite than the description of the experiment above, contained in the link. Finding such a statement is difficult since "quantum-nonlocality" is often used as a short-hand of saying "quantum - nonlocalRealism". However, many texts suggest implicitly that the entangled particles coordinate their behavior (in measurement) non-locally, depending on the measurement angles, meaning: after these angles have been chosen, and after the particles have separated already.

I did find a link to the corresponding pdf, describing the above experiment in more detail:
http://www.univie.ac.at/qfp/publications3/pdffiles/1998-04.pdf"

Also I think it is necessary to point out that local-hidden-variable models (at least usually) require both locality and realism, so in both cases (non-locality or non-realism) local-hidden-variable models are ruled out, at least those which could be called "classical", as far as I understand.

A.Zeilinger seems to tend towards a view that is both non-local and non-realist, for example there is the following comment on one of his latest experiments: "Our result suggests that giving up the concept of locality is not sufficient to be consistent with quantum experiments, unless certain intuitive features of realism are abandoned."

So far I haven't read about any model that would explain the correlations in a non-realist yet local way, and I'd be interested to hear what such a model might be like.

Bell's Theorem compares local realistic theories with Quantum Mechanics. Bell tests such as the one you reference (under strict locality conditions) are just tests of local realistic theories. The "strict locality" part does NOT mean it is testing locality alone. This is a common misconception. It may be that the "true" theory is local and non-realistic. Many folks believe this to be the case, and it is a popular (even if not the majority) interpretation of QM. If you are in this camp, you do not believe that there are causes which propagate faster than c. You also believe that the QM is "complete".

 

[colorSpace]

Bell's Theorem compares local realistic theories with Quantum Mechanics. Bell tests such as the one you reference (under strict locality conditions) are just tests of local realistic theories. The "strict locality" part does NOT mean it is testing locality alone. This is a common misconception. It may be that the "true" theory is local and non-realistic. Many folks believe this to be the case, and it is a popular (even if not the majority) interpretation of QM. If you are in this camp, you do not believe that there are causes which propagate faster than c. You also believe that the QM is "complete".

As I said, this currently only means to me that it could be one big coincidence, unless there is a more meaningful model that explains the correlations, which I haven't even heard about yet.

[Edit:] What kind of model are 'many folks' thinking about?

 

[colorSpace]

[continued from my last message]

Putting together what you said so far, it seems you are talking about a combination of local-hidden-variable models with Heisenberg uncertainty, believing that the latter would make a model non-realistic enough to avoid being ruled out by Bell's theorem. Although I'm not enough of a mathematician to tell whether that avoids Bell's argument in a purely formal way, I'm convinced that the mere assumption of Heisenberg uncertainty is not enough to potentially address the existing correlations, given that classical communication between the particles has been ruled out, as well as the origination of information from a common source. That is, I would be very surprised if the disproof of local realism, which includes local-hidden-variable models, would be defeated by the mere addition of Heisenberg uncertainty (unless this in turn would imply non-locality).

However, that makes the position you describe more understandable to me on a level of 'theoretical proof' arguments.

Nevertheless, what is apparently missing, in any case, is, practically speaking, a local explanation of the correlations which would survive the refutation of classical communication and the refutation of information carried within the particles, through experiments such as the above.

 

[DrChinese]

[continued from my last message]

Putting together what you said so far, it seems you are talking about a combination of local-hidden-variable models with Heisenberg uncertainty, believing that the latter would make a model non-realistic enough to avoid being ruled out by Bell's theorem. Although I'm not enough of a mathematician to tell whether that avoids Bell's argument in a purely formal way, I'm convinced that the mere assumption of Heisenberg uncertainty is not enough to potentially address the existing correlations, given that classical communication between the particles has been ruled out, as well as the origination of information from a common source. That is, I would be very surprised if the disproof of local realism, which includes local-hidden-variable models, would be defeated by the mere addition of Heisenberg uncertainty (unless this in turn would imply non-locality).

However, that makes the position you describe more understandable to me on a level of 'theoretical proof' arguments.

