dorsal/arxiv
View SchemaHidden Variables or Positive Probabilities?
| Authors | Tony Rothman, E. C. G. Sudarshan |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0004109 |
| URL | https://arxiv.org/abs/quant-ph/0004109 |
| Journal | Int. J. Theor. Phys. 40, 1525 (2001). |
Abstract
Despite claims that Bell's inequalities are based on the Einstein locality condition, or equivalent, all derivations make an identical mathematical assumption: that local hidden-variable theories produce a set of positive-definite probabilities for detecting a particle with a given spin orientation. The standard argument is that because quantum mechanics assumes that particles are emitted in a superposition of states the theory cannot produce such a set of probabilities. We examine a paper by Eberhard, and several similar papers, which claim to show that a generalized Bell inequality, the CHSH inequality, can be derived solely on the basis of the locality condition, without recourse to hidden variables. We point out that these authors nonetheless assumes a set of positive-definite probabilities, which supports the claim that hidden variables or "locality" is not at issue here, positive-definite probabilities are. We demonstrate that quantum mechanics does predict a set of probabilities that violate the CHSH inequality; however these probabilities are not positive-definite. Nevertheless, they are physically meaningful in that they give the usual quantum-mechanical predictions in physical situations. We discuss in what sense our results are related to the Wigner distribution.
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"abstract": "Despite claims that Bell\u0027s inequalities are based on the Einstein locality\ncondition, or equivalent, all derivations make an identical mathematical\nassumption: that local hidden-variable theories produce a set of\npositive-definite probabilities for detecting a particle with a given spin\norientation. The standard argument is that because quantum mechanics assumes\nthat particles are emitted in a superposition of states the theory cannot\nproduce such a set of probabilities. We examine a paper by Eberhard, and\nseveral similar papers, which claim to show that a generalized Bell inequality,\nthe CHSH inequality, can be derived solely on the basis of the locality\ncondition, without recourse to hidden variables. We point out that these\nauthors nonetheless assumes a set of positive-definite probabilities, which\nsupports the claim that hidden variables or \"locality\" is not at issue here,\npositive-definite probabilities are. We demonstrate that quantum mechanics does\npredict a set of probabilities that violate the CHSH inequality; however these\nprobabilities are not positive-definite. Nevertheless, they are physically\nmeaningful in that they give the usual quantum-mechanical predictions in\nphysical situations. We discuss in what sense our results are related to the\nWigner distribution.",
"arxiv_id": "quant-ph/0004109",
"authors": [
"Tony Rothman",
"E. C. G. Sudarshan"
],
"categories": [
"quant-ph"
],
"journal_ref": "Int. J. Theor. Phys. 40, 1525 (2001).",
"title": "Hidden Variables or Positive Probabilities?",
"url": "https://arxiv.org/abs/quant-ph/0004109"
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