Dependence of the time-reading process of the Salecker--Wigner quantum clock on the size of the clock

TL;DR

This paper investigates how the size of the Salecker--Wigner quantum clock influences the complexity of reading time, revealing a size-accuracy relation and proposing an optimal clock size consistent with prior estimates.

Contribution

It establishes a quantitative relation between clock size and reading complexity, identifying an optimal size that balances accuracy and complexity.

Findings

Clock size affects the complexity of time reading.

A size-accuracy relation for the Salecker--Wigner clock is derived.

An optimal clock size is proposed, aligning with previous estimates.

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.