- #141
A. Neumaier
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The classic is by Currie, Jordan and Sudarshan.vanhees71 said:There are many such theorems. Which one are you referring to?
The classic is by Currie, Jordan and Sudarshan.vanhees71 said:There are many such theorems. Which one are you referring to?
? Existence or nonexistence does not figure in my proof.Demystifier said:So by assuming non-existence of wave properties, you find that there is no interference. It's logically correct, but in my opinion too trivial to be interesting.
Why do you mention this triviality?Demystifier said:Bohmian theory is not classical in that sense, so your analysis does not exclude the Bohmian interpretation.
Yes, and the no-go theorem holds for any finite number of degrees of freedom:A. Neumaier said:The classic is by Currie, Jordan and Sudarshan.
However, their exposition is not complete enough to enable me to gain full understanding of what is happening, and why. The reason is that there is no connection between the QFT discussion of coincidence counts using 2-point correlations in Chapter 14 and the nonrelativistic QM discussion of Bell's inequality in Chapter 12.14. A good exposition should connect the two. In particular, what is missing is a discussion of how the two dichotomic observables ##A(a)## and ##B(b)## introduced in Section 12.4.2 are realized in QFT. They are informally postulated but nowhere shown to exist in terms of the QFT machinery introduced.A. Neumaier said:Actually, this is more or less done in the book by Mandel and Wolf cited in post #154.
Yes, the only well-defined one.vanhees71 said:Yes, and the no-go theorem holds for any finite number of degrees of freedom:
https://link.springer.com/article/10.1007/BF02749856
So the "natural" relativistic dynamics is field-theoretical rather than point-particle like.
I don't think it's true. As far as I can see, his proof does not have an analog of the first line in your 3-line equation.A. Neumaier said:Just as Bell in his work; his local hidden variable objects cannot interfere either.
But isn't it enough that the correlators describe the experiments correctly, which violate Bell's inequality? Also, if the however constructed observables are nonlocal, then they are not in accordance with Bell's class of "local realistic" HV theories.A. Neumaier said:However, their exposition is not complete enough to enable me to gain full understanding of what is happening, and why. The reason is that there is no connection between the QFT discussion of coincidence counts using 2-point correlations in Chapter 14 and the nonrelativistic QM discussion of Bell's inequality in Chapter 12.14. A good exposition should connect the two. In particular, what is missing is a discussion of how the two dichotomic observables ##A(a)## and ##B(b)## introduced in Section 12.4.2 are realized in QFT. They are informally postulated but nowhere shown to exist in terms of the QFT machinery introduced.
I am convinced that any construction of these would reveal that they are horribly nonlocal expressions in the quantum fields. This would constitute the natural explanation why Bell nonlocality is experimentally seen.
String theory can also describe interactions in a Lorentz covariant manner.A. Neumaier said:Yes, the only well-defined one.
In Bell's words (Speakable and unspeakable..., p.8/9): 'That so much follows from such apparently innocent assumptions leads us to question their innocence. Are the requirements imposed, which are satisfied by quantum mechanical states, reasonable requirements on the dispersion free states? Indeed they are not. [...] The danger in fact was not in the explicit but in the implicit assumptions. It was tacitly assumed that [...]''Demystifier said:Bell's argument is applicable to any local beables, ...
Demystifier said:... local beables, namely variables defined on spacetime positions. This includes both pointlike particles and fields. (But it excludes multi-local beables that appear in your thermal interpretation.)
He adds up probabilites in (6) p.37 of 'Speakable...' This is not permitted if there is interference.Demystifier said:I don't think it's true. As far as I can see, his proof does not have an analog of the first line in your 3-line equation.
The free Maxwell field discussed in my paper predated quantum mechanics, is also a (Bell) local hidden-variable theory, and also explains the experiment.Demystifier said:Let me also add that the experiment you describe can be explained by a (Bell) local hidden-variable theory. Namely, 1-particle Bohmian mechanics is a local theory.
The no-go theorem is about classical theories!Demystifier said:String theory can also describe interactions in a Lorentz covariant manner.
Whether it is enough depends on the ambitions.vanhees71 said:But isn't it enough that the correlators describe the experiments correctly, which violate Bell's inequality?
No. They are in accordance with Bell's class of "local realistic" HV theories but not in accordance with his tacit assumption that all measurable beables are local. See my post #149.vanhees71 said:Also, if the however constructed observables are nonlocal, then they are not in accordance with Bell's class of "local realistic" HV theories.
That's different. He integrates over ##\lambda##, which, by definition, is averaging over all hidden variables. That's just an application of Kolmogorov probability axioms and has nothing to do with absence of interference. You, on the other hand, integrate over all hidden variables ##\lambda## (which is OK), but in addition sum over ##k##, ##k=1,2##. It is this summation over ##k##, not present in the Bell case, that is related to absence of interference.A. Neumaier said:He adds up probabilites in (6) p.37 of 'Speakable...' This is not permitted if there is interference.
That's not different. The hidden variables determine which k is used by the particle, and the probability for the other k is simply zero. The summation over k just simplifies writing this down.Demystifier said:That's different. He integrates over ##\lambda##, which, by definition, is averaging over all hidden variables. That's just an application of Kolmogorov probability axioms and has nothing to do with absence of interference. You, on the other hand, integrate over all hidden variables ##\lambda## (which is OK), but in addition sum over ##k##, ##k=1,2##. It is this summation over ##k##, not present in the Bell case, that is related to absence of interference.
