Breaking a Combinatorial Symmetry Resolves the Paradox of Einstein-Podolsky-Rosen and Bell
We present a Monte Carlo model of Einstein–Podolsky–Rosen experiments that may be implemented on two independent computers and resembles the measurements of the Clauser–Aspect–Zeilinger-type which are performed in two distant stations <inline-formula><math xmlns="http://www.w3.org/1998...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-02-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/16/3/255 |
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| author | Jürgen Jakumeit Karl Hess |
| author_facet | Jürgen Jakumeit Karl Hess |
| author_sort | Jürgen Jakumeit |
| collection | DOAJ |
| description | We present a Monte Carlo model of Einstein–Podolsky–Rosen experiments that may be implemented on two independent computers and resembles the measurements of the Clauser–Aspect–Zeilinger-type which are performed in two distant stations <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>A</mi></mrow></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>B</mi></mrow></msub></mrow></semantics></math></inline-formula>. Our computer model is local deterministic because we show that a theorist in station <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>B</mi></mrow></msub></mrow></semantics></math></inline-formula> is able to conceive the products of the measurement outcomes of both stations, conditional to any possible equipment configuration in station <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>A</mi></mrow></msub></mrow></semantics></math></inline-formula>. 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’ev 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’s 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’s physics does not contradict the experimental findings, instantaneous influences at a distance are put into question and the paradox of Einstein–Podolsky–Rosen and Bell is, thus, resolved. |
| first_indexed | 2024-04-24T17:48:34Z |
| format | Article |
| id | doaj.art-9cf246b9e6fe490fb0f6856883abe46e |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-24T17:48:34Z |
| publishDate | 2024-02-01 |
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| series | Symmetry |
| spelling | doaj.art-9cf246b9e6fe490fb0f6856883abe46e2024-03-27T14:05:18ZengMDPI AGSymmetry2073-89942024-02-0116325510.3390/sym16030255Breaking a Combinatorial Symmetry Resolves the Paradox of Einstein-Podolsky-Rosen and BellJürgen Jakumeit0Karl Hess1Institute of Physics II, University of Cologne, 50923 Cologne, GermanyCenter for Advanced Study, University of Illinois, Urbana, IL 61801, USAWe present a Monte Carlo model of Einstein–Podolsky–Rosen experiments that may be implemented on two independent computers and resembles the measurements of the Clauser–Aspect–Zeilinger-type which are performed in two distant stations <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>A</mi></mrow></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>B</mi></mrow></msub></mrow></semantics></math></inline-formula>. Our computer model is local deterministic because we show that a theorist in station <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>B</mi></mrow></msub></mrow></semantics></math></inline-formula> is able to conceive the products of the measurement outcomes of both stations, conditional to any possible equipment configuration in station <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>A</mi></mrow></msub></mrow></semantics></math></inline-formula>. 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’ev 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’s 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’s physics does not contradict the experimental findings, instantaneous influences at a distance are put into question and the paradox of Einstein–Podolsky–Rosen and Bell is, thus, resolved.https://www.mdpi.com/2073-8994/16/3/255Einstein–Podolsky–Rosen experimentsMonte Carlo simulationcyclicitycombinatorial symmetryBell inequalitiesCHSH inequalities |
| spellingShingle | Jürgen Jakumeit Karl Hess Breaking a Combinatorial Symmetry Resolves the Paradox of Einstein-Podolsky-Rosen and Bell Symmetry Einstein–Podolsky–Rosen experiments Monte Carlo simulation cyclicity combinatorial symmetry Bell inequalities CHSH inequalities |
| title | Breaking a Combinatorial Symmetry Resolves the Paradox of Einstein-Podolsky-Rosen and Bell |
| title_full | Breaking a Combinatorial Symmetry Resolves the Paradox of Einstein-Podolsky-Rosen and Bell |
| title_fullStr | Breaking a Combinatorial Symmetry Resolves the Paradox of Einstein-Podolsky-Rosen and Bell |
| title_full_unstemmed | Breaking a Combinatorial Symmetry Resolves the Paradox of Einstein-Podolsky-Rosen and Bell |
| title_short | Breaking a Combinatorial Symmetry Resolves the Paradox of Einstein-Podolsky-Rosen and Bell |
| title_sort | breaking a combinatorial symmetry resolves the paradox of einstein podolsky rosen and bell |
| topic | Einstein–Podolsky–Rosen experiments Monte Carlo simulation cyclicity combinatorial symmetry Bell inequalities CHSH inequalities |
| url | https://www.mdpi.com/2073-8994/16/3/255 |
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