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arXiv:quant-ph/0207071

There is No Violation of Conservation Laws in Quantum Measurement

Jacques Mallah

Published Jul 11, 2002• 1 citation
arXivHTMLPDF

Abstract

For some ideal quantum measurements, conservation laws would seem to be violated systematically. It is argued that the intrinsically non-"ideal" nature of quantum measurements rescues the conservation laws.
DOI
10.48550/arxiv.quant-ph/0207071

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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.
Henry is trapped in a burning building because of Eve’s mischief. Henry’s entanglement with the hot environment is ominous: his states receive excessive energy from the environment, threatening his physiology. Can quantum effects rescue Henry from the fire? Unexpectedly, Eve comes to his rescue. She frequently measures his energy in a “quantum non-demolition” (QND) fashion which is expected to keep his state intact. Surprisingly, Henry grows hotter or colder depending on Eve’s measurement rate! These quantum effects seem to violate the laws of thermodynamics. Engraved in stone as these laws and the ensuing time directionality (time arrow) may be, they fail if the system is examined too frequently, whence time arrow loses its meaning. One may speculate over the role of such anomalies in the Big Bang. These anomalies support Parmenides’ view that time flow is determined by the observer’s choices. The appendix to this chapter elaborates on the dynamics induced by system–environment interaction changes.