{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T02:29:28Z","timestamp":1762050568244,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,5,11]],"date-time":"2022-05-11T00:00:00Z","timestamp":1652227200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In 2016, Steve Gull has outlined has outlined a proof of Bell\u2019s theorem using Fourier theory. Gull\u2019s philosophy is that Bell\u2019s theorem (or perhaps a key lemma in its proof) can be seen as a no-go theorem for a project in distributed computing with classical, not quantum, computers. We present his argument, correcting misprints and filling gaps. In his argument, there were two completely separated computers in the network. We need three in order to fill all the gaps in his proof: a third computer supplies a stream of random numbers to the two computers representing the two measurement stations in Bell\u2019s work. One could also imagine that computer replaced by a cloned, virtual computer, generating the same pseudo-random numbers within each of Alice and Bob\u2019s computers. Either way, we need an assumption of the presence of shared i.i.d. randomness in the form of a synchronised sequence of realisations of i.i.d. hidden variables underlying the otherwise deterministic physics of the sequence of trials. Gull\u2019s proof then just needs a third step: rewriting an expectation as the expectation of a conditional expectation given the hidden variables.<\/jats:p>","DOI":"10.3390\/e24050679","type":"journal-article","created":{"date-parts":[[2022,5,11]],"date-time":"2022-05-11T10:19:46Z","timestamp":1652264386000},"page":"679","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Gull\u2019s Theorem Revisited"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5821-9986","authenticated-orcid":false,"given":"Richard D.","family":"Gill","sequence":"first","affiliation":[{"name":"Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1103\/PhysicsPhysiqueFizika.1.195","article-title":"On the Einstein Podolsky Rosen paradox","volume":"1","author":"Bell","year":"1964","journal-title":"Physics"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"682","DOI":"10.1038\/nature15759","article-title":"Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres","volume":"52","author":"Hensen","year":"2015","journal-title":"Nature"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"512","DOI":"10.1214\/14-STS490","article-title":"Statistics, Causality and Bell\u2019s Theorem","volume":"29","author":"Gill","year":"2014","journal-title":"Stat. Sci."},{"key":"ref_4","unstructured":"Gull, S. (2022, May 05). 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