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Energy Non-conservation in Quantum Mechanics

Carroll, Sean M. and Lodman, Jackie (2021) Energy Non-conservation in Quantum Mechanics. Foundations of Physics, 51 (4). Art. No. 83. ISSN 0015-9018. doi:10.1007/s10701-021-00490-5.

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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 (Copenhagen) 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 (including all the branches), 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.

Item Type:Article
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URLURL TypeDescription ReadCube access Paper
Carroll, Sean M.0000-0002-4226-5758
Lodman, Jackie0000-0003-0923-9440
Additional Information:© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021. Received 13 May 2021; Accepted 23 July 2021; Published 31 July 2021. We would like to thank Anthony Bartolotta, Brad Fillipone, Jason Pollack, Ken Olum, Jonathan Oppenheim, Gil Refael, Grant Remmen, Ashmeet Singh, and Mark Wise for helpful discussions during the course of this project. This research is funded in part by the Walter Burke Institute for Theoretical Physics at Caltech, by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632, and by the Foundational Questions Institute.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Department of Energy (DOE)DE-SC0011632
Foundational Questions Institute (FQXI)UNSPECIFIED
Subject Keywords:Quantum mechanics; Energy conservation; Quantum foundations
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Issue or Number:4
Record Number:CaltechAUTHORS:20210128-100731565
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Official Citation:Carroll, S.M., Lodman, J. Energy Non-conservation in Quantum Mechanics. Found Phys 51, 83 (2021).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107784
Deposited By: Joy Painter
Deposited On:28 Jan 2021 18:16
Last Modified:14 Sep 2021 19:58

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