Conserved Quantities and Measurements
- URL: http://arxiv.org/abs/2108.08342v2
- Date: Thu, 26 Aug 2021 15:36:33 GMT
- Title: Conserved Quantities and Measurements
- Authors: Edward J. Gillis
- Abstract summary: 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.
The preparation of a system in any particular state necessarily involves interaction between the apparatus and the system.
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 can be sufficient to account for the perceived deviation from strict conservation of the quantity in question.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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