paper

Quantum Measurements and Conservation Laws

arXiv:2108.08342

Abstract

When a measurement is made on a system that is not in an eigenstate of the measured observable, it is often assumed that some conservation law has been violated. But this assumption results from ignoring the entanglement between the measured system and the preparation apparatus. The preparation of a system in any particular state necessarily involves interaction between the apparatus and the system, and this interaction generates entanglement. The amount of entanglement is very small, but the apparatus typically has an enormous number of degrees of freedom; this implies that a very tiny difference between the apparatus states that are correlated with the orthogonal states of the measured system can be sufficient to account for the perceived deviation from strict conservation of the quantity in question. After reviewing entanglement relations for a typical measurement situation with a macroscopic preparation apparatus I identify microscopic processes involving analogous entanglement relations in which measurements on both entangled systems demonstrate exact conservation of the relevant quantities. The close analogy strongly suggests that conservation laws hold exactly in all measurement processes.

arXiv commentModified title. Additional discussion and examples. References added. 11 pages

References in corpus (6)