The Theory of Duration and Clocks

In 1898, Poincaré identified two fundamental issues in the theory of time: 1)What is the basis for saying that a second today is the same as a second tomorrow? 2) How can one define simultaneity at spatially separated points? Poincaré outlined the solution to the first problem { which amounts to a theory of duration { in his 1898 paper, and in 1905 he and Einstein simultaneously solved the second problem. Einstein\'s daring and elegant approach so gripped the imagination of theoreticians, especially after Minkowski\'s introduction of spacetime,that the definition of duration, and with it the theory of clocks, has received virtually no attention for over a century. This is a remarkable state of affairs and is a major cause of the conceptual confusion surrounding the problem of time in the canonical approach to the creation of a quantum theory of gravity. In my talk I shall develop Poincaré\'s outline into a potentially definitive theory of duration and clocks.