Galilei covariance and Einstein's equivalence principle in quantum reference frames

Abstract

The covariance of the Schrödinger 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 Schrödinger equation, although form variant, is fully compatible with the aforementioned principles of relativity.

7 pages, thoroughly revised, published version

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Cited by in corpus (20)

• Quantum mechanics and the covariance of physical laws in quantum reference frames
• Quantum superposition of spacetimes obeys Einstein's Equivalence Principle
• Quantum reference frames for general symmetry groups
• Spacetime Quantum Reference Frames and superpositions of proper times
• Gravity entanglement, quantum reference systems, degrees of freedom
• The group structure of dynamical transformations between quantum reference frames
• Transformation of Spin in Quantum Reference Frames
• Quantum resource covariance
• A model of quantum spacetime
• Mesoscopic Mechanical Resonators as Quantum Non-Inertial Reference Frames
• Relativity of quantum superpositions
• Nonrelativistic spatiotemporal quantum reference frames
• Physical quantities and spatial parameters in the complex octonion curved space
• Equivalence principle and quantum mechanics: quantum simulation with entangled photons
• General Galilei Covariant Gaussian Maps
• Galilean relativity and wave-particle duality imply the Schrödinger equation
• The decoherence and interference of cosmological arrows of time for a de Sitter universe with quantum fluctuations
• Time Contraction Within Lightweight Reference Frames
• Searching for a physical description relative to a quantum system
• Puzzling out the mass-superselection rule