Abstract
The relativity of simultaneity and the relativity of length lead naturally to the strangest consequences of relativity theory: time dilation and length contraction. Time dilation means that relative to a clock taken to be at rest, a moving clock runs slow, so that relative to the moving clock the amount of time recorded by the clock at rest expands or dilates. Let us suppose that we have two clocks A and B in motion relative to each other (Figure 3.1).
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References
Albert Einstein, “On the Electrodynamics of Moving Bodies,” trans. Arthur I. Miller, Appendix to Arthur I. Miller, Albert Einstein’s Special Theory of Relativity (Reading, Mass.: Addison-Wesley, 1981), p. 396.
Of Dingle’s extensive writings on SR, see especially “Time in Relativity Theory: Measurement or Coordinate?” in The Voices of Time,2d ed., ed. with a new Introduction by J. T. Fraser (Amherst, Mass.: University of Massachusetts Press, 1981), pp. 455–472 and Science at the Crossroads (London: Martin Brian & O’Keefe, 1972). See also his Auseinandersetzung with Max Born in Herbert Dingle, “Letters to the Editor: Physics: Special Theory of Relativity,” Nature 195 (8 September 1962): 985–986; Max Born, “Letters to the Editor: Physics: Special Theory of Relativity,” Nature 197 (30 March 1963): 1287; Herbert Dingle, “Special Theory of Relativity,” Nature 197 (30 March 1963): 1248–1249, and with Epstein in Paul S. Epstein, “The Time Concept in Restricted Relativity,” American Journal of Physics 10 (1942): 1–6; Herbert Dingle, “The Time Concept in Restricted Relativity,” American Journal of Physics 10 (1942): 203–205; Paul S. Epstein, “The Time Concept in Restricted Relativity—A Rejoinder,” American Journal of Physics 10 (1942): 205–208; L. Infeld, “Clocks, Rigid Bodies, and Relativity Theory,” American Journal of Physics 11 (1943): 219–222. For a similar argument see G. Burniston Brown, “What Is Wrong with Relativity?” Bulletin of the Institute of Physics and the Physical Society 18 (1967): 71–77, and the reply in “News and Comment,” Physics Bulletin 19 (1968): 22.
Dingle, “Time in Relativity Theory,” p. 465; idem, Science at the Crossroads,p. 11.
Dingle, Science at the Crossroads,p. 45.
Often the issue is blurred by reinterpreting Dingle’s objection to involve a plurality of A and B clocks (e.g.,L. Marder, Time and the Space-Traveller [London: George Allen & Unwin, 1971], p. 57; Lewis Carroll Epstein, Relativity Visualized [San Francisco: Insight Press, 1981] p. 99), which it does not, thereby concealing the radicalness of the solution.
This is also the fallacy in the defense of absolutism given by J. L. Mackie, “Three Steps toward Absolutism,” in Space, Time, and Causality,ed. Richard Swinburne, Synthèse Library 157 (Dordrecht: D. Reidel, 1983), pp. 16–20. Mackie invites us to imagine two photons emitted along paths A and B in opposite directions from the point of origin O. Pick an arbitrary point Con path A; there will be a point D on path B corresponding to C. “I do not claim,” avers Mackie, “that there is any way of determining the point that corresponds to C; I say only that there is one. And nothing but the sort of extreme verificationism which I mentioned, but set asidechrw(133)would rule out this claim as meaningless” (Ibid., pp. 18–19). At C and D photons sent to the right and left respectively will meet at a point G. By choosing a series of points C,C,, C2,chrw(133)and D, D 1 , D2, …,we construct the world line G, G 1 ,G2,…of an object which is at absolute rest. Once Jon Dorling, “Reply to Mackie,” in Space, Time, and Causality,p. 27, concedes that there is a unique point D correlated with C,the game is over. His attempt to elude Mackie’s conclusion by saying that “there is a preferred frame of reference associated with that burst of radiationchrw….But it is not an absolute frame, because it will be different for different bursts of radiation” is incoherent. Rather the problem is that no unique point D exists. Which point on B is correlated with C will vary with reference frames. For further discussion, see J. R. Lucas and P. E. Hodgson, Spacetime and Electromagnetism (Oxford: Clarendon Press, 1990), pp. 106–108. It is also worth adding that the same verificationism which Mackie rejects actually underlies the assumption, which he accepts, that the light cone structure is invariant, for this is not the case for aether compensatory theories.
For a clear statement of this point, see Alfred Schild, “The Clock Paradox in Relativity Theory,” American Mathematical Monthly 66 (1959): 10–11, who substitutes two twins separated at birth for the two clocks: “The two twins can be together once, at birth, and there can compare their ages directly. But they can never do so again in the future. Thus, the whole problem as to which twin is younger and which twin is older disappears completely. When the two twins are flying apart it is a physically meaningless statement to say that one is younger or older than the other.”
See Marder, Time and the Space-Traveller,pp. 58–60.
Robert Resnick, Introduction to Special Relativity (New York: John Wiley & Sons, 1968), p. 64. See the intriguing illustration of L. Epstein, Relativity Visualized pp. 71–72 (Fig. a).
See the comprehensive review, to which I am much indebted, by Marder, Time and the Space Traveller.
