Discussion of A. Neumaier's claim that classical EM can violate Bell's theorem

[JesseM]

Discussion continued from [post=3248292]this post[/post] on another thread...

His particles are local but e/m waves are not.

Bell's proof does not involve any notions of "particles" or "waves" whatsoever, it only involves observed experimental results combined with the idea that the theory generating them is local realistic. Again, do you agree or disagree that according to my definition of "local realism" in 1) and 2) (which seems to be the same as Bell's definition of local causality in the "nouvelle cuisine" paper), classical electromagnetism would be a local realistic theory?

The reason 1) and 2) apply to classical EM is that if you specify the local electromagnetic field vector at every point in a region of spacetime (along with local properties of any particles in that region), that's a complete specification of the physical state of that region as far as EM is concerned, and the state of any point can only be causally influenced by the state of regions in the past light cone of that point. So if you have spacetime regions 1,2,3 as illustrated on this page of Bell's paper, and A represents the outcome of some experiment in region 1 with detector setting a while B represents the outcome of some experiment in region 2 with detector setting b, while c represents a complete specification of the local variables (here electromagnetic field vectors and particles) at every point in region 3 (Bell also uses λ to represent the state of hidden variables in region 3 but we don't need that here), then P(A|B,a,b,c) should be equal to P(A|a,c), equivalent to the step Bell makes in going from equation 6.9.2 to 6.9.3 on this page. In other words, if you already know the information c about region 3 then your estimate of the probability of A occurring in region 1 should in no way change given additional knowledge about the result B from a region 2 at a spacelike separation from 1. Again, tell me if you disagree with any of this. If not you should agree that P(A,B|a,b,c)=P(A|a,c)*P(B|b,c), and from this you can derive a Bell inequality (the CHSH inequality) just as Bell does in the paper.

My slides contain a setting in which the Bell inequalities can be violated although everything is described by the classical Maxwell equations. So whatever Bell's arguments are, they cannot be valid in this setting.

Which Bell inequality are you saying is violated?

 

[A. Neumaier]

Discussion continued from [post=3248292]this post[/post] on another thread...

Bell's proof does not involve any notions of "particles" or "waves" whatsoever, it only involves observed experimental results combined with the idea that the theory generating them is local realistic. Again, do you agree or disagree that according to my definition of "local realism" in 1) and 2) (which seems to be the same as Bell's definition of local causality in the "nouvelle cuisine" paper), classical electromagnetism would be a local realistic theory?

Just to remind of the context:

1. The complete set of physical facts about any region of spacetime can be broken down into a set of local facts about the value of variables at each point in that regions (like the value of the electric and magnetic field vectors at each point in classical electromagnetism)

2. The local facts about any given point P in spacetime are only causally influenced by facts about points in the past light cone of P, meaning if you already know the complete information about all points in some spacelike cross-section of the past light cone, additional knowledge about points at a spacelike separation from P cannot alter your prediction about what happens at P itself (your prediction may be a probabilistic one if the laws of physics are non-deterministic).

On first sight, this looks like a reasonable description of local realism, fitting Maxwell's theory.

The reason 1) and 2) apply to classical EM is that if you specify the local electromagnetic field vector at every point in a region of spacetime (along with local properties of any particles in that region), that's a complete specification of the physical state of that region as far as EM is concerned, and the state of any point can only be causally influenced by the state of regions in the past light cone of that point. So if you have spacetime regions 1,2,3 as illustrated on this page of Bell's paper, and A represents the outcome of some experiment in region 1 with detector setting a while B represents the outcome of some experiment in region 2 with detector setting b, while c represents a complete specification of the local variables (here electromagnetic field vectors and particles) at every point in region 3 (Bell also uses λ to represent the state of hidden variables in region 3 but we don't need that here), then P(A|B,a,b,c) should be equal to P(A|a,c), equivalent to the step Bell makes in going from equation 6.9.2 to 6.9.3 on this page. In other words, if you already know the information c about region 3 then your estimate of the probability of A occurring in region 1 should in no way change given additional knowledge about the result B from a region 2 at a spacelike separation from 1. Again, tell me if you disagree with any of this. If not you should agree that P(A,B|a,b,c)=P(A|a,c)*P(B|b,c), and from this you can derive a Bell inequality (the CHSH inequality) just as Bell does in the paper.

But this is not what is experimentally tested in 1-photon entanglement experiments.
The whole experimental arrangement concerns one single, nonlocal electromagnetic field.

Which Bell inequality are you saying is violated?