Nevertheless, what is apparently missing, in any case, is, practically speaking, a local explanation of the correlations which would survive the refutation of classical communication and the refutation of information carried within the particles, through experiments such as the above.

There are 2 separate issues here, and they often get mixed together. Here are the issues:

A. Bell's Theorem defines a "realistic" theory as one in which particle observables have well-defined values independent of the act of observation. It then shows that NO realistic theory can make experimental predictions compatible with those of Quantum Mechanics. Bell then states that if there exist non-local forces between measuring apparati, that would allow a mechanism in which a realistic theory could still exist AND yield results compatible with the predictions of QM.

B. The question arises, HOW could a local non-realistic theory explain the correlations seen in QM? Note that this has nothing to do with A. above. Bell's Theorem says that it is possible that a local non-realistic theory OR a non-local realistic theory could exist that mimics the predictions of QM. It will take another breakthrough - which may or may not ever happen - to understand how either of these could be represented in some "physical" manner.

It is actually no simple matter to hypothesize that there are non-local forces which communicate between measuring apparati as a "solution" to the problem posed by Bell's Theorem. IF there are such forces, why are they nowhere else to be found?

On the other hand, there is something else which is found all over the place: the Heisenberg Uncertainty Principle. That is as "non-realistic" as it gets!

So I would say: don't take it for granted that a non-local solution is automatically more understandable and intuitive than a non-realistic solution. I think either one is a head-scratcher.

 

[colorSpace]

Thanks for the response, I find it very interesting to go further into these matters.

There are 2 separate issues here, and they often get mixed together. Here are the issues:

A. Bell's Theorem defines a "realistic" theory as one in which particle observables have well-defined values independent of the act of observation. It then shows that NO realistic theory can make experimental predictions compatible with those of Quantum Mechanics. Bell then states that if there exist non-local forces between measuring apparati, that would allow a mechanism in which a realistic theory could still exist AND yield results compatible with the predictions of QM.

B. The question arises, HOW could a local non-realistic theory explain the correlations seen in QM? Note that this has nothing to do with A. above. Bell's Theorem says that it is possible that a local non-realistic theory OR a non-local realistic theory could exist that mimics the predictions of QM. It will take another breakthrough - which may or may not ever happen - to understand how either of these could be represented in some "physical" manner.

Yes, these are different issues and that is important. I agree that from Bell's theorem it can only be concluded (when correlations have been shown), that a theory must be either non-local or non-realist or, of course, both non-local and non-realist.

However I'd like to point out:

1. Real-life experiments, such as the one I referenced above, have implications for both (A) and (B). That is, such an experiment goes beyond demonstrating the Bell conditions and allowing the corresponding conclusions.

Such experiments also establish limits (outside of Bell's theorem) for what kind of local non-realist theories may be possible, and potentially, whether they are possible at all.

2. I'm not aware that Bell's theorem considers a local non-realistic theory positively possible (except perhaps for the trivial case that everything is one big coincidence). Maybe it does, but so far I only know it just can't exclude such a theory, which would be a difference.

3. Perhaps a local non-realist theory would have to be very "hand-waving", as is, in a certain way, the Uncertainty principle. You seem to be indicating that in addition to Heisenberg uncertainty, only explanations similar to those in local-hidden-variable theories would be necessary. However I think many of the common classical explanations have been disproved by experiments in 1998 and later, such as the above, even if this is outside of Bell's theorem.

4. In the case of non-local realism, a specific theory with a physical, detailed, ontological description already exists: the deBroglie-Bohm model, with Bohmian mechanics. (Though I wouldn't know whether it is developed to a level similar to QM).

5. On the other end, apparently a local non-realist theory doesn't exit (yet).

It is actually no simple matter to hypothesize that there are non-local forces which communicate between measuring apparati as a "solution" to the problem posed by Bell's Theorem. IF there are such forces, why are they nowhere else to be found?

Actually, I personally wouldn't be surprised if non-locality will be found elsewhere, in case that matters... ;) BTW, these "forces", or connections, are said to operate between the particles, rather than between measuring apparati. Which is of course why the particles are called "entangled".

