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The Clock Paradox in the Special Theory of Relativity

Published online by Cambridge University Press:  14 March 2022

Adolf Grünbaum
Adolf Grünbaum*
Affiliation:
Lehigh University
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Extract

1. Introduction. The germ of the clock paradox was contained in Einstein's fundamental paper on the special theory of relativity, where he declares that the retardation of a moving clock “still holds good if the clock moves from A to B in any polygonal line, and also when the points A and B coincide.” This remark soon gave rise to a criticism which was to play a prominent role in the discussions of the consistency of the theory of relativity. It was charged that this theory allows the paradoxical conclusion that at the instant of the return of a moving clock U1 to its point of departure A, the time shown by Ul is both earlier and later than the corresponding reading of a clock U2 which has remained stationary at A during U1's journey. Critics based this contention on the following assumptions, for which they claimed the sanction of relativity: (i) The relative motion of U1 and U2 is such that the kinematic process seen by an observer on one of these clocks is of the same character as that seen by an observer on the other, and this symmetry allows each of these two clocks to be used as a reference frame from which to describe the motion of the other, and (ii) there is reciprocity between these two reference frames such that in each of them, the moving clock must be slow upon returning to the stationary one.

Type
Research Article
Information
Philosophy of Science , Volume 21 , Issue 3 , July 1954 , pp. 249 - 253
Copyright
Copyright © Philosophy of Science Association 1954

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References

1 Annalen der Physik, 1905, 17, §4.

2 Cf. W. P. Montague, Phil. Review, 1924, 33, 156; A. O. Lovejoy, Phil. Review, 1931, 40, 48, 152, 549, and the references given there.

3 A. Einstein, Naturwissenschaften, 1918, 6, 697.

4 H. Thirring, Naturwissenschaften, 1921, 9, 209; H. Reichenbach, Philosophie der Raum-Zeit-Lehre, Berlin, 1928, p. 224; H. Törnebohm, A Logical Analysis of the Theory of Relativity, Göteborg, 1952, pp. 41–42; R. Dugas, Histoire de la Mécanique, Neuchâtel, 1950, pp. 481–2.

5 Cf. A. Kopff, Grundzüge der Einsteinschen Relativitätstheorie, Leipzig, 1921, pp. 117, 189; R. C. Tolman, Relativity, Thermodynamics and Cosmology, Oxford, 1934, pp. 194–197; E. L. Hill, Physical Review, 1947 (2), 72, 236; C. Møller, The Theory of Relativity, Oxford, 1952, §98, and the references given there on p. 258; F. I. Mikhail, Proc. Cambridge Phil. Soc, 1952 48, 608, and the references given there on p. 615.

6 W. H. McCrea, Nature, 1951, 167, 680. An earlier analysis, lacking generality and not clear in all respects, was given by E. B. McGilvary, Phil. Review, 1931, 40, 375–377.

7 A. O. Lovejoy, Phil. Review, 1931, 40, 63.