Does violation of Bell's Inequality imply a preferred frame

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  • #1
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trying to soak in this paper.
https://arxiv.org/abs/gr-qc/0205035

The following statement is found early on:

"The violation of Bell’s inequality proves that any realistic interpretation
of quantum theory needs a preferred frame."

Whether anyone agrees or disagrees I'd appreciate a sketch of the argument.
 
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  • #3
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Sorry, I had not seen that.
 
  • #4
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Page 2, second paragraph: "Giving up realism means giving up the search for realistic explanations of observable phenomena. Before giving up such a fundamental scientific principle, the alternatives should be evaluated carefully."
Before reading the other thread jtbell linked, I would point out that while the math of spacetime is used to determine quantum properties, it does not restrict it to exist necessarily in realistic spacetime in any frame. The results such as DCQE produce show quantum properties can't be restricted by spatial realism.
 
  • #5
atyy
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It's a subtle question. Does non-locality imply the violation of Lorentz invariance? Bell himself did not know the answer, as can be seen from http://www.tau.ac.il/~vaidman/IQM/BellAM.pdf. He doesn't rule out the possibility of Lorentz invariant versions of nonlocal hidden variable proposals such as GRW.

Here are some attempts to construct such models. I haven't read these closely enough to know if they are correct, and I think there is not yet any consensus about them


http://arxiv.org/abs/1103.3974
Relativistic state reduction model
Daniel Bedingham
[This paper was pointed out to me by Richard Gill in a another thread on PF. Bedingham explicitly comments on why he thinks his model is nonlocal even though it is Lorentz invariant in his section 3.7]

http://arxiv.org/abs/1111.1425
Matter Density and Relativistic Models of Wave Function Collapse
Daniel Bedingham, Detlef Duerr, GianCarlo Ghirardi, Sheldon Goldstein, Roderich Tumulka, Nino Zanghi

http://arxiv.org/abs/1205.1992
Relativistic Quantum Mechanics and Quantum Field Theory
H. Nikolic
 
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He doesn't rule out the possibility of Lorentz invariant versions of nonlocal hidden variable proposals such as GRW.

Here are some attempts to construct such models.
Are we talking about Lorentz invariance only or also satisfying the POR?
 
  • #7
atyy
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Are we talking about Lorentz invariance only or also satisfying the POR?
I assumed they were the same?
 
  • #8
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I assumed they were the same?
No, the Lorentz Ether Theory doesn't satisfy the POR but is of course Lorentz invariant.
 
  • #9
atyy
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  • #11
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But regardless, to put it more directly: does GRW's theory respect the POR?
GRW as Bell meant it was not Lorentz invariant, so it did not respect the relativistic POR.
 
  • #12
zonde
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"The violation of Bell’s inequality proves that any realistic interpretation
of quantum theory needs a preferred frame."

Whether anyone agrees or disagrees I'd appreciate a sketch of the argument.
As I see the argument consists of two parts.
Part one is that violation of Bell’s inequality excludes any relativity-local explanation for quantum entanglement.
Second part should be how any relativity-non-local explanation for quantum entanglement implies preferred frame.

Are you asking sketch for both parts of argument or only one of them?
 
  • #13
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As I see the argument consists of two parts.
Part one is that violation of Bell’s inequality excludes any relativity-local explanation for quantum entanglement.
Second part should be how any relativity-non-local explanation for quantum entanglement implies preferred frame.

Are you asking sketch for both parts of argument or only one of them?
Second part.

I don't want to restart a closed thread but there was a statement made by @PeterDonis in thread referenced in post #2 that I'm not quite sure I follow.

"In QFT, the requirement of causality is that field operators at spacelike separated events commute. That requirement does not imply that the Bell inequalities must be satisfied. So QFT can account for violations of the Bell inequalities while still having spacetime and causality. I don't think "realism" is a precise enough term to add anything here."

I thought Bell's experiment was just a way of demonstrating the fact stated in the first sentence - which is a reality plenty puzzling for me.

If two things can be space-like separated and instantaneously coordinated, even if their coordination is just to spit out the same random number, that seems profound to me. If "a field does it" what is that "field" made of that could cause that? Where does it get it's rules? I took (heuristically) the author to be saying an understanding the mechanics of raw space time was needed in order to try and answer that.
 
