Energy Non-conservation in Quantum Mechanics

Foundations of Physics 51 (4):1-15 (2021)
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Abstract

We study the conservation of energy, or lack thereof, when measurements are performed in quantum mechanics. The expectation value of the Hamiltonian of a system changes when wave functions collapse in accordance with the standard textbook treatment of quantum measurement, but one might imagine that the change in energy is compensated by the measuring apparatus or environment. We show that this is not true; the change in the energy of a state after measurement can be arbitrarily large, independent of the physical measurement process. In Everettian quantum theory, while the expectation value of the Hamiltonian is conserved for the wave function of the universe, it is not constant within individual worlds. It should therefore be possible to experimentally measure violations of conservation of energy, and we suggest an experimental protocol for doing so.

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Sean M. Carroll
Johns Hopkins University

Citations of this work

Prime Matter and the Quantum Wavefunction.Robert C. Koons - 2024 - Ancient Philosophy Today 6 (1):92-119.

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References found in this work

Mad-Dog Everettianism: Quantum Mechanics at Its Most Minimal.Sean M. Carroll & Ashmeet Singh - 2019 - In Anthony Aguirre, Brendan Foster & Zeeya Merali (eds.), What is Fundamental? Cham: Springer Verlag. pp. 95-104.
”Relative state’ formulation of quantum mechanics.Hugh Everett - 1957 - Reviews of Modern Physics 29 (3):454--462.
'Relative State' Formulation of Quantum Mechanics.Hugh Everett - 1957 - Reviews of Modern Physics 29 (3):454-462.

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