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

Authors
Sean M. Carroll
California Institute of Technology
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.
Keywords quantum mechanics, energy conservation
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DOI 10.1007/s10701-021-00490-5
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References found in this work BETA

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? Springer Verlag. pp. 95-104.
Wavefunction Collapse and Conservation Laws.Philip Pearle - 2000 - Foundations of Physics 30 (8):1145-1160.
”Relative State’ Formulation of Quantum Mechanics.Hugh Everett - 1957 - Reviews of Modern Physics 29 (3):454--462.

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