But yes, for physics that is certainly a big step to make. However that step, IMHO, should have been made a long time ago. Meanwhile, research has gone on, while it seems in many discussions, and to a certain extent on the wiki pages, that the experiments from 1998 and forward are seemingly being ignored, while all kinds of hidden-variable theories still flourish in the internet biotope.

On the other hand, there is something else which is found all over the place: the Heisenberg Uncertainty Principle. That is as "non-realistic" as it gets!

Yes, however the uncertainty principle alone, without non-locality (if that is actually possible to consider), doesn't seem to be able to explain the meanwhile firmly established reality of entanglement.

So I would say: don't take it for granted that a non-local solution is automatically more understandable and intuitive than a non-realistic solution. I think either one is a head-scratcher.

I usually use both hands to scratch my head... ;)

 

[jambaugh]

Jambaugh, perhaps you are not aware [...] the outcome of the last measurement can be predicted definitely, based on the previous measurements, so that is not a statistical prediction anymore.

Statistical assertions are a larger class containing as a subset those definite assertions where the statistical frequencies are 0 or 100%. The definite prediction of which you speak doesn't cease to be a statistical one at all.

This is because with multiple entangles particles, a contradiction to local models arises even in those cases where the angle difference of the measurements allows a definite prediction of the outcome.

Only for 2 particles are these cases explainable by local models.

You misunderstand the point I made. It is not the "local" but the (reality based) "model" which is contrary to quantum mechanics' predictions.

Your description doesn't seem to mention the measurement angles as a variable, which I find noteworthy since it is this variable on which the proof of non-locality is based. Non-locality is certainly worth a lot of attention. :)

No, I didn't mention any variable per se. You can as easily "entangle" any observables, be they spin components, momenta, etc. And thence observe Bell inequality violations in correlated measurements between, say, the momentum and the spin of the very same quantum particle. Of course such cases are harder to execute as independent measurements but the violation is there just the same.

Any variable (observable) is classically presumed to partition the state set for the system into subsets (corresponding to states with the particular values of the observable/variable). Distributions of probabilities then classically form measures on these sets of states and you have the classical probabilities which are contrary to quantum prediction. It is the very concept of state which is the essential assumption in deriving Bell's inequalities and it is the assumptions inherent in this word which are contradicted by QM.

 

[colorSpace]

Statistical assertions are a larger class containing as a subset those definite assertions where the statistical frequencies are 0 or 100%. The definite prediction of which you speak doesn't cease to be a statistical one at all.

I know, but in the case of GHZ experiments, complex statistical calculation are not necessary to disprove local realism, and I mentioned this since it seems that the GHZ experiments are not well known yet. The general assumption seems to be that only the statistical calculations for non-matching angles are able to make the case, so I think it is worthwhile to add this information.

With entanglement of 3 or more particles, one can define a set of 4 experiments, each involving a definite prediction for the last particle, and any local-hidden-variable model will be able to correctly predict at most 3 of these 4 experiments. AFAIK.

You misunderstand the point I made. It is not the "local" but the (reality based) "model" which is contrary to quantum mechanics' predictions.

Not all "reality-based" models are contrary to quantum theory, for example Bohmian mechanics are realist yet able to make the same prediction as quantum theory due to being a non-local model.

However the most common assumption seems to be that QT is both non-local and non-realist (the latter in terms of the Heisenberg uncertainty). In entanglement, the entangled properties are Heisenberg-uncertain for both particles (until one is measured, which then has implications for the other depending on the conservation constraints, for example the constraint to keep the total spin momentum at zero).

All attempts to explain the correlations with a (usually limited) local model, at least those that I know about, have been disproved by experiments of the kind which I mentioned above.

It seems in the MWI (many-worlds) area there are some attempts to come up with a local model, but I personally have strong doubts that even with all the fundamentally changed assumptions in MWI it will be possible to come up with a viable idea, since even the splitting of worlds is, I think in most variations of MWI, already a non-local process; but I know only little about MWI and could easily be missing something.

No, I didn't mention any variable per se. You can as easily "entangle" any observables, be they spin components, momenta, etc. And thence observe Bell inequality violations in correlated measurements between, say, the momentum and the spin of the very same quantum particle. Of course such cases are harder to execute as independent measurements but the violation is there just the same.