See p.50 of http://arnold-neumaier.at/ms/lightslides.pdf
Actually, I remembered incorrectly. It is not a Bell inequality but an even sharper equality prediction, along the arguments used in typical Bell-type proofs.

But I referred on p.46 to a number of papers with Bell-type experiments for single particles. In all these the quantum predictions (which at times violate the corresponding Bell inequalities) are satisfied for classical Maxwell fields. Thus the latter can violate these Bell inequalities. (Note that the term Bell inequalities is applied to arbitrary tensor product systems, not only to tensor products of position representations.)

2-photon entanglement experiments are different. They are not explained by Maxwell's equations. One would need a nonlocal classical theory to explain these.

 

[JesseM]

See p.50 of http://arnold-neumaier.at/ms/lightslides.pdf
Actually, I remembered incorrectly. It is not a Bell inequality but an even sharper equality prediction, along the arguments used in typical Bell-type proofs.

But I referred on p.46 to a number of papers with Bell-type experiments for single particles. In all these the quantum predictions (which at times violate the corresponding Bell inequalities) are satisfied for classical Maxwell fields. Thus the latter can violate these Bell inequalities. (Note that the term Bell inequalities is applied to arbitrary tensor product systems, not only to tensor products of position representations.)

Are any of the papers on p.46 available online? Are they dealing with multiple successive measurements of a particle/field, measurements with a timelike rather than a spacelike separation? I assume one would have to add more assumptions besides local realism to derive a Bell type inequality in such a situation.

2-photon entanglement experiments are different. They are not explained by Maxwell's equations. One would need a nonlocal classical theory to explain these.

OK, perhaps we do not actually disagree then. So when you say on p. 58 that "the traditional hidden variable assumption only amounts to a hidden classical particle assumption", you are only talking about the assumptions made in deriving these specific kinds of inequalities, and not the assumptions made in deriving more common Bell inequalities? If so this could be made a bit clearer, especially since on the same page you immediately go on to talk about "all proofs of Bell type results" (in that paragraph you say that all such proofs "become invalid when particles have a temporal and spatial extension over the whole experimental domain", which is also a bit ambiguous because it's not clear whether this would or wouldn't apply to classical field theories like Maxwell's equations in an experiment where each of two detectors was measuring an extended electromagnetic field, but the two measurements are made at a spacelike separation)

 

[A. Neumaier]

Are any of the papers on p.46 available online?

I got them all online, though through my library. You can find out the possible sources by copying the titles into scholar.google.com . Some sources may well be free.

Are they dealing with multiple successive measurements of a particle/field, measurements with a timelike rather than a spacelike separation? I assume one would have to add more assumptions besides local realism to derive a Bell type inequality in such a situation.

They are dealing with standard situations, and take them as proof of quantumness. The papers speak for themselves, but my lectures used them just as examples - the main message is quite independent of these details. I don't remember the details since I lost interest in these kind of arguments and experiments after having understood that they just probe certain wave aspects of QM, and tell (me at least) nothing of importance about hidden variables. It is obvious that QM is a wave theory, and that it therefore conflicts with simplified classical models that do not take this into account.

OK, perhaps we do not actually disagree then. So when you say on p. 58 that "the traditional hidden variable assumption only amounts to a hidden classical particle assumption", you are only talking about the assumptions made in deriving these specific kinds of inequalities, and not the assumptions made in deriving more common Bell inequalities?

The standard CHSH inequality (but also any other inequality or equality of this kind) is simply an inequality about states of pairs of independent observations, and has nothing per se to do with contexts or locality. If these observations are nonlocal observations about identically prepared single photons they are violated by the interpretation in terms of the Maxwell equations (no matter what the detailed set-up or the precise inequality tested) as long as the setting interpreted by standard QM violates these conditions.

So what? It just says that QM is correct, whatever it predicts, and that a classical interpretation would have to match these predictions. That such an interpretation must be more complex that a simple classical description is clear since QM has much more degrees of freedom. But I don't think it poses essential difficulties for a classical field theory if one makes the fields complex enough. Whether such a classical interpretation is warranted is another matter - I don't think it adds any value to the usefulness of QM.

If so this could be made a bit clearer, especially since on the same page you immediately go on to talk about "all proofs of Bell type results" (in that paragraph you say that all such proofs "become invalid when particles have a temporal and spatial extension over the whole experimental domain", which is also a bit ambiguous because it's not clear whether this would or wouldn't apply to classical field theories like Maxwell's equations in an experiment where each of two detectors was measuring an extended electromagnetic field, but the two measurements are made at a spacelike separation)

It depends on the kinds of interactions one allows for the fields to have. There are many instances of classical field equations involving not only derivatives but also integrals over space, and all these are nonlocal. Thus nonlocality is nothing weird although it makes the mathematics much more messy than local field theory.

