Hidden Variables and Incompatible Observables in Quantum Mechanics
Bibliographic Data
| ID | 8396256 |
|---|---|
| Authors | Benjamin Feintzeig (0000-0001-7692-5155, University of California, Irvine, corresponding author) |
| Year | 2015 |
| Volume | 66 |
| Issue | 4 |
| Pages | 905-927 |
| Publication date | 2015-12-01 |
| Peer Reviewed | Yes |
| Open Access | No |
| Type | ARTICLE |
| Venue | The British Journal for the Philosophy of Science (JOURNAL) |
| Journal identifiers | ISSN: 0007-0882 • E-ISSN: 1464-3537 |
| Publisher | Oxford University Press (PUBLISHER • GB) |
| DOI | 10.1093/bjps/axu017 |
| OpenAlex | W2118081312 |
| Language | EN |
| Citations received | 1 |
| References cited | 11 |
This article takes up a suggestion that the reason we cannot find certain hidden variable theories for quantum mechanics, as in Bell’s theorem, is that we require them to assign joint probability distributions on incompatible observables. These joint distributions are problematic because they are empirically meaningless on one standard interpretation of quantum mechanics. Some have proposed getting around this problem by using generalized probability spaces. I present a theorem to show a sense in which generalized probability spaces can’t serve as hidden variable theories for quantum mechanics, so the proposal for getting around Bell’s theorem fails. 1 Introduction2 Bell’s Theorem and Classical Probability Spaces 2.1 Bell’s derivation of the Bell inequalities 2.2 Pitowsky’s derivation of the Bell inequalities3 Incompatible Observables4 Generalized Probability Spaces5 A ‘No-Go’ Theorem6 Conclusions
Bell test experiments · Bell's theorem · Fundamental theorem · Hidden variable theory · Interpretations of quantum mechanics · Joint probability distribution · Kochen–Specker theorem · Local hidden variable theory · No-go theorem · Observable · Physics · Probability amplitude · Pure mathematics · Quantum · Quantum dynamics · Quantum entanglement · Quantum mechanics · Quantum no-deleting theorem · Quantum probability · Quantum process · Statistics · Theoretical physics · Mathematics · Philosophy and History of Science · Philosophy and Theoretical Science · Quantum Mechanics and Applications
| Unique citing works | 1 |
|---|---|
| Citations per year | 0,2 |
| Citation span | 2021 - 2021 (1) |
| Citation velocity | historical |
| Highly cited | No |
| Citation types | Neutral: 1 |