Quantum Limitations of the Measurement of Space-Time Distances

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Abstract
This article deals with the limitations which the quantized nature of microscopic systems imposes on the possibility of measuring distances between space-time events. It is proposed to use only clocks for measuring space-time distances and to avoid the use of measuring rods which are essentially macrophysical objects. The accuracy of reading a clock with a given mass is considered and examples for microphysical clocks are given. It is shown that the mass of the clock, and the uncertainty (spread) of this quantity, exceed certain values which depend on the accuracy with which the time interval is to be measured, the magnitude of this time interval (the running time of the clock) and the size of the clock. The minimum mass uncertainty of the clock is given by Heisenberg's relation; the minimum mass itself is higher by the ratio of the running time and the accuracy.

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