 

[JesseM]

They are dealing with standard situations, and take them as proof of quantumness. The papers speak for themselves, but my lectures used them just as examples - the main message is quite independent of these details

I don't know what you mean by "standard situations" though. The "situations" that Bell was considering very specifically dealt with measurements made at a spacelike separation, I don't think he would have said any "proof of quantumness" (in the sense of violating the 'local causality' he was concerned with) can be found in other types of experiments.

The papers speak for themselves, but my lectures used them just as examples - the main message is quite independent of these details.

I found one of the papers, but without knowing much about quantum optics, and without being able to read the theoretical proposal that led to this experiment, I don't think I can understand it (I can't even see anywhere in the paper where they compare quantum predictions with some inequality derived from local realism, it seems like all the equations deal exclusively with the quantum predictions and the reader is expected to know which ones violate some Bell inequality). Can you just tell me whether these experiments demonstrating "single photon nonlocality" involve looking at correlations between results at two or more detectors, results which experimenters in the neighborhood of each detector could in principle write down before learning anything about the result at the other detector?

The standard CHSH inequality (but also any other inequality or equality of this kind) is simply an inequality about states of pairs of independent observations, and has nothing per se to do with contexts or locality.

That's true, but a derivation of the claim that violations of the CHSH inequality are incompatible with local realism does require some assumption about measurements made at a spacelike separation.

I don't remember the details since I lost interest in these kind of arguments and experiments after having understood that they just probe certain wave aspects of QM, and tell (me at least) nothing of importance about hidden variables. It is obvious that QM is a wave theory, and that it therefore conflicts with simplified classical models that do not take this into account.

When you say "nothing of importance about hidden variables", are you denying that experiments of the type envisioned by Bell could definitively rule out any theory of local hidden variables (where the value of a given local variable cannot be causally influenced by anything outside of its past light cone), or do you just not consider that "important", perhaps because you weren't interested in local hidden variable theories in the first place?

If these observations are nonlocal observations about identically prepared single photons they are violated by the interpretation in terms of the Maxwell equations (no matter what the detailed set-up or the precise inequality tested) as long as the setting interpreted by standard QM violates these conditions.

So what? It just says that QM is correct, whatever it predicts, and that a classical interpretation would have to match these predictions. That such an interpretation must be more complex that a simple classical description is clear since QM has much more degrees of freedom. But I don't think it poses essential difficulties for a classical field theory if one makes the fields complex enough. Whether such a classical interpretation is warranted is another matter - I don't think it adds any value to the usefulness of QM.

But what does "complex enough" mean? A local theory of the type I described could have arbitrarily complicated values at each point in spacetime (for example the values might be tensors rather than vectors, or any other type of mathematical object), as long as the values at each point were not causally influenced by anything outside the past light cone of that point. Maybe you're talking about a nonlocal theory where the values of the field aren't associated with particular points in spacetime, or where FTL causal influences can occur? I'm not sure I would still call either of those a "classical" field theory, I don't know if that term has a standard definition though.

 

[A. Neumaier]

I don't know what you mean by "standard situations" though. The "situations" that Bell was considering very specifically dealt with measurements made at a spacelike separation, I don't think he would have said any "proof of quantumness" (in the sense of violating the 'local causality' he was concerned with) can be found in other types of experiments..

look at the papers to see what sitauations they actually discuss. ''standard'' was just short for nothing particularly interesting or deviating, so not worth discussing it in detail (I don't remember the details, and don't want to waste my time looking things up again.)

I found one of the papers, but without knowing much about quantum optics, and without being able to read the theoretical proposal that led to this experiment, I don't think I can understand it (I can't even see anywhere in the paper where they compare quantum predictions with some inequality derived from local realism, it seems like all the equations deal exclusively with the quantum predictions and the reader is expected to know which ones violate some Bell inequality). Can you just tell me whether these experiments demonstrating "single photon nonlocality" involve looking at correlations between results at two or more detectors, results which experimenters in the neighborhood of each detector could in principle write down before learning anything about the result at the other detector?.

They look at verifying the predictions of inequalities of the kind also discussed by CHSH. There are _many_ variations on the theme =; the literature is huge.

