dorsal/arxiv
View SchemaBell's theorem: Critique of proofs with and without inequalities
| Authors | Karl Hess, Walter Philipp |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0410015 |
| URL | https://arxiv.org/abs/quant-ph/0410015 |
| DOI | 10.1063/1.1874568 |
Abstract
Most of the standard proofs of the Bell theorem are based on the Kolmogorov axioms of probability theory. We show that these proofs contain mathematical steps that cannot be reconciled with the Kolmogorov axioms. Specifically we demonstrate that these proofs ignore the conclusion of a theorem of Vorob'ev on the consistency of joint distributions. As a consequence Bell's theorem stated in its full generality remains unproven, in particular, for extended parameter spaces that are still objective local and that include instrument parameters that are correlated by both time and instrument settings. Although the Bell theorem correctly rules out certain small classes of hidden variables, for these extended parameter spaces the standard proofs come to a halt. The Greenberger-Horne-Zeilinger (GHZ) approach is based on similar fallacious arguments. For this case we are able to present an objective local computer experiment that simulates the experimental test of GHZ performed by Pan, Bouwmeester, Daniell, Weinfurter and Zeilinger and that directly contradicts their claim that Einstein-local elements of reality can neither explain the results of quantum mechanical theory nor their experimental results.
{
"annotation_id": "eb44863e-b907-4fed-9108-7eca48cf066c",
"date_created": "2026-03-02T18:02:10.331000Z",
"date_modified": "2026-03-02T18:02:10.331000Z",
"file_hash": "c9e71ebfde01ba2de412e56636f19993331074ef3bc32c0f4d9c9d5373728282",
"private": false,
"record": {
"abstract": "Most of the standard proofs of the Bell theorem are based on the Kolmogorov\naxioms of probability theory. We show that these proofs contain mathematical\nsteps that cannot be reconciled with the Kolmogorov axioms. Specifically we\ndemonstrate that these proofs ignore the conclusion of a theorem of Vorob\u0027ev on\nthe consistency of joint distributions. As a consequence Bell\u0027s theorem stated\nin its full generality remains unproven, in particular, for extended parameter\nspaces that are still objective local and that include instrument parameters\nthat are correlated by both time and instrument settings. Although the Bell\ntheorem correctly rules out certain small classes of hidden variables, for\nthese extended parameter spaces the standard proofs come to a halt. The\nGreenberger-Horne-Zeilinger (GHZ) approach is based on similar fallacious\narguments. For this case we are able to present an objective local computer\nexperiment that simulates the experimental test of GHZ performed by Pan,\nBouwmeester, Daniell, Weinfurter and Zeilinger and that directly contradicts\ntheir claim that Einstein-local elements of reality can neither explain the\nresults of quantum mechanical theory nor their experimental results.",
"arxiv_id": "quant-ph/0410015",
"authors": [
"Karl Hess",
"Walter Philipp"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.1874568",
"title": "Bell\u0027s theorem: Critique of proofs with and without inequalities",
"url": "https://arxiv.org/abs/quant-ph/0410015"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "79af5497-b5da-4eff-90bd-8a4633e1f405",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}