No-Really. The Problem of Time

Gordon Belot
Department of Philosophy, New York University


The general covariance of general relativity is supposed to lead to a problem of time for classical and quantum theories of gravity. The problem is supposed to be that there is some sort of difficulty in making out the sense in which there is change in generally covariant theories. Many philosophers are skeptical-surely a solution like an FRW solution represents the universe as expanding, and hence as changing? Skeptics have wondered: whether there is a problem of time; whether it is really a problem; what it has to do with general covariance; what it has to do with change. Often all of this is tied up with a feeling that the source of confusion must lie in the 3+1 decompositions of spacetime from which presentations of the problem of time typically depart. I will discuss formulations of general relativity in which no 3+1 decomposition is made-the space of state is a space of solutions, rather than a space of initial data. In such a formulation, it is easy to see what the problem of time is, why it is a problem, what it has to do with change, and what it has to do with general covariance.