Universal Journal of Physics and Application Vol. 2(1-2), pp. 113 - 136
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NOTES ON THE THEORY OF QUANTUM CLOCK

AUTHOR(S) INFORMATION: Tralle I. and Pellonpaa J.-P.

ABSTRACT

In this paper we argue that the notion of time, whatever complicated and difficult to define as the philosophical category, from physicist's point of view is nothing else but the sum of 'lapses of time' measured by a proper clock. As far as Quantum Mechanics is concerned, we distinguish a special class of clocks, the 'atomic clocks'. It is because at atomic and subatomic level there is no other possibility to construct a 'unit of time' or 'instant of time' as to use the quantum transitions between chosen quantum states of a quantum object such as atoms, atomic nuclei and so on, to imitate the periodic circular motion of a clock hand over the dial. The clock synchronization problem is also discussed in the paper. We study the problem of defining a time difference observable for two-mode oscillator system. We assume that the time difference observable is the difference of two single-mode covariant time observables which are represented as a time shift covariant normalized positive operator measures. The difficulty of finding the correct value space and normalization for time difference is discussed.