I never talked of interference of particles. In Bohmian mechanics, for instance, it is waves that interfere.A. Neumaier said:what do you mean by interference of particles in a hidden variable model?
OK, but then you assume that your hidden variables are "classical", in a sense in which Bell doesn't assume.A. Neumaier said:That's not different. The hidden variables determine which k is used by the particle, and the probability for the other k is simply zero. The summation over k just simplifies writing this down.
Classical = satisfy the rules of probability theory,and that the hidden variables determine every physically relevant fact. Just as Bell does.Demystifier said:OK, but then you assume that your hidden variables are "classical", in a sense in which Bell doesn't assume.
So it is also in my Maxwell explanation - it corresponds to Bohmian theory in Bell's papers.Demystifier said:I never talked of interference of particles. In Bohmian mechanics, for instance, it is waves that interfere.
No, you have an additional assumption of classicality. You assume that your hidden variables involve only particles and not waves. Bell's local hidden variables are much more general than that, in particular they allow a possibility that each particle is guided by its own wave (without entanglement), in a local manner.A. Neumaier said:Classical = satisfy the rules of probability theory,and that the hidden variables determine every physically relevant fact. Just as Bell does.
Not quite true. The Bell's assumption that hidden variables are local does not exclude the possibility of single-particle Bohmian mechanics, or many-particle Bohmian mechanics without entanglement.A. Neumaier said:But this is irrelevant in Bell's derivation, which does not apply to the Bohmian theory, as you well know.
Thus it disproves (as claimed in the abstract) the hidden variable particle concept even without assuming locality.Demystifier said:@A. Neumaier perhaps the crucial observation on your experiment is this. In your experiment, there are no correlations between spatially separated measurement outcomes. So, no matter how one interprets your experiment in terms of hidden variables, the experiment itself is not an evidence of nonlocality.
Yes, that's the whole point of my paper.Demystifier said:You assume that your hidden variables involve only particles and not waves.
only with a very diluted notion of 'every' ... (count the number of threads in Quantum Physics, and work out the ratio!)AndreasC said:every thread eventually descends into a Demystifier vs A. Neumaier debate sooner or later
But this is utter nonsense, because the polarization of electrons and other elementary or composed particles are observables (I don't care about strange philosophical buzz words like "beables"; for me there are observables, and they are defined by a quantity that can be measured), and as any observable it's defined by (an equivalence class of) measurement procedures (e.g., the just now very much discussed (g-2) measurement on anti-muons at Fermilab and hopefully soon also at Jefferson lab. Another fascinating example are polarization measurements on ##\Lambda##s in semi-central heavy-ion collisions hinting at an enormous vorticity of the created strongly interacting medium.A. Neumaier said:Thus it disproves (as claimed in the abstract) the hidden variable particle concept even without assuming locality.
Because of that, polarization is in Bohmian mechanics not a beable, as you observed in this post:
''In the Bohmian interpretation it means that electron, as a pointlike particle, always has a position and never has a spin. When we measure spin, we don't really measure a property of the electron alone, but a property that can be attributed to the electron and the apparatus together.''
Point particles are simply a defective, idealized notion, as also seen in the many instances discussed in
- J.C. Baez, Struggles with the Continuum, arXiv:1609:01421
I agree that Bohmian mechanics (and every interpretation of quantum mechanics or classical relativistic mechanics) that features point particles) is utter nonsense, and gives only a make-believe interpretation. The unreal spin admitted by @Demystifier and the lack of Lorentz covariance of Bohmian theories are vivid example of this.vanhees71 said:But this is utter nonsense, because the polarization of electrons and other elementary or composed particles are observables
I was being hyperbolic. It's interesting though.A. Neumaier said:only with a very diluted notion of 'every' ... (count the number of threads in Quantum Physics, and work out the ration!)
For Bohmian mechanics it's not important that the particles are exactly pointlike. If you like they can be balls of the Planck size, it doesn't change anything important.A. Neumaier said:Point particles are simply a defective, idealized notion
So you rule out something that nobody believed in the first place.A. Neumaier said:Yes, that's the whole point of my paper.
There are many threads, for instance, where @A. Neumaier and me were together against @vanhees71 .AndreasC said:I like how every thread eventually descends into a Demystifier vs A. Neumaier debate sooner or later lol
I'd indeed say that Bohmian mechanics in its version for non-relativistic QM provides not so much a point-particle but rather a hydrodynamical picture. The Bohmian trajectories are contructed after all from the quantum-mechanical probability current ##\vec{j} = -\frac{\mathrm{i}}{2m} (\psi^* \vec{\nabla} \psi - \psi \vec{\nabla} \psi^*)##. That's a continuum-mechanical rather than a point-particle mechanical idea. That underslines the fact that the single-particle Bohmian trajectories are not observable but the hydro-like flow pattern from averaging over many single-particle trajectories. This is equivalent to the standard statistical interpretation. So at the end the Bohmian trajectories are nothing that needs to be even calculated to confront QT with experiment and thus are simply a superfluous addition from a physics point of view.Demystifier said:For Bohmian mechanics it's not important that the particles are exactly pointlike. If you like they can be balls of the Planck size, it doesn't change anything important.
I call that "anomalous vanhees effect".Demystifier said:There are many threads, for instance, where @A. Neumaier and me were together against @vanhees71 .