Combining stochastic dynamical state-vector reduction with spontaneous localization
Abstract
A linear equation of motion for the state vector is presented, in which an anti-Hermitian Hamiltonian that fluctuates randomly is added to the usual Hamiltonian of the Schr\"odinger equation. It is shown how the resulting theory describes the continuous evolution of a state vector to an ensemble of reduced state vectors while retaining important physical features of the Ghirardi, Rimini, and Weber [Phys. Rev. D 34, 470 (1986)] theory of spontaneous localization, in which the state vector reduction occurs discontinuously. A novel aspect, compared with ordinary quantum theory, is that the state-vector norm changes with time. The squared norm of each state vector is interpreted as being proportional to the probability possessed by that state vector in the ensemble of state vectors. This interpretation is shown to be consistent with the independent Markovian evolution of each state vector.
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Assumption (Q) is manifestly violated by theories that postulate a modification of standard quantum mechanics, such as spontaneous and gravity-induced collapse models.
“Assumption (Q) is manifestly violated by theories that postulate a modification of standard quantum mechanics, such as spontaneous16–20 and gravity-induced21–23 collapse models (cf. 24 for a review).”
From Quantum theory cannot consistently describe the use of itself (2018) · cites this paper as [18]
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- Authors
- Pearle, P.
- Affiliations
- Hamilton College (US)
- Corresponding author
- Pearle, Philip
- ORCID
- Pearle, Philip
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1989-03-01
- Volume
- 39
- Issue
- 5
- Pages
- 2277-2289
- ISSN
- 0556-2791 (ISSN-L)
- OpenAlex
- W1994358697
- Cited by
- 942
- References
- 0
- Citations by year
- 2026: 51 · 2025: 25 · 2024: 62 · 2023: 62 · 2022: 34 · 2021: 24 · 2020: 54 · 2019: 55 · 2018: 24 · 2017: 27 · 2016: 35 · 2015: 29 · 2014: 27 · 2013: 30 · 2012: 28
- FWCI
- 15.25
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review A (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- spontaneous localization, state vector reduction, Markovian evolution, measurement problem
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