{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:47:16Z","timestamp":1760143636303,"version":"build-2065373602"},"reference-count":13,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,2,20]],"date-time":"2024-02-20T00:00:00Z","timestamp":1708387200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We present a Monte Carlo model of Einstein\u2013Podolsky\u2013Rosen experiments that may be implemented on two independent computers and resembles the measurements of the Clauser\u2013Aspect\u2013Zeilinger-type which are performed in two distant stations SA and SB. Our computer model is local deterministic because we show that a theorist in station SB is able to conceive the products of the measurement outcomes of both stations, conditional to any possible equipment configuration in station SA. We show that the Monte Carlo model violates Bell-type inequalities and approaches the results of quantum theory for certain relationships between the number of measurements performed and the number of possible different physical properties of the entangled photon pairs. These relationships are clearly linked to Vorob\u2019ev cyclicities, which always enforce Bell-type inequalities. The realization of this cyclicity depends, however, on combinatorial symmetry considerations that, in turn, depend on the mathematical properties of Einstein\u2019s elements of physical reality. Because these mathematical properties have never been investigated and, therefore, may be free to be chosen in the models for all published experiments, Einstein\u2019s physics does not contradict the experimental findings, instantaneous influences at a distance are put into question and the paradox of Einstein\u2013Podolsky\u2013Rosen and Bell is, thus, resolved.<\/jats:p>","DOI":"10.3390\/sym16030255","type":"journal-article","created":{"date-parts":[[2024,2,20]],"date-time":"2024-02-20T04:04:14Z","timestamp":1708401854000},"page":"255","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Breaking a Combinatorial Symmetry Resolves the Paradox of Einstein-Podolsky-Rosen and Bell"],"prefix":"10.3390","volume":"16","author":[{"given":"J\u00fcrgen","family":"Jakumeit","sequence":"first","affiliation":[{"name":"Institute of Physics II, University of Cologne, 50923 Cologne, Germany"}]},{"given":"Karl","family":"Hess","sequence":"additional","affiliation":[{"name":"Center for Advanced Study, University of Illinois, Urbana, IL 61801, USA"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1103\/PhysRev.47.777","article-title":"Can quantum-mechanical description of physical reality be considered complete?","volume":"47","author":"Einstein","year":"1935","journal-title":"Phys. Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1103\/Physics.8.123","article-title":"Closing the door on Einstein and Bohr\u2019s quantum debate","volume":"8","author":"Aspect","year":"2015","journal-title":"Physics"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1103\/PhysRevLett.18.575","article-title":"Polarization correlation of photons emitted in an atomic cascade","volume":"18","author":"Kocher","year":"1967","journal-title":"Phys. Rev. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.chemphys.2018.04.001","article-title":"Entangled photons from single atoms and molecules","volume":"507","year":"2018","journal-title":"Chem. Phys."},{"key":"ref_5","first-page":"195","article-title":"On the einstein podolsky rosen paradox","volume":"1","author":"Bell","year":"1964","journal-title":"Phys. Phys. 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Weighing the Odds, Cambridge University Press.","DOI":"10.1017\/CBO9781139164795"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1167","DOI":"10.4236\/jmp.2023.148064","article-title":"Malus-law models for aspect-type experiments","volume":"14","author":"Hess","year":"2023","journal-title":"J. Mod. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1137\/1107014","article-title":"Consistent families of measures and their extensions","volume":"7","year":"1962","journal-title":"Theory Probab. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1063\/1.880968","article-title":"Is the moon there when nobody looks? Reality and the quantum theory","volume":"38","author":"Mermin","year":"1985","journal-title":"Phys. Today"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Leggett, A.J. (2006). The Problems of Physics, Oxford Academic.","DOI":"10.1093\/acprof:oso\/9780199211241.001.0001"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/3\/255\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:02:33Z","timestamp":1760104953000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/3\/255"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,20]]},"references-count":13,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2024,3]]}},"alternative-id":["sym16030255"],"URL":"https:\/\/doi.org\/10.3390\/sym16030255","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2024,2,20]]}}}