Morgan, Peter (2022) The collapse of a quantum state as a joint probability construction. J. Phys. A: Math. Theor. 55 254006 (2022), 55.
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Text (Resubmission (with moderate changes) to JPhysA on April 10th, 2022. Accepted May 12th, 2022.)
2101.10931v4.pdf - Accepted Version Download (741kB) | Preview |
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Slideshow (Presentation to the Lisbon Philosophy of Physics Seminar May 17th, 2023.)
Lisbon2023AsGivenV.pdf - Supplemental Material Download (1MB) | Preview |
Abstract
The collapse of a quantum state can be understood as a mathematical way to construct a joint probability density even for operators that do not commute. We can formalize that construction as a non-commutative, non-associative collapse product that is nonlinear in its left operand as a model for joint measurements at timelike separation, in part inspired by the sequential product for positive semi-definite operators. The familiar collapse picture, in which a quantum state collapses after each measurement as a way to construct a joint probability density for consecutive measurements, is equivalent to a no-collapse picture in which Lüders transformers applied to subsequent measurements construct a Quantum-Mechanics--Free-Subsystem of Quantum Non-Demolition operators, not as a dynamical process but as an alternative mathematical model for the same consecutive measurements. The no-collapse picture is particularly simpler when we apply signal analysis to millions or billions of consecutive measurements.
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| Item Type: | Published Article or Volume | ||||||
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| Additional Information: | Part of the content of this article is presented in the video of a talk on May 17th, 2023 to the Lisbon Philosophy of Physics Seminar is available on YouTube, https://www.youtube.com/watch?v=5Jx2WIa5eTs (where a PDF of the slides may be found in the comments). | ||||||
| Keywords: | quantum mechanics, measurement problem, signal analysis, quantum non-demolition measurement, Koopman classical mechanics | ||||||
| Subjects: | Specific Sciences > Physics > Classical Physics Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Statistical Mechanics/Thermodynamics Specific Sciences > Physics > Symmetries/Invariances |
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| Depositing User: | Mr Peter Morgan | ||||||
| Date Deposited: | 02 Jun 2024 15:40 | ||||||
| Last Modified: | 02 Jun 2024 15:40 | ||||||
| Item ID: | 23511 | ||||||
| Journal or Publication Title: | J. Phys. A: Math. Theor. 55 254006 (2022) | ||||||
| Publisher: | IOP Publishing Ltd | ||||||
| Official URL: | https://doi.org/10.1088/1751-8121/ac6f2f | ||||||
| DOI or Unique Handle: | 10.1088/1751-8121/ac6f2f | ||||||
| Subjects: | Specific Sciences > Physics > Classical Physics Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Statistical Mechanics/Thermodynamics Specific Sciences > Physics > Symmetries/Invariances |
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| Date: | 1 June 2022 | ||||||
| Volume: | 55 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/23511 |
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