Energy Non-Conservation in Quantum Mechanics

Citation

Lodman, Jackie Julia (2020) Energy Non-Conservation in Quantum Mechanics. Senior thesis (Major), California Institute of Technology. doi:10.7907/4a55-jt21. https://resolver.caltech.edu/CaltechTHESIS:09062020-104208324

Abstract

Conservation of energy is an integral component of modern physics, but questions remain in quantum mechanics. In traditional quantum mechanics, superpositions of energy eigenstates collapse into a single energy eigenstate upon measurement, and any change in energy after measurement is thought to be lost/gained in the measurement process. However, we argue that energy non-conservation in quantum mechanics cannot be entirely accounted for by leakage to the apparatus/environment. We first present a comprehensive Hamiltonian where energy is not conserved in any considered interpretation according to an observer. Next, we present a protocol for developing experiments to observe this non-conservation, then we use our protocol to develop an example thought experiment. In both the comprehensive Hamiltonian and thought experiment examples, energy is not conserved to an observer in all considered interpretations, but it is conserved when considering the universe's global wave function in Everettian quantum mechanics. Finally, we discuss implications for the status of conservation of energy and other conservation laws. The work presented in this thesis will be adapted into an upcoming paper, Carroll and Lodman.

Thesis Files