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arXiv:1501.00840 · Foundations of Physics

Dependence of the Time-Reading Process of the Salecker–Wigner Quantum Clock on the Size of the Clock

Andor Frenkel

Published Jul 16, 2015• 4 citations
arXivHTMLPDF
DOI
10.1007/s10701-015-9938-x

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Dependence of the Time-Reading Process of the Salecker–Wigner Quantum Clock on the Size of the Clock

Andor Frenkel

It is shown in the present note that the degree of the complexity of the time-reading process of the Salecker–Wigner clock depends on the size of the clock. This dependence leads to a relation between the size and the accuracy of the clock, and suggests a precise optimal value for the size in agreement with the order of magnitude value established by Salecker and Wigner.

•Jan 1, 2015•2 citations

Extended Salecker-Wigner formula for optimal accuracy in reading a clock via a massive signal particle

Shoju Kudaka, Shuichi Matsumoto

In order to acquire an extended Salecker-Wigner formula from which to derive the optimal accuracy in reading a clock with a massive particle as the signal, von Neumann's classical measurement is employed, by which simultaneously both position and momentum of the signal particle can be measured approximately. By an appropriate selection of wave function for the initial state of the composite system (a clock and a signal particle), the formula is derived accurately. Valid ranges of the running time of a clock with a given optimal accuracy are also given. The extended formula means that contrary to the Salecker-Wigner formula there exists the possibility of a higher accuracy of time measurement, even if the mass of the clock is very small.

Physical Review A•Jul 11, 2007•1 citation

Can the Salecker-Wigner clock be microscopic?

Andor Frenkel

Half a century ago H. Salecker and E. P. Wigner examined the functioning of a quantum clock of very simple construction [1]. They raised the question whether such a clock can be microscopic or not, but no clear-cut answer has been reached in [1] (see also [2]). In this note it is shown that their clock can have a microscopic mass and size only if its accuracy is poor, but if the size is macroscopic, a decent accuracy can be achieved even if the mass is microscopic.

arXiv:quant-ph/0503171•Mar 21, 2005•1 citation
In order to acquire an extended Salecker-Wigner formula from which to derive the optimal accuracy in reading a clock with a massive particle as the signal, von Neumann's classical measurement is employed, by which simultaneously both position and momentum of the signal particle can be measured approximately. By an appropriate selection of wave function for the initial state of the composite system (a clock and a signal particle), the formula is derived accurately. Valid ranges of the running time of a clock with a given optimal accuracy are also given. The extended formula means that contrary to the Salecker-Wigner formula there exists the possibility of a higher accuracy of time measurement, even if the mass of the clock is very small.