Back reaction of clocks and limitations on observability in closed systems

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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 paper is that while doing so, we can no longer neglect the back reaction due to the measurement on the clock. For a von Neumann measurement model, 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 subclass of observables in a closed system cannot be realized by a von Neumann–like measurement.

Original languageEnglish
Pages (from-to)7
Number of pages1
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume62
Issue number4
DOIs
StatePublished - 2000

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