The Conventionality of Slow-Transport Synchrony

Abstract

The conventionality of distant simultaneity, as maintained by Hans Reichenbach and Adolf Grünbaum, is by now so widely known that it can be stated very briefly. Let us consider two points A and B which are separated from one another in an inertial frame K. For a light signal emitted from A and reflected at B back to A, we compare the time interval for the out-going trip to that for the round trip. This ratio is called ‘epsilon’ (≤). In formulating the special theory of relativity, Einstein effectively took ≤ to be ½ thus, we may use ≤=½ in defining what is now called ‘standard signal synchrony’. Reichenbach views ⊀ as being restricted only by the causal relations involved in the signaling process. That is, the reflection of the light ray at B must take place after the ray’s emission at A but before its return to A. These considerations require us to restrict ∈ between zero and one, but Reichenbach (1958, p. 127) insists that within these limits values of ∈≠ ½ “could not be called false”. He claims that there are no facts which would mediate against using these values in definitions which are now called ‘nonstandard signal synchrony’. This allegedly physical possibility of choosing ∈ between zero and one is the conventionality of distant simultaneity as determined by signals. Grünbaum (1973, p. 353) also argues for this thesis, making clear that it obtains within a single inertial frame.¹ In this paper I will not be concerned with the situation in more than one inertial frame.² Rather, I will consider a nonsignaling definition of synchrony and ask what sort of conventionality it manifests in a single inertial frame.

This paper derives from section F of Bowman (1972): it summarizes subsection 2 and follows subsection 5 with only minor changes ut the exposition.