Any variable (observable) is classically presumed to partition the state set for the system into subsets (corresponding to states with the particular values of the observable/variable). Distributions of probabilities then classically form measures on these sets of states and you have the classical probabilities which are contrary to quantum prediction. It is the very concept of state which is the essential assumption in deriving Bell's inequalities and it is the assumptions inherent in this word which are contradicted by QM.

My point is that the measurement angles need to be mentioned since they are used to prove that there is no local interaction between A and B. Also, without considering measurement angles as a variable, in a two particle experiment the results could be explained by a hypothetical local-realist model, at least when the angles are the same. But maybe you have addressed this in some other way which isn't obvious to me.

 

[Gordon Watson]

Bell's theorem and Meadow's theorem

Every once in a while I try to stretch my feeble mind and pick up layman books on quantum physics as a change of pace from the many clinical/medical journals I have to constantly keep up with. I have a BS in chemistry and understand basic quantum mechanics but as much as I try, I cannot fully understand Bell's theorum...just when I think I've got it , it escapes my brain. A fellow cardiologist has tried to explain it to me (he used to be a physicist) but I don't quite understand his explanation. Would anyone take a gander at explaining it to a lowly non physicist? And I won't feel insulted if you baby the language a little.

Given your medical interests, it might help to compare the work of the medico Professor Roy Meadow (now de-registered) with that of the physicist John Bell. Meadow's theorem was invoked to convict a British woman (since exonerated) of child-murder. Bell's theorem is invoked in attempts to murder Einstein's baby (LOCALITY). Relevant analysis/experiments support neither Meadow's theorem nor Bell's theorem. In both cases, theorem failure may be attributed to false assumptions about reality. Your understanding might therefore be assisted by retaining "Einstein-locality" and critically examining/rejecting "Bell-realism".

 

[colorSpace]

Non-locality is, as far as I can tell, commonly not understood as an alternative to non-realism in the sense of Heisenberg uncertainty, but on the contrary, the reasoning is that the two work together for an entangled pair of particles.

It is simply how the joint system conserves, for example, total momentum, when one of the particles goes into a definite state through measurement. Then the other particle will instantly acquire, for example, (a disposition for) an opposite spin, so that the total momentum remains zero. (In the beginning, both spins are uncertain for an entangled pair).

 

[colorSpace]

This is how Brian Greene, in "The Fabric of the Cosmos", ends the chapter on "Entangling Space":

Nevertheless, it is truly amazing that these connections do exist, and that in carefully arranged laboratory conditions they can be directly observed over significant distances. They show us, fundamentally, that space is not what we once thought it was. What about time?

He says it as plain as that. Not that this would prove anything by itself, but this is the language spoken by many top physicists.

 

[Gordon Watson]

Non-locality is, as far as I can tell, commonly not understood as an alternative to non-realism in the sense of Heisenberg uncertainty, but on the contrary, the reasoning is that the two work together for an entangled pair of particles.

It is simply how the joint system conserves, for example, total momentum, when one of the particles goes into a definite state through measurement. Then the other particle will instantly acquire, for example, (a disposition for) an opposite spin, so that the total momentum remains zero. (In the beginning, both spins are uncertain for an entangled pair).

My suggestion was intended to encourage the OP in the search for "understanding". By holding fast (initially) to Einstein-locality, the OP can focus on the "Bell-reality" assumptions. In my view, rejection of "Bell-reality" is unproblematic. Thus there is no need (for me; and possibly the OP) to abandon that (initial) Einstein-locality assumption.

IF, like me, you have no problem with HUP, then this approach appears to be fully compatible with (even favored by) Dr Chinese's analysis (see his post above).

Then: While both spins may be uncertain, it is certain that total momentum is conserved ... with or without a measurement. But this takes us into the need to understand quantum states ... and I'd like to think that the OP will be led in that direction after rejecting "Bell-realism".

