Galilei covariance and Einstein's equivalence principle in quantum reference frames
Open accessAbstract
The covariance of the Schr\"odinger equation under Galilei boosts and the compatibility of nonrelativistic quantum mechanics with Einstein's equivalence principle have been constrained for so long to the existence of a superselection rule which would prevent a quantum particle from being found in superposition states of different masses. In an effort to avoid this expedient, and thus allow nonrelativistic quantum mechanics to account for unstable particles, recent works have suggested that the usual Galilean transformations are inconsistent with the nonrelativistic limit implied by the Lorentz transformation. Here we approach the issue in a fundamentally different way. Using a formalism of unitary transformations and employing quantum reference frames rather than immaterial coordinate systems, we show that the Schr\"odinger equation, although form variant, is fully compatible with the aforementioned principles of relativity.
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Ways to overcome Bargmann's superselection rule have been suggested by some authors.
“ways to overcome it have been suggested by some authors [8, 10, 17, 18].”
From Equivalence principle and quantum mechanics: quantum simulation with entangled photons (2018) · cites this paper as [10]
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- Authors
- Pereira, S. T., & Angelo, R. M.
- Affiliations
- Universidade Federal do Paraná (BR)
- ORCID
- Angelo, R. M.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2015-02-10
- Volume
- 91
- Issue
- 2
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2055476267
- Cited by
- 31
- References
- 26
- Citations by year
- 2026: 3 · 2025: 2 · 2024: 5 · 2023: 2 · 2022: 2 · 2021: 6 · 2020: 2 · 2019: 2 · 2018: 3 · 2017: 2 · 2016: 1 · 2015: 1
- FWCI
- 1.19
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- arXiv (Cornell University)
- Funders
- Conselho Nacional de Desenvolvimento Científico e Tecnológico
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Keywords
- Galilean covariance, Schrödinger equation, Einstein equivalence principle, quantum reference frames, superselection rules, non-relativistic quantum mechanics, Lorentz transformation, unitary transformation, unstable particles
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