H. E. Ives, J. Opt. Sec. Am. 27, 305 (1937).
G. Builder, Australian J. Phys. //, 279 (1958).
H. Dingle, Nature, 179, 866 (1957)” (C. W. Sherwin, “Some Recent Experimental Tests of the `Clock Paradox’,” Physical Review 120 [ 1960 ]: 17–21 ).
A. Einstein, “Dialog fiber Einwände gegen die Relativitätstheorie,” Naturwissenschaften (1918): 697–702. Unfortunately, general relativistic treatments only complicate the problem and often lack physical significance, as shown by Geoffery Builder, “The Resolution of the Clock Paradox,” Australian Journal of Physics 10 (1957): 246–262.
As implied by Ray d’Inverno, Introducing Einstein’s Relativity (Oxford: Clarendon, 1992), p. 38: “The resolution rests on the fact that the accelerations, however brief, have immediate and finite effects on B but not on A who remains inertial throughout.”
Schild, “Clock Paradox,” p. 14; see also Yakov P. Terletskii, Paradoxes in the Theory of Relativity,with a Foreword by Banesh Hoffmann (New York: Plenum Press, 1968), p. 41; Lucas and Hodgson, Spacetime and Electromagnetism,p. 76.
Hermann Bondi, Relativity and Common Sense (New York: Dover Publications, 1964), p. 87; cf H. Bondi, “The Space Traveller’s Youth,” Discovery 18 (December 1957): 505–510. Davies also interprets the Twin Paradox as a sort of uni-directional time travel (P. C. W. Davies, Space and Time in the Modern Universe [Cambridge: Cambridge University Press, 1977], p. 39). Similarly, Fritz Rohrlich, From Paradox to Reality (Cambridge: Cambridge University Press, 1987), p. 70: “What is wrong is our concept of time: it is neither absolute (as Newton thought) nor universal (as we as wont to believe). Time depends on the history of the traveler through space.” Rindler, on the other hand, interprets the situation in a significantly different way. During the twin’s initial acceleration from zero to L’,he transfers himself into an inertial frame in which the distance to the turn-around point undergoes such tremendous length contraction that more than half his joumey is already completed by the time L’ is reached. Therefore, he accomplishes his trip in less time (Wolfgang Rindler, Introduction to Special Relativity [Oxford: Clarendon Press, 1982], p. 35). See also Capek’s struggle to explain how the two times are in some sense contemporaneous (Milic Capek, The Philosophical Impact of Contemporary Physics [Princeton: D. Van Nostrand, 1961], pp. 206–212).
An accelerated reference frame for a given observer 0 is a scheme of labeling of all events with four coordinates (three spatial and one temporal) such that O’s space coordinates are (0,0,0) and that all objects with constant space coordinates are (in some sense) at a fixed distance from O.
Bondi, Relativity and Common Sense,pp. 80–82. Notice that if bullets were used instead of light signals, relativity would not result because B’s bullets would travel slower than C’s due to addition of velocities; but because light velocity is invariant, relativity obtains.
Peter Kroes, Time: Its Structure and Role in Physical Theories, Synthese Library 179 (Dordrecht: D. Reidel, 1985), p. 47; Waldyr A. Rodrigues, Jr. and Marcio A. F. Rosa, “The Meaning of Time in the Theory of Relativity and `Einstein’s Later View of the Twin Paradox’,” Foundations of Physics 19 (1989): 705–724.
Epstein, Relativity Visualized,p. 39.
I borrow these examples from Marder, Time and the Space-Traveller,pp. 145–163; Edwin F. Taylor and John Archibald Wheeler, Spacetime Physics (San Francisco: W. H. Freeman, 1966), p. 18 of “Answers to the Exercises of Chapter I.”
See, for example, Arthur Eddington, Space, Time and Gravitation, Cambridge Science Classics (1920; rep. ed.: Cambridge, Cambridge University Press, 1987 ), pp. 22–23.
James Terrell, “Invisibility of the Lorentz Contraction,” Physical Review 116 (1959): 1041–1045: cf. V. F. Weisskopf. “The Visual Appearance of Rapidly Moving Objects,” Physics Today 13 (September 1960), pp. 24–27. The key difference between seeing an object and observing it via measurement is that the former involves the simultaneous reception of light quanta from the object whereas the latter involves simultaneous emission of light quanta from it.
There does not seem to be any absolute effect due to length contraction as there is due to time dilation in the twin paradox. Although Kroes attempts to find such an effect (Peter Kroes, “The Physical Status ofTime Dilation within the Special Theory of Relativity,” paper presented at the International Conference of the British Society for the Philosophy of Science, “Physical Interpretations of Relativity Theory,” Imperial College of Science and Technology, London, 16–19 September, 1988), all he shows is that length contraction leaves permanent traces in spacetime distances, not spatial distances.
For example. W. G. V. Rosser, Introductory Relativity (New York: Plenum Press, 1967), pp. 58–59, speaks of a “contraction” occurring in the measured length of an object. Posing the question whether the contraction is “real,” Rosser declines to answer, saying only that the measures of particular quantities are different in different co-ordinate systems and that there is no absolute length.
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Craig, W.L. (2001). Time Dilation and Length Contraction. In: Craig, W.L. (eds) Time and the Metaphysics of Relativity. Philosophical Studies Series, vol 84. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3532-2_3
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