That's true, but a derivation of the claim that violations of the CHSH inequality are incompatible with local realism does require some assumption about measurements made at a spacelike separation..

In my lecture I specified all assumptions _I_ made. I don't really care much about the precise assumptions others make, if they look reasonable to me.

When you say "nothing of importance about hidden variables", are you denying that experiments of the type envisioned by Bell could definitively rule out any theory of local hidden variables (where the value of a given local variable cannot be causally influenced by anything outside of its past light cone), or do you just not consider that "important", perhaps because you weren't interested in local hidden variable theories in the first place?.

Everything depends on assumptions, and there are now 30 years of discussions about possible loopholes. Impotrance is a subjective notion. I am not interested in particular assumptions about hidden variables, but only about whether reasonable solutions are actually found. (I don't consider the Bohmian solution reasonable.)

But what does "complex enough" mean? I'm not sure I would still call either of those a "classical" field theory, I don't know if that term has a standard definition though.

Classical just means ''based on an underlying deterministic model''. It is not about complexity. It is clear that it must be more complex that classical field theory, since this doesn't explain some quantum effects. How much more complex is unknown. Concentrating on disproving local hidden variables when all actual systems are extended is, in my opinion, misguided.

 

[gpran]

I came to know about this concept of ‘Thermal Interpretation’ from the thread ‘Quantum Interpretation Poll (2011)’. I am writing this to get clarification about some of the basic concepts.

1) Please see the slide show: http://arnold-neumaier.at/ms/optslides.pdf. It mentions that the intensity of the beam is S0 = ψ*ψ. Does it mean that ψ*ψ gives classical intensity of the beam and not probability? I believe that probability is of statistical nature whereas intensity is real. May be, it is suggested that probability of finding a particle is more if intensity of beam is greater in a particular location. This is acceptable where we have large number of particles but what about a single particle?
2) The Schrödinger equation is obtained in the paper through a mathematical exercise. Can we say that the equation has been derived and not presented as a postulate? Is it because we are assuming a classical beam of particles for the derivation?
3) What is exact picture of a particle? If you suggest that a particle is like a beam or wavepacket then it is equally confusing or abstract. If a charged particle electron is like a beam then does it mean that the mass and charge are spread throughout the space? If there are two particles then the two beams may mix with each other leading to a bigger particle. For a neutral particles like photons this is acceptable but for charged particles like electron this may not be acceptable. In widely accepted Q.M. interpretation, ψ is not real and therefore addition does not lead to a bigger particle.
4) I presume that there is no problem of wavefunction collapse in this approach. Is it because the theory assumes a classical beam of particles/photons?

I may be asking these basic questions because I have not really understood what is said in the slides. My problem is that I am trying to compare every statement made in the slides with the traditional interpretations taught in the textbooks. I feel that a short note/chart about the concept giving the differences with the presently accepted interpretations may help. I request help from anybody who is working on this theory.

 

[A. Neumaier]

I came to know about this concept of ‘Thermal Interpretation’ from the thread ‘Quantum Interpretation Poll (2011)’. I am writing this to get clarification about some of the basic concepts.

You shouldn't post the same thing in two threads. I answered this in the thread
https://www.physicsforums.com/showthread.php?t=490492

 

[my_wan]

I pulled this from the thread that this one spun off from. It is in essence the same as what was posted here but contained an explicit statement (I colored red) that I wanted to address.

The proof deals with any theory where the specification of the state of a region of spacetime can be broken down into a set of local facts about the state of each point--what Bell called local "beables"--and where the state at each point in space and time can only be causally influenced by local states in the past light cone of that point. This would certainly apply to classical field theories like classical electromagnetism!

Now consider what we can say about "local facts" at "each point" in a classical wave. In fact when a classical wave traverses some distance across a medium classically speaking the "local facts", particles within the medium, do NOT traverse the same distance. Classical waves do NOT carry particles anywhere. Now if this wave is more or less localized, and we define the localized wave as itself being a particle, then we try to define the properties which are dynamically generated and transferred from particle to particle in the substructure as some kind of innate point property of a fundamental particle we are most certainly going to run into causality issues as defined by realism.

Take something grossly analogous like a tornado. What are the "local facts" of a tornado at "each point"? Which of these points defines the point location of a tornado? In fact, as defined by realism, there is not even a requirement that any real molecule exist at the point location the tornado is defined to be. Classically speaking there is no such thing as "local facts" at "each point" that persist beyond a single moment in time no matter what reference frame you use.

This is in fact the flaw that Neumaier pointed out as described phenomenologically.