 

[Count Iblis]

http://arxiv.org/abs/quant-ph/0701097"

 

[Gordon Watson]

This is how Brian Greene, in "The Fabric of the Cosmos", ends the chapter on "Entangling Space":

Nevertheless, it is truly amazing that these connections do exist, and that in carefully arranged laboratory conditions they can be directly observed over significant distances. They show us, fundamentally, that space is not what we once thought it was. What about time?

He says it as plain as that. Not that this would prove anything by itself, but this is the language spoken by many top physicists.

Perhaps (like many top physicists) Greene simply abandons Einstein-locality? Then his personal observation naturally follows: For space would sure be weird without Einstein-locality!

I'm suggesting that the OP will not need to follow that (troublesome) line of thought; especially with an understanding of Meadow's error and HUP.

 

[colorSpace]

JenniT:

OK, let's abondon "Bell's realism" first, in favor of HUP, so as to lead the OP into a future without trouble. Even if that doesn't get us anything except uncertainty, since the "with ... measurement" part then implies nonlocality. :)

Count Iblis:

That's a funny link, I was already wondering how a dedicated Spinozist would respond to all this... :)

 

[Gordon Watson]

JenniT:

OK, let's abondon "Bell's realism" first, in favor of HUP, so as to lead the OP into a future without trouble. Even if that doesn't get us anything except uncertainty, since the "with ... measurement" part then implies nonlocality. :)

I'd like to respond but I don't understand the point that you are making. Could you add some maths to support your contention of "implied nonlocality"?

You do understand that the measured correlations follow directly from pair-creation in the singlet-state? That is: The twinned-particles share a common heritage a bit like the one that Professor Meadow overlooked?

 

[colorSpace]

I'd like to respond but I don't understand the point that you are making. Could you add some maths to support your contention of "implied nonlocality"?

I'm discussing on the level of plausibility arguments. I take it that the two subsystems wave functions are not independent, and imposes a joint constraint. For example, in order to conserve momentum, when one particle goes from superposition to specific spin, the other particle must then go from superposition to opposite spin.

You do understand that the measured correlations follow directly from pair-creation in the singlet-state? That is: The twinned-particles share a common heritage a bit like the one that Professor Meadow overlooked?

I don't know about Prof.Meadows, but entanglement, including the troublesome correlations, also persists with so-called "entanglement-swapping", where then two particles are entangled that have no "common heritage", and have never been in the same place, may even, theoretically, have been spacelike separated since their "creation". AFAIK.

[Edit: however, in the latter case of spacelike separation, which I'm not so sure about, there would be a third-party point of view from which they would not be spacelike separated. However, this amounts to discussion of local-hidden-variables, which are for example nicely disproved by the GHZ experiments.]

 

[colorSpace]

Here is a quote I found in an article on DrChinese' very nice and interesting website.

It is from Alain Aspect, apparently in an 1999 article in Nature and/or on nature.com.

The violation of Bell’s inequality, with
strict relativistic separation between the cho-
sen measurements, means that it is impossi-
ble to maintain the image ‘à laEinstein’
where correlations are explained by com-
mon properties determined at the common
source and subsequently carried along by
each photon. We must conclude that an
entangled EPR photon pair is a non-separa-
ble object; that is, it is impossible to assign
individual local properties (local physical
reality) to each photon. In some sense, both
photons keep in contact through space and
time.

I'd like to highlight the last sentence: "In some sense, both
photons keep in contact through space and
time."

Alain Aspect is clearly someone who is familiar with all the if's and but's of Bell's theorem.

[Edit:] At the end of the article, he points out that it is meanwhile a matter of 30 standard deviations.

 

[colorSpace]

I'm discussing on the level of plausibility arguments. I take it that the two subsystems wave functions are not independent, and imposes a joint constraint. For example, in order to conserve momentum, when one particle goes from superposition to specific spin, the other particle must then go from superposition to opposite spin.

I was expecting a continued discussion to give me ample opportunity to elaborate on this point. So instead I'm quoting myself in order to clarify this point for the quick reader.

The two subsystems in the quote above are two entangled particles, A and B.

When A acquires a specific spin (caused by measurement), then B is required, due to the dependencies in their wave function, to acquire the opposite spin (when measurement angles are the same).

