Conserved Quantities and Measurements

TL;DR

This paper argues that apparent violations of conservation laws during measurements are due to entanglement effects between the system and apparatus, which are often overlooked, and that conservation laws remain valid.

Contribution

It highlights the role of entanglement in measurement interactions, showing that small correlations can explain perceived conservation violations.

Findings

Entanglement between system and apparatus is inevitable during measurement.

Tiny differences in apparatus states can account for perceived conservation deviations.

Measurements do not necessarily violate conservation laws due to entanglement effects.

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. Discussions of the effect of measurements on conserved quantities often overlook the possibility of 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. Since entanglement is a generic result of interaction, as shown by Gemmer and Mahler[1], and by Durt[2,3] one would expect some nonzero entanglement between apparatus and measured system, even though the amount of such entanglement is extremely small. Because the apparatus has an enormous number of degrees of freedom relative to the measured system, even 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. Hence measurements need not violate conservation laws.