A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. II
Abstract
In this paper, we shall show how the theory of measurements is to be understood from the point of view of a physical interpretation of the quantum theory in terms of "hidden" variables, developed in a previous paper. We find that in principle, these "hidden" variables determine the precise results of each individual measurement process. In practice, however, in measurements that we now know how to carry out, the observing apparatus disturbs the observed system in an unpredictable and uncontrollable way, so that the uncertainty principle is obtained as a practical limitation on the possible precision of measurements. This limitation is not, however, inherent in the conceptual structure of our interpretation. We shall see, for example, that simultaneous measurements of position and momentum having unlimited precision would in principle be possible if, as suggested in the previous paper, the mathematical formulation of the quantum theory needs to be modified at very short distances in certain ways that are consistent with our interpretation but not with the usual interpretation.We give a simple explanation of the origin of quantum-mechanical correlations of distant objects in the hypothetical experiment of Einstein, Podolsky, and Rosen, which was suggested by these authors as a criticism of the usual interpretation.Finally, we show that von Neumann's proof that quantum theory is not consistent with hidden variables does not apply to our interpretation, because the hidden variables contemplated here depend both on the state of the measuring apparatus and the observed system and therefore go beyond certain of von Neumann's assumptions.In two appendixes, we treat the problem of the electromagnetic field in our interpretation and answer certain additional objections which have arisen in the attempt to give a precise description for an individual system at the quantum level.
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Bohmian mechanics violates L but not the other assumptions.
“Bohmian mechanics [8, 9] violates L but not the other assumptions.”
From A strong no-go theorem on the Wigner’s friend paradox (2020) · cites this paper as [9]
The usual uncertainty relations for noncommuting observables become a corollary of the quantum equilibrium hypothesis ρ=|ψ|^2 once the dynamical role of the wave function is taken into account.
“More generally, the usual uncertainty relations for noncommuting 'observables' become a corollary of the quantum equilibrium hypothesis ρ = | ψ | 2 as soon as the dynamical role of the wave function is taken into account; a detailed analysis can be found in [14,18,29].”
From Quantum equilibrium and the origin of absolute uncertainty (1992) · cites this paper as [14]
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- Authors
- Bohm, D.
- Venue
- Physical Review
- Publisher
- American Physical Society (APS)
- Published
- 1952-01-15
- Volume
- 85
- Issue
- 2
- Pages
- 180-193
- ISSN
- 0031-899X (ISSN-L)
- OpenAlex
- W4249821837
- Cited by
- 2,052
- References
- 5
- Citations by year
- 2026: 68 · 2025: 82 · 2024: 107 · 2023: 92 · 2022: 87 · 2021: 80 · 2020: 85 · 2019: 72 · 2018: 82 · 2017: 67 · 2016: 107 · 2015: 69 · 2014: 58 · 2013: 61 · 2012: 96
- FWCI
- 4.23
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review (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
- Social Sciences › Arts and Humanities › History and Philosophy of Science › Philosophy and History of Science
- Keywords
- hidden variables, quantum measurement, physical interpretation of quantum mechanics, uncertainty principle, EPR paradox, quantum correlations, measurement instruments, electromagnetic fields
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