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arXiv:0909.2678 · Journal of Russian Laser Research

A model of extended mechanics and nonlocal hidden variables for quantum theory

T. F. Kamalov

Published Sep 1, 2009• 21 citations
arXivHTMLPDF
DOI
10.1007/s10946-009-9098-6

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It was shown by Bell that no local hidden variable model is compatible with quantum mechanics. If, instead, one permits the hidden variables to be entirely nonlocal, then any quantum mechanical predictions can be recovered. In this Letter, we consider general hidden variable models which can have both local and nonlocal parts. We show the existence of (experimentally verifiable) quantum correlations that are incompatible with any hidden variable model having a nontrivial local part, such as the model proposed by Leggett.
There are two issues concerning hidden variables in quantum mechanics: 1.Whether the outcomes of quantum measurements are hidden variables has long been debated. Experiments violating Bell's inequalities have essentially refuted local hidden variable theories. 2.Quantum entanglement provides nonlocal effects that alter wave functions. However, these changes cannot transmit signals, making the exact time of such nonlocal effects a hidden variable. Theories about hidden variables are difficult to verify experimentally due to their unobservability. This paper connects these two hidden variable theories in quantum mechanics, proposing the spacetime relationship that nonlocal effects from entanglement must satisfy to prevent quantum measurement outcomes from being local hidden variables. It further outlines the spacetime relationship that any causal effects should adhere to. Based on this, the paper demonstrates the universal temporal order between relativistic spacelike events. On this foundation, it integrates the locally deterministic relativistic spacetime structure with the nonlocal phenomena of probabilistic quantum mechanics, thereby establishing the universal ordered spacetime structure. key words: ordered spacetime structure ; local hidden variable ; nonlocal effects; uncertainty principle;
We criticize Colbeck and Renner's (CR's) statement that "any hidden variable model can only be compatible with quantum mechanics if its local part is trivial" [Phys. Rev. Lett. 101, 050403 (2008)]. We note that CR's attempt to divide a nonlocal hidden variable model into a "local part" and a "nonlocal part" contains a restriction on the latter. This restriction implies that the division is really into a "local part" and a "nonsignaling nonlocal part." CR's nonsignaling requirement on the "nonlocal part" cannot be physically motivated, since the hidden variables cannot be accessed by experimenters. Nor is it a natural mathematical generalization from the local hidden variable case, since it is simple to make a generalization without CR's requirement. We give an explicit nonlocal hidden variable model that, in the case the restriction is not enforced, contains nontrivial local hidden variables.