- 9 The Conventionality Thesis
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The authors of the early articles and textbooks on relativity in general emphasized the importance of the concept of simultaneity for the construction of the time coordinate of an inertial reference system but rarely paid attention to the conventionality of its deﬁnition. A typical example is Max von Laue’s text, Die Relativitätstheorie, ﬁrst published in 1911. He devoted a whole section to “a complete clariﬁcation of the notion of simultaneity”1 and its derivation from the synchronization of clocks. This synchronization, however , was obtained assuming that the one-way velocity of the propagation of light is a universal constant c. Nowhere did he mention that the thus deﬁned simultaneity is ultimately based on the convention of the isotropy of the velocity of light. The ﬁrst author of a text on relativity to emphasize the conventionality in the deﬁnition of distant simultaneity was the Cambridge astronomer Arthur Stanley Eddington, who led the Principle Island expedition that conC H A P T E R N I N E The Conventionality Thesis 1 “Machen wir uns den Begriff der Gleichzeitigkeit ganz klar.” M. von Laue, Die Relativitätstheorie (Braunschweig: Vieweg, 1911, 1952), p. 30. 172 Concepts of Simultaneity ﬁrmed the gravitational deﬂection of light in 1919, and who introduced general relativity to the English-speaking world. Whereas in his popular book Space, Time and Gravitation, published in 1920, he only denied the existence of an absolute simultaneity in nature,2 in his more technical treatise The Mathematical Theory of Relativity3 he stressed the conventionality in the deﬁnition of simultaneity. In the section entitled “Simultaneity at different places,” Eddington declared that two possibilities of establishing distant simultaneity exist: Einstein ’s light-signal method and the method of transporting clocks with “in- ﬁnitesimal velocity.” In either case, he claimed: a convention is introduced as to the reckoning of the time differences at different places; this convention takes in the two methods the alternative forms: (1) A clock moved with inﬁnitesimal velocity from one place to another continues to read the correct time at its new station, or (2) the forward velocity of light along any line is equal to the backward velocity. Neither statement is by itself a statement of observable fact, nor does it refer to any intrinsic property of clocks or of light; it is simply an announcement of the rule by which we propose to extend ﬁctitious time-partitions through the world. But the mutual agreement of the two statements is a fact which could be tested by observation, though owing to the obvious practical difﬁculties it has not been possible to verify it directly.4 Eddington’s characterization of the time partitions, into which we divide the space–time extension of the world, as “ﬁctitious” refers to his preceding comments in which he explained that the demand for a worldwide partition or instants arose as the result of a mistake. This mistake dates back to the times before Römer’s discovery of the ﬁnite velocity of light when it was taken for granted that external events, and not only their sense impressions, take place in the time succession of our consciousness. “Physics borrowed the idea of world-wide instants from the rejected theory, and constructed mathematical continuations of the instants in the consciousness of the observer, making in this way time-partitions throughout the four-dimensional world.”5 2 A. S. Eddington, Space, Time and Gravitation (Cambridge: Cambridge University Press, 1920), p. 12. 3 A. S. Eddington, The Mathematical Theory of Relativity (Cambridge: Cambridge University Press, 1923, 1952), p. 29. 4 Ibid., p. 29. 5 Ibid., p. 24. In his Gifford Lectures in 1927, Eddington reiterated that the special theory of relativity does not admit the notion of an absolute simultaneity or of an absolute “Now.” After describing the partition of Minkowski space–time into Here–Now, the absolute future and past, and the wedge-shaped neutral zone between the two light cones, Eddington illustrated the nonexistence of an absolute simultaneity or an absolute “Now” by the following example. Suppose that you are in love with a lady on Neptune and that she returns the sentiment . It will be some consolation for the melancholy separation if you can say to yourself at some—possible prearranged—moment, “she is thinking of me now.” Unfortunately a difﬁculty has arisen because we have had to abolish Now. There is no absolute Now, but only the various relative Nows differing according to the...

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