The Topology of Quantum Theory and Social Choice
Based on the axioms of quantum theory, we identify a class of topological singularities that encode a fundamental difference between classic and quantum probability, and explain quantum theory’s puzzles and phenomena in simple mathematical terms so they are no longer ‘quantum paradoxes’. The singula...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-06-01
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| Series: | Quantum Reports |
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| Online Access: | https://www.mdpi.com/2624-960X/4/2/14 |
| _version_ | 1797482846447730688 |
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| author | Graciela Chichilnisky |
| author_facet | Graciela Chichilnisky |
| author_sort | Graciela Chichilnisky |
| collection | DOAJ |
| description | Based on the axioms of quantum theory, we identify a class of topological singularities that encode a fundamental difference between classic and quantum probability, and explain quantum theory’s puzzles and phenomena in simple mathematical terms so they are no longer ‘quantum paradoxes’. The singularities provide also new experimental insights and predictions that are presented in this article and establish a surprising new connection between the physical and social sciences. The key is the topology of spaces of <i>quantum events</i> and of the <i>frameworks</i> postulated by these axioms. These are quite different from their counterparts in classic probability and explain mathematically the interference between quantum experiments and the existence of several frameworks or ‘violation of unicity’ that characterizes quantum physics. They also explain entanglement, the Heisenberg uncertainty principle, order dependence of observations, the conjunction fallacy and geometric phenomena such as Pancharatnam–Berry phases. Somewhat surprisingly, we find that the same topological singularities explain the impossibility of selecting a <i>social preference</i> among different individual preferences: which is Arrow’s <i>social choice paradox: </i> the foundations of social choice and of quantum theory are therefore mathematically equivalent. We identify necessary and sufficient conditions on how to restrict experiments to avoid these singularities and recover unicity, avoiding possible interference between experiments and also quantum paradoxes; the same topological restriction is shown to provide a resolution to the social choice impossibility theorem of Chichilnisky. |
| first_indexed | 2024-03-09T22:38:21Z |
| format | Article |
| id | doaj.art-0dc06e52646a43738777e7e64b9b3b83 |
| institution | Directory Open Access Journal |
| issn | 2624-960X |
| language | English |
| last_indexed | 2024-03-09T22:38:21Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Quantum Reports |
| spelling | doaj.art-0dc06e52646a43738777e7e64b9b3b832023-11-23T18:43:25ZengMDPI AGQuantum Reports2624-960X2022-06-014220122010.3390/quantum4020014The Topology of Quantum Theory and Social ChoiceGraciela Chichilnisky0Development Economics, International Macroeconomics, International Trade, Macroeconomics, Microeconomics, Columbia University, New York, NY 10027, USABased on the axioms of quantum theory, we identify a class of topological singularities that encode a fundamental difference between classic and quantum probability, and explain quantum theory’s puzzles and phenomena in simple mathematical terms so they are no longer ‘quantum paradoxes’. The singularities provide also new experimental insights and predictions that are presented in this article and establish a surprising new connection between the physical and social sciences. The key is the topology of spaces of <i>quantum events</i> and of the <i>frameworks</i> postulated by these axioms. These are quite different from their counterparts in classic probability and explain mathematically the interference between quantum experiments and the existence of several frameworks or ‘violation of unicity’ that characterizes quantum physics. They also explain entanglement, the Heisenberg uncertainty principle, order dependence of observations, the conjunction fallacy and geometric phenomena such as Pancharatnam–Berry phases. Somewhat surprisingly, we find that the same topological singularities explain the impossibility of selecting a <i>social preference</i> among different individual preferences: which is Arrow’s <i>social choice paradox: </i> the foundations of social choice and of quantum theory are therefore mathematically equivalent. We identify necessary and sufficient conditions on how to restrict experiments to avoid these singularities and recover unicity, avoiding possible interference between experiments and also quantum paradoxes; the same topological restriction is shown to provide a resolution to the social choice impossibility theorem of Chichilnisky.https://www.mdpi.com/2624-960X/4/2/14social choicetopological singularitiesunicity assumptionquantum eventsframework selection |
| spellingShingle | Graciela Chichilnisky The Topology of Quantum Theory and Social Choice Quantum Reports social choice topological singularities unicity assumption quantum events framework selection |
| title | The Topology of Quantum Theory and Social Choice |
| title_full | The Topology of Quantum Theory and Social Choice |
| title_fullStr | The Topology of Quantum Theory and Social Choice |
| title_full_unstemmed | The Topology of Quantum Theory and Social Choice |
| title_short | The Topology of Quantum Theory and Social Choice |
| title_sort | topology of quantum theory and social choice |
| topic | social choice topological singularities unicity assumption quantum events framework selection |
| url | https://www.mdpi.com/2624-960X/4/2/14 |
| work_keys_str_mv | AT gracielachichilnisky thetopologyofquantumtheoryandsocialchoice AT gracielachichilnisky topologyofquantumtheoryandsocialchoice |