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Back-Reaction of Clocks and Limitations on Observability in Closed Systems

Aharon Casher·Benni Reznik
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Abstract

Measurements are ordinarily described with respect to absolute "Newtonian" time. In reality however, the switching-on of the measuring device at the instance of the measurement requires a timing device. Hence the classical time $t$ must be replaced by a suitable quantum time variable $τ$ of a physical clock. The main issue raised in this article is that while doing so, we can no longer neglect the {\em back-reaction} due to the measurement on the clock. This back-reaction yields a bound on the accuracy of the measurement. When this bound is violated the result of a measurement is generally not an eigenvalue of the observable, and furthermore, the state of the system after the measurement is generally not a pure state. We argue that as a consequence, a sub-class of observables in a closed system cannot be realized by a measurement.

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Aharon Casher, Benni Reznik. 1999-09-02. Back-Reaction of Clocks and Limitations on Observability in Closed Systems. https://doi.org/10.1103/physreva.62.042104

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