Simultaneity by Slow Clock Transport in the Special Theory of Relativity

Abstract

P. W. Bridgman’s recent (1962) method of synchronism by infinitely slow clock transport as an alternative to Einstein’s light signal method is examined in its bearing on the philosophical status of simultaneity in the Special Theory of Relativity (STR). Critical attention is focused on the claim, made in a 1967 paper by B. Ellis and P. Bowman (E & B), that Bridgman’s alternative to Einstein’s clock synchronization rule refutes the philosophical conception of simultaneity which Hans Reichenbach attributed to Einstein. It is contended that in the STR. synchronism by slow clock transport neither refutes nor trivializes the ingredience of a convention in that theory’s distant simultaneity.To provide a basis for this defense of the Einstein-Reichenbach conception of simultaneity, attention is first given to the bearing of clock transport and of causal chains generally, including gravitational influences, on simultaneity in Newton’s world. It is pointed out how these Newtonian physical agencies make for simultaneity relations which are both intersystemically invariant and non-conventional. Thus, the absolute simultaneity relations in Newton’s world are shown to hold as a matter of fact, although the particular identity of the time coordinate assigned alike to all members of a simultaneity class is trivially conventional. Here it is also noted why there is no incompatibility in Newton’s world between the simultaneity of two events and their being the termini of gravitational influence chains, whereas all causally connectible events arc non-simultaneous in the universe of the STR (barring tachyons).Next, the status of simultaneity in a so-called ‘quasi-Newtonian’ world is assessed. The latter world differs from Newton’s as follows: both light rays and gravitational influences have the same finite round-trip velocity in any one inertial system, while also being the fastest causal chains capable of connecting any two space points. This world resembles the Newtonian one in that transported clocks can be said to furnish consistent and even invariant simultaneity relations. But, in opposition to E & B, it is argued that in the quasi-Newtonian world, simultaneity relations involve a non-trivial conventional ingredient, in contrast to those of Newton’s world, which hold as a matter of temporal physical fact.Finally, it is indeed agreed that the slowly transported clock presents us with a unique time coordinate for any particular event, while the light ray of signal synchrony delivers no such time coordinate except by our stipulation. But it is held that this physical fact does not sustain E & B’s philosophical thesis. Comparison of simultaneity by slow clock transport synchrony in the universe of the STR with simultaneity in the quasi-Newtonian world refutes the philosophical thesis which E & B have based on the facts of slow clock transport. For this comparison shows that in the STR, slow clock transport cannot confer factual physical truth on the particular simultaneity relations asserted by the Lorentz transformations, any more than an exchange of light signals can do so. The Einstein-Reichenbach conception of simultaneity is thus vindicated in the face of the facts of slow clock transport.This conclusion is reinforced by the results from the General Theory of Relativity (GTR) in Allen Janis’s paper (Philososphy of Science 36 (1969) 74–81). Janis shows that there is a large class of non-inertial frames, which includes the rotating disk in flat space- time, in which slow transport synchrony fails. Hence there would be scope for conventional choices of simultaneity in all of these cases, even if E & B had given a correct philosophical characterization of simultaneity by slow transport synchrony.KeywordsInertial FrameLorentz TransformationSpecial TheoryInertial SystemSlow TransportThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.