I've been thinking about Einstein's nice argument for the relativity of simultaneity in his popular book. The argument starts with the assumption that the speed of light is the same in every inertial reference frame, and uses this to construct a method for determining whether two events are simultaneous. Basically, this method involves having an inertial observer spatially equidistant between the two events checking whether light reaches her simultaneously from the two events. Given the constancy of the speed of light and the equidistance assumption, it seems to follow that the two events are simultaneous if and only if light reaches the observer simultaneously from the two events. And then Einstein gives a very nice argument that applying this method gives different answers depending on the osberve, and concludes that simultaneity is relative to the reference frame.
But there is something that has been worrying me conceptually about Einstein's account of simultaneity. That account takes for granted that we know what it means for the observer to observe two events simultaneously. But isn't the task to define simultaneity?
I guess not. Einstein seems to presupposing that we already have the notion of simultaneity of events at the location of an observer. Moreover, the details of Einstein's argument assume this principle which I think he doesn't discuss:
- Two events befalling the same observer occur simultaneously in the reference frame of the observer if and only if they occur at the same point in spacetime.