dorsal/arxiv
View SchemaAccardi contra Bell (cum mundi): The Impossible Coupling
| Authors | Richard D. Gill |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0110137 |
| URL | https://arxiv.org/abs/quant-ph/0110137 |
| Journal | pp. 133-154 in: Mathematical Statistics and Applications: Festschrift for Constance van Eeden. Eds: M. Moore, S. Froda and C. L\'eger. IMS Lecture Notes -- Monograph Series, Volume 42 (2003). Institute of Mathematical Statistics. Beachwood, Ohio |
Abstract
An experimentally observed violation of Bell's inequality is supposed to show the failure of local realism to deal with quantum reality. However, finite statistics and the time sequential nature of real experiments still allow a loophole for local realism, known as the memory loophole. We show that the randomized design of the Aspect experiment closes this loophole. Our main tool is van de Geer's (2000) supermartingale version of the classical Bernstein (1924) inequality guaranteeing, at the root n scale, a not-heavier-than-Gaussian tail of the distribution of a sum of bounded supermartingale differences. The results are used to specify a protocol for a public bet between the author and L. Accardi, who in recent papers (Accardi and Regoli, 2000a,b, 2001; Accardi, Imafuku and Regoli, 2002) has claimed to have produced a suite of computer programmes, to be run on a network of computers, which will simulate a violation of Bell's inequalites. At a sample size of thirty thousand, both error probabilities are guaranteed smaller than one in a million, provided we adhere to the sequential randomized design. The results also show that Hess and Philipp's (2001a,b) recent claims are mistaken that Bell's theorem fails because of time phenomena supposedly neglected by Bell.
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"abstract": "An experimentally observed violation of Bell\u0027s inequality is supposed to show\nthe failure of local realism to deal with quantum reality. However, finite\nstatistics and the time sequential nature of real experiments still allow a\nloophole for local realism, known as the memory loophole. We show that the\nrandomized design of the Aspect experiment closes this loophole. Our main tool\nis van de Geer\u0027s (2000) supermartingale version of the classical Bernstein\n(1924) inequality guaranteeing, at the root n scale, a\nnot-heavier-than-Gaussian tail of the distribution of a sum of bounded\nsupermartingale differences. The results are used to specify a protocol for a\npublic bet between the author and L. Accardi, who in recent papers (Accardi and\nRegoli, 2000a,b, 2001; Accardi, Imafuku and Regoli, 2002) has claimed to have\nproduced a suite of computer programmes, to be run on a network of computers,\nwhich will simulate a violation of Bell\u0027s inequalites. At a sample size of\nthirty thousand, both error probabilities are guaranteed smaller than one in a\nmillion, provided we adhere to the sequential randomized design. The results\nalso show that Hess and Philipp\u0027s (2001a,b) recent claims are mistaken that\nBell\u0027s theorem fails because of time phenomena supposedly neglected by Bell.",
"arxiv_id": "quant-ph/0110137",
"authors": [
"Richard D. Gill"
],
"categories": [
"quant-ph",
"math.PR",
"math.ST",
"stat.TH"
],
"journal_ref": "pp. 133-154 in: Mathematical Statistics and Applications:\n Festschrift for Constance van Eeden. Eds: M. Moore, S. Froda and C. L\\\u0027eger.\n IMS Lecture Notes -- Monograph Series, Volume 42 (2003). Institute of\n Mathematical Statistics. Beachwood, Ohio",
"title": "Accardi contra Bell (cum mundi): The Impossible Coupling",
"url": "https://arxiv.org/abs/quant-ph/0110137"
},
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