Quantum Theory without the Axiom of Choice, and Lefschetz Quantum Physics
In this paper, we discuss quantum formalisms that do not use the axiom of choice. We also consider the fundamental problem that addresses the (in)correctness of having the complex numbers as the base field for Hilbert spaces in the København interpretation of quantum theory, and propose a new approa...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-12-01
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| Series: | Physics |
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| Online Access: | https://www.mdpi.com/2624-8174/5/4/72 |
| _version_ | 1797379620586127360 |
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| author | Koen Thas |
| author_facet | Koen Thas |
| author_sort | Koen Thas |
| collection | DOAJ |
| description | In this paper, we discuss quantum formalisms that do not use the axiom of choice. We also consider the fundamental problem that addresses the (in)correctness of having the complex numbers as the base field for Hilbert spaces in the København interpretation of quantum theory, and propose a new approach to this problem (based on the Lefschetz principle). Rather than a theorem–proof paper, this paper describes two new research programs on the foundational level, and focuses on basic open questions that arise in these programs. |
| first_indexed | 2024-03-08T20:25:46Z |
| format | Article |
| id | doaj.art-267aeb4d81104e749f7c4acf53c2f4e0 |
| institution | Directory Open Access Journal |
| issn | 2624-8174 |
| language | English |
| last_indexed | 2024-03-08T20:25:46Z |
| publishDate | 2023-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Physics |
| spelling | doaj.art-267aeb4d81104e749f7c4acf53c2f4e02023-12-22T14:33:13ZengMDPI AGPhysics2624-81742023-12-01541109112510.3390/physics5040072Quantum Theory without the Axiom of Choice, and Lefschetz Quantum PhysicsKoen Thas0Department of Mathematics, Algebra and Geometry, Ghent University, Krijgslaan 281, S25, B-9000 Ghent, BelgiumIn this paper, we discuss quantum formalisms that do not use the axiom of choice. We also consider the fundamental problem that addresses the (in)correctness of having the complex numbers as the base field for Hilbert spaces in the København interpretation of quantum theory, and propose a new approach to this problem (based on the Lefschetz principle). Rather than a theorem–proof paper, this paper describes two new research programs on the foundational level, and focuses on basic open questions that arise in these programs.https://www.mdpi.com/2624-8174/5/4/72modal quantum theoryaxiom of choiceLefschetz principlefoundations of quantum theorythought experiments |
| spellingShingle | Koen Thas Quantum Theory without the Axiom of Choice, and Lefschetz Quantum Physics Physics modal quantum theory axiom of choice Lefschetz principle foundations of quantum theory thought experiments |
| title | Quantum Theory without the Axiom of Choice, and Lefschetz Quantum Physics |
| title_full | Quantum Theory without the Axiom of Choice, and Lefschetz Quantum Physics |
| title_fullStr | Quantum Theory without the Axiom of Choice, and Lefschetz Quantum Physics |
| title_full_unstemmed | Quantum Theory without the Axiom of Choice, and Lefschetz Quantum Physics |
| title_short | Quantum Theory without the Axiom of Choice, and Lefschetz Quantum Physics |
| title_sort | quantum theory without the axiom of choice and lefschetz quantum physics |
| topic | modal quantum theory axiom of choice Lefschetz principle foundations of quantum theory thought experiments |
| url | https://www.mdpi.com/2624-8174/5/4/72 |
| work_keys_str_mv | AT koenthas quantumtheorywithouttheaxiomofchoiceandlefschetzquantumphysics |