Extrinsic Temporal Metrics

Abstract

When distinguishing absolute, true, and mathematical time from relative, apparent, and common time, Newton wrote: “absolute, true, and mathematical time, in and of itself and of its own nature, without reference to anything external, flows uniformly” [Newton 2004b: 64]. Newton thought that the temporal metric is intrinsic. Many philosophers have argued—for empiricist reasons or otherwise—that Newton was wrong about the nature of time. They think that the flow of time does involve “reference to something external.” They think that the temporal metric is extrinsic. Among others, Mach, Poincaré, and Grünbaum seem to accept this view.1 And these are not the only two views available. Perhaps both Newton and his opponents are wrong and there is no temporal metric at all. Who is right? On the standard ways of understanding general relativity, quantum mechanics, special relativity, and Newtonian mechanics, these theories all postulate an intrinsic temporal (or spatiotemporal) metric. So, although we cannot know what future theories will look like, the evidence favors an intrinsic temporal metric. There are dissenters, though; Julian Barbour does not think there is an intrinsic temporal metric, and has developed alternative physical theories that do without one.2