Concepts of Simultaneity: From Antiquity to Einstein and Beyond

10 The Promulgation of the Conventionality Thesis

It was only in the late 1950s that Reichenbach’s philosophy of space and time, and his thesis of the conventionality of simultaneity, found the attention they deserve. An important factor in this development was the publication of his Philosophie der Raum-Zeit-Lehre in an English translation by his wife Maria Reichenbach and John Freund. In his introduction to the English edition Rudolf Carnap declared: “The constant careful attention to scientifically established facts and to the content of the scientific hypotheses to be analyzed and logically reconstructed, the exact formulation of the philosophical results, and the clear and cogent presentation of the arguments supporting them, make this work a model of scientific thinking in philosophy.”1 The stimulus to this translation was given in 1955 when Adolf Grünbaum published an important essay in the widely read American Journal of Physics in which he stated that “my treatment of several of the issues is greatly indebted to two outstanding works on the philosophy of relativity by Hans Reichenbach, C H A P T E R T E N The Promulgation of the Conventionality Thesis 1 Chapter 9, note 14, p. VII. which are not available in English.”2 It was actually a pure accident that Grünbaum became acquainted with Reichenbach’s philosophy while still a Ph.D. student at Yale. Whenever they were in New York, he and his colleague and friend Robert S. Cohen would visit book stores in search of rare or out-of-print books on the philosophy of science. On one of these occasions Bob Cohen purchased a copy of Reichenbach’s Philosophie der Raum-Zeit-Lehre and gave it to Grünbaum , who, born and educated in Cologne, had no difficulty in reading the German text. How deeply Grünbaum was influenced by this book is described in his essay entitled “Hans Reichenbach’s Definitive Influence on me.”3 In his influential 1955 paper Grünbaum argued that for a correct understanding of the special theory of relativity it is essential to note, first of all, that “the relativity of simultaneity . . . arises, in the first instance, within a single Galilean [inertial] frame” (called intrasystemic simultaneity in contrast to intersystemic simultaneity, which latter refers to different inertial systems as has been dealt with by Einstein in his 1905 paper). Grünbaum therefore devotes the second chapter on his paper, entitled “the relativity of simultaneity ,” to this subject. He began his exposition by pointing out that in a world of arbitrarily fast causal chains the concept of absolute simultaneity would have a perfectly physical meaning even in a temporal description of nature given by a relational theory of time. However, a theory, like the special theory of relativity, that denies the existence of an infinitely fast causal chain, deprives the concept of absolute simultaneity of its physical meaning even within a single inertial system. . . . But since the metrical concept of velocity presupposes that we know the meaning of a transit time and since such a time, in turn, depends on a prior criterion of clock synchronization or simultaneity, we must first formulate the limiting property of electromagnetic chains [the fastest causal chain] without using the concept of simultaneity of noncoincident events.4 To define intrasystemic simultaneity Grünbaum offered the following nonmetrical formulation of Einstein’s limiting postulate: “No kind of causal chain (moving particles, radiation), emitted at a given point P1 together with a light The Promulgation of the Conventionality Thesis 193 2 A. Grünbaum, “Logical and philosophical foundations of the special theory of relativity,” American Journal of Physics 23, 450–464 (1955); reprinted in A. Danto and S. Morgenbesser (eds.), Philosophy of Science (Cleveland, Ohio: The World Publishing Company, 1960), pp. 399–434. 3 In H. Reichenbach, Selected Writings, 1909–1953 (Dordrecht: Reidel, 1978), vol. 1. 4 Note 2, p. 453. 194 Concepts of Simultaneity pulse can reach any other point P2 earlier—as judged by a local clock at P2 which merely orders events there in a metrically arbitrary fashion—than this light pulse.”5 Applying this postulate to the case of two points, P1 and P2, fixed in a reference frame S and connected by light signals as shown in figure 10.1, we see that: Instead of E being the only event at P1 which is neither earlier nor later than E2 at P2, as in the...