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  • #14
zonde
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Second part.
As I see the second part of argument is that violation of POR implies preferred frame. I don't think it's strictly true. It needs assumption that at least in one frame laws of physics are isotropic. But on the other hand if we have two similar models where one has such an isotropic reference frame and another one where there is no such reference frame (all reference frames are anisotropic) we should prefer the first one as it's assumption can be falsified and the we would fall back to the more general second one.

I don't want to restart a closed thread but there was a statement made by PeterDonis in thread referenced in post #2 that I'm not quite sure I follow.

"In QFT, the requirement of causality is that field operators at spacelike separated events commute. That requirement does not imply that the Bell inequalities must be satisfied. So QFT can account for violations of the Bell inequalities while still having spacetime and causality. I don't think "realism" is a precise enough term to add anything here."
This question is related to first part of the argument.
QFT requirement that field operators at spacelike separated events commute ensures that there can be no superluminal causality at phenomenological level. It means that result does not change in what order you perform measurements at spacelike separated places (statistical result of measurement at one place does not change whether measurement at the other place is already performed or not).
And considering that no intermediate elements in QFT have correspondence to physical reality there is no conflict with relativity.
On the other hand you might not consider such a phenomenological model as an explanation. For an explanation we might require that there are intermediate elements in the model that have claimed correspondence to physical reality. And in that case PeterDonis example does not contradict the first part of the argument (that violation of Bell’s inequality excludes any relativity-local explanation for quantum entanglement).
 
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  • #15
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As I see the second part of argument is that violation of POR implies preferred frame. I don't think it's strictly true. It needs assumption that at least in one frame laws of physics are isotropic. But on the other hand if we have two similar models where one has such an isotropic reference frame and another one where there is no such reference frame (all reference frames are anisotropic) we should prefer the first one as it's assumption can be falsified and the we would fall back to the more general second one.


This question is related to first part of the argument.
QFT requirement that field operators at spacelike separated events commute ensures that there can be no superluminal causality at phenomenological level. It means that result does not change in what order you perform measurements at spacelike separated places (statistical result of measurement at one place does not change whether measurement at the other place is already performed or not).
And considering that no intermediate elements in QFT have correspondence to physical reality there is no conflict with relativity.
On the other hand you might not consider such a phenomenological model as an explanation. For an explanation we might require that there are intermediate elements in the model that have claimed correspondence to physical reality. And in that case PeterDonis example does not contradict the first part of the argument (that violation of Bell’s inequality excludes any relativity-local explanation for quantum entanglement).
I think I understand. The phenomenological distinction helps as does the word "isotropy" in this context.
I had been wondering about the author's use of absolute time (as well as Smolin's). I realize I was imagining isotropy there in both schemas. Confusing, kind of thought that was the point.

If I understand correctly that's the rub with GR - no such isotropy of physical laws can exist for space-time (Lorenz transformations). But, and this is the part about preferred frames and pure relation-ism that I find interesting, if you assert that physical laws including Noether's beautiful theorem do not describe reality but only abstract it we don't have to abandon useful symmetry while we ease the requirement of strict perfect (arguably un-physical) symmetry - maybe instead we expect "near symmetry" or "near perfect similarity".

Smolin plays with a Similarity metric, which seems relevant. Or I at least I'm trying to guess where he's going with that. As I understand it his pure relation-ism and the author's universal "preferred frame" though different are both trying to distinguish all events, or to suppose this. Maybe I really have that wrong. The author of the paper then uses the preferred frame to derive Lorenz symmetry. But doesn't perfect symmetry between events mean identity (Leibniz' Principle of the Identity of the Indiscernible). How can that fit with an absolute time and a preferred frame?

I hope this doesn't get this thread closed though I understand if it does. Still, I'd rather ask the question and have that happen than not ask.
 
  • #16
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I think the Lorentz Ether Theory is not Lorentz invariant, because the ether violates it
It violates the basic symmetry assumptions of an inertial frame ie a frame that is homogeneous in space and time and isotropic. It represents a complete departure of the modern conception of relativity. It doesn't disprove it of course but seriously undermines the theories elegance. For example it would invalidate the presentation of classical mechanics as found in Landau - Mechanics. One would constantly need to have caveats on symmetry statements.

