Reichenbach’s ε-Definition of Simultaneity in Historical and Philosophical Pespective

§ 1. It is well-known that in the special theory of relativity the simultaneity of distant events is frame-relative: two events simultaneous according to the standard Einstein criterion as applied in one inertial frame are not simultaneous according to the same criterion applied in a relatively moving inertial frame. Not so well known is whether, given a fixed inertial frame, there is a fact of the matter whether a pair of distant events are really simultaneous relative to that frame. Einstein thought not. Reichenbach, at least according to the lore philosophers of science are taught, thought not. And up until roughly a quarter century ago, the thesis that frame-relative simultaneity is a matter of convention was the prevailing view. Not any more. There is now a widely espoused anti-conventionalist view inspired by a result published by David Malament in 1977: the standard Einstein criterion is the only candidate for a frame-relative simultaneity criterion definable from the causal structure of Minkowski space-time. Hence, according to the neo-anti-conventionalist, if frame-relative simultaneity is conventional, then it is conventional only in some minimal and not very exciting or robust sense. However, claims as to what is exiting or robust, if they are to be meaningful, must be claims about comparisons. I want to take this opportunity to compare and contrast two possible conventionalist positions on frame-relative simultaneity, one of them decidedly more robust than the other. The more robust of these is implicitly suggested by Einstein’s 1905 paper. The other, I shall suggest, is the most plausible reading of Reichenbach’s conventionalism in connection with his celebrated “ε-definition” of distant simultaneity. This will give me the chance not only to engage in a bit of Reichenbach scholarship, but also to impress upon the neo-anti-conventionalist camp that there is more than a minimal conventionality thesis to take into account.