Energy Non-Conservation in Quantum Mechanics

TL;DR

This paper investigates energy non-conservation during quantum measurements, demonstrating that energy can change arbitrarily and proposing an experimental protocol to detect such violations, challenging traditional conservation assumptions.

Contribution

It reveals that energy can be non-conserved during quantum measurements and proposes an experimental method to observe these violations, which is a novel insight in quantum theory.

Findings

Energy change during measurement can be arbitrarily large.

Energy is not conserved in individual quantum worlds.

Proposes an experimental protocol to detect energy non-conservation.

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 can clearly change 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.