by gill1109 » Thu Oct 08, 2020 9:14 pm
Joy Christian wrote:gill1109 wrote:I guess that with half a brain you can see that S (the CHSH combination of four correlations) can’t exceed 4, merely by definition, whatever experiment you do. It was, of course, never observed to exceed 4. Obviously, Nature is local. We don’t need to study physics to know that. There is nothing to explain. End of discussion.
You still don't get it. Let me rephrase the above comment to make it correct: "...S (the CHSH combination of four correlations) can’t exceed 2, merely by definition, whatever experiment you do. It was, of course, never observed to exceed 2\sqrt{2} (which are the correct local-realistic bounds on S, as demonstrated in
my paper). Obviously, Nature is local. We don’t need to study "Bell's so-called theorem" to know that. There is nothing to explain. End of discussion."
Von Neumann's 'No Hidden Variables' Proof: A Re-Appraisal
Jeffrey Bub
Since the analysis by John Bell in 1965, the consensus in the literature is that von Neumann's 'no hidden variables' proof fails to exclude any significant class of hidden variables. Bell raised the question whether it could be shown that any hidden variable theory would have to be nonlocal, and in this sense 'like Bohm's theory.' His seminal result provides a positive answer to the question. I argue that Bell's analysis misconstrues von Neumann's argument. What von Neumann proved was the impossibility of recovering the quantum probabilities from a hidden variable theory of dispersion free (deterministic) states in which the quantum observables are represented as the 'beables' of the theory, to use Bell's term. That is, the quantum probabilities could not reflect the distribution of pre-measurement values of beables, but would have to be derived in some other way, e.g., as in Bohm's theory, where the probabilities are an artefact of a dynamical process that is not in fact a measurement of any beable of the system.
https://arxiv.org/abs/1006.0499Incidentally, Woerdman observed a value of S larger than 3 a few years ago.
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.92.217901How to Observe High-Dimensional Two-Photon Entanglement with Only Two Detectors
S. S. R. Oemrawsingh, A. Aiello, E. R. Eliel, G. Nienhuis, and J. P. Woerdman
Phys. Rev. Lett. 92, 217901 – Published 24 May 2004
We propose a novel setup to investigate the entanglement of orbital angular momentum states living in a high-dimensional Hilbert space. We incorporate noninteger spiral phase plates in spatial analyzers, enabling us to use only two detectors. The two-photon states that are produced are not confined to a 2x2-dimensional Hilbert space, and the setup allows the probing of correlations in a high-dimensional space. For the special case of half-integer spiral phase plates, we predict that the Clauser-Horne-Shimony-Holt-Bell parameter S is larger than achievable for two qubits (S=2√2), namely, S=3 1/5.
[quote="Joy Christian"][quote="gill1109"]I guess that with half a brain you can see that S (the CHSH combination of four correlations) can’t exceed 4, merely by definition, whatever experiment you do. It was, of course, never observed to exceed 4. Obviously, Nature is local. We don’t need to study physics to know that. There is nothing to explain. End of discussion.[/quote]
You still don't get it. Let me rephrase the above comment to make it correct: "...S (the CHSH combination of four correlations) can’t exceed 2, merely by definition, whatever experiment you do. It was, of course, never observed to exceed 2\sqrt{2} (which are the correct local-realistic bounds on S, as demonstrated in [url=https://arxiv.org/abs/1704.02876]my paper[/url]). Obviously, Nature is local. We don’t need to study "Bell's so-called theorem" to know that. There is nothing to explain. End of discussion."[/quote]
Von Neumann's 'No Hidden Variables' Proof: A Re-Appraisal
Jeffrey Bub
Since the analysis by John Bell in 1965, the consensus in the literature is that von Neumann's 'no hidden variables' proof fails to exclude any significant class of hidden variables. Bell raised the question whether it could be shown that any hidden variable theory would have to be nonlocal, and in this sense 'like Bohm's theory.' His seminal result provides a positive answer to the question. I argue that Bell's analysis misconstrues von Neumann's argument. What von Neumann proved was the impossibility of recovering the quantum probabilities from a hidden variable theory of dispersion free (deterministic) states in which the quantum observables are represented as the 'beables' of the theory, to use Bell's term. That is, the quantum probabilities could not reflect the distribution of pre-measurement values of beables, but would have to be derived in some other way, e.g., as in Bohm's theory, where the probabilities are an artefact of a dynamical process that is not in fact a measurement of any beable of the system.
[url]https://arxiv.org/abs/1006.0499[/url]
Incidentally, Woerdman observed a value of S larger than 3 a few years ago.
[url]https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.92.217901[/url]
How to Observe High-Dimensional Two-Photon Entanglement with Only Two Detectors
S. S. R. Oemrawsingh, A. Aiello, E. R. Eliel, G. Nienhuis, and J. P. Woerdman
Phys. Rev. Lett. 92, 217901 – Published 24 May 2004
We propose a novel setup to investigate the entanglement of orbital angular momentum states living in a high-dimensional Hilbert space. We incorporate noninteger spiral phase plates in spatial analyzers, enabling us to use only two detectors. The two-photon states that are produced are not confined to a 2x2-dimensional Hilbert space, and the setup allows the probing of correlations in a high-dimensional space. For the special case of half-integer spiral phase plates, we predict that the Clauser-Horne-Shimony-Holt-Bell parameter S is larger than achievable for two qubits (S=2√2), namely, S=3 1/5.