Abstract
We address a long-standing criticism of the stochastic mechanics approach to quantum theory by one of its pioneers, Edward Nelson: Multi-time correlations in stochastic mechanics differ from those in textbook quantum theory. We elaborate upon an answer to this criticism by Blanchard et al. (Phys Rev D 34(12):3732-3738, 1986), who showed that if the (derived) wave function in stochastic mechanics is assumed to collapse to a delta function in a position measurement, the collapse will change the stochastic process for the particles (because the stochastic process depends on derivatives of the wave function), and the resulting multi-time correlations will agree with those in textbook quantum theory. We show that this assumption can be made rigorous through the tool of ‘effective collapse’ familiar from pilot-wave theories, and we illustrate this with an example involving the double-slit experiment. Hence one of the major lingering objections to stochastic mechanics is dissolved. We finally show that in the case of multi-time correlations between multiple particles, effective collapse implies nonlocal influences between particles.
Original language | English |
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Title of host publication | Boston Studies in the Philosophy and History of Science |
Publisher | Springer |
Pages | 61-78 |
Number of pages | 18 |
ISBN (Electronic) | 978-3-031-49861-9 |
ISBN (Print) | 978-3-031-49860-2 |
DOIs | |
Publication status | Published - 18 Jun 2024 |
Publication series
Name | Boston Studies in the Philosophy and History of Science |
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Volume | 344 |
ISSN (Print) | 0068-0346 |
ISSN (Electronic) | 2214-7942 |
Bibliographical note
Publisher Copyright:© The Author(s).
Keywords
- Effective collapse
- Multi-time correlations
- Stochastic mechanics