Posted by: Xhyra Graf | 15 February 2007


Convention[ality] Theory & Simultaneity

In his first paper on the special theory of relativity, Einstein indicated that the question of whether or not two spatially separated events were simultaneous did not necessarily have a definite answer, but instead depended on the adoption of a convention for its resolution. Some later writers have argued that Einstein’s choice of a convention is, in fact, the only possible choice within the framework of special relativistic physics, while others have maintained that alternative choices, although perhaps less convenient, are indeed possible.

The Conventionality Thesis

The debate about the conventionality of simultaneity is usually carried on within the framework of the special theory of relativity. Even prior to the advent of that theory, however, questions had been raised (see, e.g., Poincaré, 1898) as to whether simultaneity was absolute; i.e., whether there was a unique event at location A that was simultaneous with a given event at location B. In his first paper on relativity, Einstein (1905) asserted that it was necessary to make an assumption in order to be able to compare the times of occurrence of events at spatially separated locations (Einstein, 1905, pp. 38-40 of the Dover translation or pp. 125-127 of the Princeton translation; but note Scribner, 1963, for correction of an error in the Dover translation). His assumption, which defined what is usually called standard synchrony, can be described in terms of the following idealized thought experiment, where the spatial locations A and B are fixed locations in some particular, but arbitrary, inertial (i.e., unaccelerated) frame of reference: Let a light ray, traveling in vacuum, leave A at time t1 (as measured by a clock at rest there), and arrive at B coincident with the event E at B. Let the ray be instantaneously reflected back to A, arriving at time t2. Then standard synchrony is defined by saying that E is simultaneous with the event at A that occurred at time (t1+ t2)/2. This definition is equivalent to the requirement that the one-way speeds of the ray be the same on the two segments of its round-trip journey between A and B.

The thesis that the choice of standard synchrony is a convention, rather than one necessitated by facts about the physical universe (within the framework of the special theory of relativity), has been argued particularly by Reichenbach (see, for example, Reichenbach, 1958, pp. 123-135) and Grünbaum (see, for example, Grünbaum, 1973, pp. 342-368). They argue that the only nonconventional basis for claiming that two distinct events are not simultaneous would be the possibility of a causal influence connecting the events. In the pre-Einsteinian view of the universe, there was no reason to rule out the possibility of arbitrarily fast causal influences, which would then be able to single out a unique event at A that would be simultaneous with E. In an Einsteinian universe, however, no causal influence can travel faster than the speed of light in vacuum, so from the point of view of Reichenbach and Grünbaum, any event at A whose time of occurrence is in the open interval between t1 and t2 could be defined to be simultaneous with E.



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