Discussion of Probability Relations between Separated Systems
Abstract
The probability relations which can occur between two separated physical systems are discussed, on the assumption that their state is known by a representative in common. The two families of observables, relating to the first and to the second system respectively, are linked by at least one match between two definite members, one of either family. The word match is short for stating that the values of the two observables in question determine each other uniquely and therefore (since the actual labelling is irrelevant) can be taken to be equal. In general there is but one match, but there can be more. If, in addition to the first match, there is a second one between canonical conjugates of the first mates, then there are infinitely many matches, every function of the first canonical pair matching with the same function of the second canonical pair. Thus there is a complete one-to-one correspondence between those two branches (of the two families of observables) which relate to the two degrees of freedom in question. If there are no others, the one-to-one correspondence persists as time advances, but the observables of the first system (say) change their mates in the way that the latter, i.e. the observables of the second system, undergo a certain continuous contact-transformation.
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All information contained in the singlet state defines only joint properties.
“All information contained in the state in Eq. ( 15) defines only joint properties (Schrödinger, 1935).”
From Multiphoton entanglement and interferometry (2012) · cites this paper as Schrödinger, 1935
Relative to the wave function, Bohmian mechanics is completely local; its nonlocality derives solely from the nonlocality built into standard quantum theory via a wave function on configuration space.
“We wish to emphasize, however, that relative to the wave function , Bohmian mechanics is completely local : the nonlocality in Bohmian mechanics derives solely from the nonlocality built into the structure of standard quantum theory, as provided by a wave function on configuration space.”
From Quantum equilibrium and the origin of absolute uncertainty (1992) · cites this paper as [52]
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“(24) defines only joint properties (Schrödinger, 1935): the two spins, if measured with respect to the same direction, will be found opposite.”
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- Authors
- Schrödinger, E.
- Corresponding author
- Schrödinger, E.
- Venue
- Mathematical Proceedings of the Cambridge Philosophical Society
- Publisher
- Cambridge University Press (CUP)
- Published
- 1935-10
- Volume
- 31
- Issue
- 4
- Pages
- 555-563
- ISSN
- 0305-0041 (ISSN-L)
- 1469-8064
- OpenAlex
- W2040794877
- Cited by
- 3,124
- References
- 1
- Citations by year
- 2026: 127 · 2025: 176 · 2024: 175 · 2023: 231 · 2022: 206 · 2021: 188 · 2020: 163 · 2019: 198 · 2018: 167 · 2017: 172 · 2016: 156 · 2015: 152 · 2014: 89 · 2013: 114 · 2012: 101
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Mathematical Proceedings of the Cambridge Philosophical Society (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 › Quantum chaos and dynamical systems
- Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
- Keywords
- bijections, contact transformations, quantum mechanics, statistical mechanics, observables
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