“Definability,” “Conventionality,” and Simultaneity in Einstein–Minkowski Space-Time

In this article, I attempt to clarify certain misunderstandings that have contributed to continuing controversy over the status of the concept of relative simultaneity in the special theory of relativity. I also correct a number of technical errors in the literature of the subject, and present several new technical results that may further serve to clarify matters.

Controversy over the status of the concept of relative simultaneity in the special theory of relativity has proved remarkably durable. Very recently (within two days of first writing these words), as a result of ruminations on a recent paper of Adolf Grüunbaum's, I have come to believe that an important contributing factor to the persistence of the dispute is the use of certain key words (or phrases) in quite different senses by some of the disputants. One central aim of this paper, therefore, is to (try to) clarify these misunderstandings, and thereby both to reduce the number of the points of disagreement, and for the remaining points—for one can hardly expect all disagreement to be thus dispelled—at least to help clarify what the disagreements really are. A second aim is to correct some technical errors in the literature of the subject, and to state and prove some new technical results that may help contribute to clarity in the matter.