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
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).
Wiener, N., Acta Math., 55, 117 (1930).
Birkhoff, G. D., Proc. U.S. Nat. Acad. Sci., 17, 650 (1931).
Lévy, P., Compositio Math., 7, 283 (1939).
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WIENER, N., WINTNER, A. Random Time. Nature 181, 561–562 (1958). https://doi.org/10.1038/181561a0
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DOI: https://doi.org/10.1038/181561a0
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