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

Andor Frenkel

Published Jan 1, 2015• 2 citations
OpenAlex

Abstract

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.

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

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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.

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Can the Salecker-Wigner clock be microscopic?

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Comment on ‘The smallest clock’

L. Brualla

It has been suggested that Wigner's clock inequalities can be applied to biological systems. Pesic was the first to suggest this by applying these inequalities to the reproduction time of a mycoplasma (1993 Eur. J. Phys. 14 90). More recently, Goel applied Wigner's clock inequalities to the system formed by a Taq DNA polymerase reading a phage lambda DNA strand, concluding that the behaviour of polymerases is governed by quantum mechanical processes. By means of a counterexample, using a Pfu DNA polymerase, I show that current experimental evidence does not allow us to conclude that Wigner's inequalities govern the behaviour of polymerases. Furthermore, both works are based on an incorrect interpretation of the concept of position uncertainty.

European Journal of Physics•Apr 9, 2013•2 citations
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.
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.
A clock is, from an information-theoretic perspective, a system that emits information about time.One may therefore ask whether the theory of information imposes any constraints on the maximum precision of clocks.Here we show a quantum-over-classical advantage for clocks or, more precisely, the task of generating information about what time it is.The argument is based on information-theoretic considerations: we analyze how the accuracy of a clock scales with its size, measured in terms of the number of bits that could be stored in it.We find that a quantum clock can achieve a quadratically improved accuracy compared to a purely classical one of the same size.
It has been suggested that Wigner's clock inequalities can be applied to biological systems. Pesic was the first to suggest this by applying these inequalities to the reproduction time of a mycoplasma (1993 Eur. J. Phys. 14 90). More recently, Goel applied Wigner's clock inequalities to the system formed by a Taq DNA polymerase reading a phage lambda DNA strand, concluding that the behaviour of polymerases is governed by quantum mechanical processes. By means of a counterexample, using a Pfu DNA polymerase, I show that current experimental evidence does not allow us to conclude that Wigner's inequalities govern the behaviour of polymerases. Furthermore, both works are based on an incorrect interpretation of the concept of position uncertainty.