If one assumes Heisenberg Uncertainty in a non-realist fashion, this means (in my understanding) that one assumes that there is no underlying cause for why particle A acquires this specific spin (out of the two possibilities depending on the measurement angle). This means that there cannot be the same cause already present at particle B, since there is no such cause. Which in turn means that there must be a non-local connection between A and B, since experiments verify that particle B will indeed acquire the opposite spin when measured along the same angle, whichever one that is. (Experiments verify this even when the shortness of the time window between relevant events excludes communication between A and B at speeds comparable to the speed of light).

So in my understanding, as long as one takes it as a given that the wave functions are indeed interdependent in this way (as Quantum Theory says AFAIK), the assumption of Heisenberg Uncertainty to have no underlying cause (non-realism in this regard) implies non-locality.

 

[DrChinese]

3. Perhaps a local non-realist theory would have to be very "hand-waving", as is, in a certain way, the Uncertainty principle. You seem to be indicating that in addition to Heisenberg uncertainty, only explanations similar to those in local-hidden-variable theories would be necessary. However I think many of the common classical explanations have been disproved by experiments in 1998 and later, such as the above, even if this is outside of Bell's theorem.

4. In the case of non-local realism, a specific theory with a physical, detailed, ontological description already exists: the deBroglie-Bohm model, with Bohmian mechanics. (Though I wouldn't know whether it is developed to a level similar to QM).

5. On the other end, apparently a local non-realist theory doesn't exit (yet).

Actually, I personally wouldn't be surprised if non-locality will be found elsewhere, in case that matters... ;) BTW, these "forces", or connections, are said to operate between the particles, rather than between measuring apparati. Which is of course why the particles are called "entangled".

A lot of people (though perhaps not a majority) think that orthodox QM is an example of a local non-realistic theory. It is local because causes and effects are limited to c, and it is non-realistic because the HUP is a complete representation of a particle's observables.

Also, regarding the relative settings of the measurement apparati: it was the apparati that are being ruled out as being in non-local communication (in tests of strict non-locality such as the Innsbruck experiment you mention). The point is that Bell imagined as follows:

"In a theory in which parameters are added to Quantum Mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, so that such a theory could not be Lorentz invariant."

 

[colorSpace]

A lot of people (though perhaps not a majority) think that orthodox QM is an example of a local non-realistic theory. It is local because causes and effects are limited to c, and it is non-realistic because the HUP is a complete representation of a particle's observables.

So how do these 'people' address the fact that the correlations, even the obvious ones, depend on the relative measurement angles? Are they even aware of this fact? Or do they maintain a position that has been formed in absence of this understanding, and/or before the experiments of 1998 and later had made the case these things really happen (even when either of the loopholes are closed)? It seems to me that these experiments and related developments (such as GHZ experiments) since 1998 are being ignored in a significant way.

Do they not realize that the experiments themselves demonstrate effects that need to be explained, regardless of Bell's theorem? Or am I perhaps mistaken about this?

Also, regarding the relative settings of the measurement apparati: it was the apparati that are being ruled out as being in non-local communication (in tests of strict non-locality such as the Innsbruck experiment you mention). The point is that Bell imagined as follows:

"In a theory in which parameters are added to Quantum Mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, so that such a theory could not be Lorentz invariant."

I'm having difficulties to see how this quote is related to our discussion. It is not quite clear to me whether this text is talking about possibilities of how a hidden-variable theory might work, but perhaps that's what it does.

Why would it be necessary to rule out that the apparati might communicate non-locally? Usually the loophole that needs to be ruled out is that they might communicate classically. And in any case, how would that be related to what we are, or what we have been, discussing?

 

[Gordon Watson]

I was expecting a continued discussion to give me ample opportunity to elaborate on this point. So instead I'm quoting myself in order to clarify this point for the quick reader.

The two subsystems in the quote above are two entangled particles, A and B.

When A acquires a specific spin (caused by measurement), then B is required, due to the dependencies in their wave function, to acquire the opposite spin (when measurement angles are the same).

