Random Time

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Abstract

IF the point of the hand of a clock moves along the circumference of the unit circle with constant angular velocity ω, then the time measured is determined by the position: This formulation depends, however, on the abstraction of a ‘uniform time’, a concept which, after Mach's critique, fails to be meaningful and cannot be made legitimate even if a built clock is replaced by a clock determined by the gyrations of the Earth (or, for that matter, of a galaxy). Clearly, the conceptual difficulty remains unaltered if, instead of astronomical clocks, recourse is had to electron clocks—those supplied by electromagnetic or spectroscopie measurements.

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References

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    Wiener, N., “The Fourier Integral and Certain of its Applications”, Chapter 4 (Camb. Univ. Press, 1933). For further developments, cf. Wiener, N., and Wintner, A., J. Math. and Phys. (M.I.T.), 17, 233 (1939); and Wiener, N., and Wintner, A., Amer. J. Math., 63, 796 (1941).

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    Wiener, N., Acta Math., 55, 117 (1930).

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    Birkhoff, G. D., Proc. U.S. Nat. Acad. Sci., 17, 650 (1931).

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    Lévy, P., Compositio Math., 7, 283 (1939).

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WIENER, N., WINTNER, A. Random Time. Nature 181, 561–562 (1958) doi:10.1038/181561a0

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