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Some remarks on the extended Galilean transformation
Abstract
The Galilean transformation carries one inertial frame into another with a different velocity. The extended Galilean transformation carries an inertial frame into a rigid frame with uniform spatial, but arbitrary translational acceleration x′=x+ξ (t). Besides being useful in discussing the equivalence principle, this transformation provides a physical interpretation for the theorem in nonrelativistic quantum mechanics, that we cannot coherently combine states of different mass. This restriction comes about because we cannot distinguish between coordinate and proper time in nonrelativistic physics.
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To ensure covariance of the Schrödinger equation, the wave functions ψ and ψ' in the two reference frames differ by a mass-dependent phase term, which could cause mass-dependent diffraction and interference effects.
“However, to ensure covariance of the Schr¨ odinger equation the wave functions ψ and ψ ' in the two reference frames differ each other for a massdependent phase term [Eqs.(3) and (4)], which could eventually cause mass-dependent diffraction and interference effects [8,34].”
From Equivalence principle and quantum mechanics: quantum simulation with entangled photons (2018) · cites this paper as [34]
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Background
Metadata
- Authors
- Greenberger, D. M.
- Affiliations
- City College of New York (US)
- Corresponding author
- Greenberger, Daniel M.
- Venue
- American Journal of Physics
- Published
- 1979-01-01
- Volume
- 47
- Issue
- 1
- Pages
- 35-38
- ISSN
- 0002-9505 (ISSN-L)
- 1943-2909
- OpenAlex
- W1969086417
- Cited by
- 34
- References
- 0
- Citations by year
- 2025: 2 · 2024: 1 · 2023: 1 · 2019: 4 · 2018: 1 · 2017: 1 · 2016: 3 · 2015: 1 · 2012: 1
- FWCI
- 1.78
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- American Journal of Physics (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- rigid frames, non-inertial frames, equivalence principle, non-relativistic quantum mechanics, proper time, coordinate time, inertial frames
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