Simultaneity, language, and experience

Abstract

As part of his special theory of relativity, Einstein introduced two definitions of the word “simultaneity”—the coordinated-clocks definition in his famous 1905 paper and the mid-point definition in his 1916 book. Einstein never discussed the relation between these two definitions. Neither has anyone else, to my knowledge. I show that these definitions are not equivalent because they have different scopes of applicability, but that they are equivalent wherever both apply. My proof of this partial equivalence is a corollary of my proof that both of Einstein’s definitions clash with the natural ticking of monochromatic light, which I call an electromagnetic wave clock. Einstein disparaged the idea of absolute simultaneity, but the reasons he gave were not good ones. He suggested that the idea originated in a confusion between happening simultaneously and being seen simultaneously. This thesis is dubious. It is also irrelevant, because an idea that originates in a confusion need not be a confused idea. He suggested that there could be no experimental test for absolute simultaneity. I refute this suggestion by describing an experimental test for absolute simultaneity, which I call the melt-mark test. The empirical credentials of Einstein’s definitions are not superior to those of absolute simultaneity. Einstein writes as if he can banish the idea of absolute “simultaneity” by merely giving the word “simultaneity” a new meaning. But many words have multiple meanings; Einstein merely made simultaneity such a word. The meanings of “simultaneity” that there is reason to disparage are Einstein’s definitions, because they clash with the electromagnetic wave clock. None of these points is properly appreciated by today’s physics community, where Einstein’s assertions about simultaneity continue to enjoy broad acclaim. Physical theories that employ the idea of absolute simultaneity are often wrongly rejected because they do.