If one assumes Heisenberg Uncertainty in a non-realist fashion, this means (in my understanding) that one assumes that there is no underlying cause for why particle A acquires this specific spin (out of the two possibilities depending on the measurement angle). This means that there cannot be the same cause already present at particle B, since there is no such cause. Which in turn means that there must be a non-local connection between A and B, since experiments verify that particle B will indeed acquire the opposite spin when measured along the same angle, whichever one that is. (Experiments verify this even when the shortness of the time window between relevant events excludes communication between A and B at speeds comparable to the speed of light).

So in my understanding, as long as one takes it as a given that the wave functions are indeed interdependent in this way (as Quantum Theory says AFAIK), the assumption of Heisenberg Uncertainty to have no underlying cause (non-realism in this regard) implies non-locality.

The OP seeks an "understandable explanation of Bell's theorem" so it seems best to me if we each elaborate our personal understandings. Then, to assist the OP, we might best begin with the simplest (and very impressive) case: using paired-photons that are identically correlated in the singlet state. [Explaining that typically in QM: Alice tests one of the pair (A) and far-away Bob tests the other (B).] We might add: In Bell's theorem, the photons are akin to identical-twin humans subject to Meadow's theorem! The OP's medical background should then see the error in this approach; a similar error (IMO) lying at the heart of Bell's theorem!

Thus it is that my understanding follows from the assumption that allowable states lie on a loop (ie, a path that begins and ends at the same point). So when Alice finds (via a measurement interaction) that her photon A has an allowable state a then we know (from their birthing correlation) that B also has an allowable state a. (a and b being unit-vectors denoting the direction of the measured polarizations; the loop then being a circle.)

Then, for all of Alice's tests that reveal A -> a, when Bob is measuring for the state b, (ie, B -> b) he is (unknowingly) evaluating the conditional probability:

P(B -> b| B -> a) = cos^2 (a,b); all elements in this formulation being local for Bob by virtue of the photonic birthing circumstances/correlations associated with the singlet state!

 

[colorSpace]

Year, thanks for the post, however I'm not quite sure how this experiment rules out a hiddenvariable model. I'm a little stumped with what they define as a "classical" model. Why is it that the classical model _must_ be a product of four different functions of the different angles? And why is it that each of these functions must be continues? Most likely I am misunderstanding what they are writing, could you clearify?

Sorry, jVincent, I overlooked that you had replied to my post, since while I was writing a reply to Peter's message a lot of other messages came in.

The mathematics behind these papers are usually very complex, even if in this case the presented results look very simple; they are often shorthands for much more complex expressions, and usually beyond my understanding.

As far as I can tell, the functions for the particles' results have only the measurement angle as a meaningful input (aside from the hidden variables), and if they belong to a local model, they must be independent of each other, that is, the function for each particle can only use that particles measurement angle as an input, none of the other angles. For the cases which allow definite predictions, the result of the last particle is a simple function of the other particles' results, similar as for the spins of two particles where the second is always the opposite of the first.

With multiple particles it is however a bit trickier, so that one can define a set of four experiments such that any possible local-hidden-variable model will make the right predictions only for at most 3 of those 4 experiments, AFAIK. This is because a local model then has more cases to care about than it can accommodate based on having only the measurement angle (and the hidden variables) as an input. The impact of the other measurement angles creates to many different cases, as though it could do something that would be right for any such case. As far as I understand.

As I understand the different in the two views is:
Classical: Spin direction is born at the particle birth.
QT: spin direction is born at time of fist measurement.
But this doesn't seem to be what the experiment is regarding.

That is also my understanding, but I think that is also the assumption in this experiment, except that the hidden variables are "born" at particle birth, and the spin is then an outcome of the hidden variables AND the measurement angle on this particle.

Heisenberg uncertainty implies that the spin does not have a 'predefined' value for the first measurement, and that no hidden variables are recognized. (Even though in the case of Bohmian mechanics, the spin will be pseudo-random, so to speak, instead of random).

This is why I don't understand the attempts to accept Heisenberg uncertainty and, at the same time, to assume that the information comes from the common "birth". If one accepts uncertainty, then that means exactly that there will be no such information available, such as from any common "birth". I would think. From my point of view, this kind of local non-realism therefore looks like a non-starter. Yet I might be missing something, and if so, would like to find out.