Thanks
Bill
 
  • #17
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I think that with LET you prove POR, instead of assuming it as an axiom. In any inertial frame POR holds, because of the "conspiracy" of Lorentz contraction and "local" time dilation. Having done that you can then go ahead and assume it in your work. That is, you can use SR math and techniques. For example, transform to the most convenient frame for calculations (usually someone's rest frame). All comparisons will hold; for instance, the same twin is younger by the same amount. But you can then ask an additional set of questions, if you want (not necessary), about who's "really" moving, or contracting, etc. This approach makes it seem inevitable that in some extreme conditions, currently beyond experiment, POR will break down; but for practical purposes those can be ignored. There's an additional question, "how does the ether work?" It has to be an extremely unusual substance. I suppose one needs to simply assume "Ether works somehow" as an axiom, which of course Occam won't like.

It's similar to the situation in Bohmian mechanics. The math and physical representations are considerably more complicated than with normal QM approaches, but give equivalent answers in all currently testable circumstances. If for some reason you want to use it, the first thing is to prove that equivalence; then go ahead and use the normal, simpler, math techniques. But in extreme conditions, with currently unavailable test equipment, it makes different predictions; so if ever dealing with those, use the more complicated Bohm approach.

So I think (please correct me if wrong) with LET, after first proving POR for all accessible tests, presentation of classical mechanics as found in Landau - Mechanics would then go through without modification; with the understanding that in extreme circumstances it might break down.
 
  • #18
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I think that with LET you prove POR, instead of assuming it as an axiom.
It explicitly violates the POR. The laws of physics are different depending on the direction of the aether wind.

Mechanics obeys the POR. We know EM applies to inter-molecular forces - it would be really strange it didn't apply to that as well. It may - but it would be rather strange and not in line with the simplicity of nature.

Thanks
Bill
 
  • #19
atyy
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I think the question with whether LET is Lorentz invariant and respects POR depends on how one asks the question. I think that if one restricts to the "observable" or "dynamical fields" then LET is Lorentz invariant and respects POR, but if one does not use that restriction, there is an invisible vector field which is not Lorentz invariant and does not respect POR.

It's perhaps a bit like asking whether GR is "diff invariant" in a way that is different from SR (yes and no, depending on how one phrases the question).
 
  • #20
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The laws of physics are different depending on the direction of the aether wind.
But since there is no ether, nor ether wind, you can't make that statement! At least, we have no idea how it would work, if it did exist. Without some new and unknown physics your statement is not meaningful.

My point is, if you wanted to use LET, you would have to assume ether is a substance with such unusual properties that it does somehow allow laws of physics to work equally in either direction, since that's what really happens. (Except, perhaps, in extreme cases currently untestable). Then, you'd have to accept the job of someday explaining how this magical ether works. Occam will complain! But there's no logical inconsistency here; you would just have to have some very good reason for taking this more difficult route.

there is an invisible vector field which is not Lorentz invariant and does not respect POR.
Right; as long as it remains invisible and undetectable there's no problem; except, justifying bothering with it.
 
  • #21
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Perhaps an historical note would clarify.

In 1895, "Michelson's Interference Experiment", Lorentz shows that his contraction hypothesis accounts for Michelson-Morley failure to detect ether wind.

In 1904, "Electromagnetic Phenomena in a System Moving with any Velocity less than that of Light", Lorentz never mentions ether at all. He shows that, given the assumption that all particles (not just electrons), obey his transformation laws regarding length, time and mass, then all actual phenomena (comprising, essentially, measured / detected speed of light constancy and POR) are accounted for. Again, there's no reference at all to ether. What he does refer to is absolute spacetime; not explicitly, but with phrases such as "at rest", "in motion", and "local time".

It's clear from reading that paper that ether per se was a non-issue to him. Since this is the paper that summarized and completed his work from 1895, 1900, and 1902 (if I recall correctly) it would be more historically accurate to call LET something like "Lorentz Absolute Spacetime Theory" (LAST).
 
  • #22
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It violates the basic symmetry assumptions of an inertial frame ie a frame that is homogeneous in space and time and isotropic. It represents a complete departure of the modern conception of relativity. It doesn't disprove it of course but seriously undermines the theories elegance. For example it would invalidate the presentation of classical mechanics as found in Landau - Mechanics. One would constantly need to have caveats on symmetry statements.

Thanks
Bill
I was going to ask whether the second law isn't already a big caveat on expectations of Symmetry... but then I found this.
https://en.wikipedia.org/wiki/T-symmetry

I've been to that page before but...

What in the world are "spinors" and how are they related to the Second Law (or not)? I mean I see them referenced all the time (Susskind's QM for example) but I just sort of thought they were QM observables related to spinning particles in the SM

But now I gather they are pretty deep geometrically and related to T-symmetry which is a special component of CPT symmetry.
?:)
 
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