The timelessness of quantum gravity: I. The evidence from the classical theory

The issue of time is addressed. It is argued that time as such does not exist but that instants, defined as complete relative configurations of the universe, do. It is shown how the classical mechanics (both non-relativistic and generally relativistic) of a complete universe can be expressed solely in terms of such relative configurations. Time is therefore a redundant concept, as are external inertial frames of reference (so that Machian ideas about the relativity of motion are fully implemented). Although time plays no role in kinematics, it can be recovered as an effective concept associated with any classical history of the universe. In the case of classical mechanics, this operationally defined time is identical to the astronomers' ephemeris time. In the case of general relativity it is shown how local proper time is a kind of local ephemeris time. It is argued that because general relativity is timeless in a deep and precise sense, the standard representation of the theory as a theory of curved spacetime disguises important aspects of its structure and that just these aspects may be the most important for the quantum form of the theory. This issue and the effective recovery of time from a genuinely timeless quantum theory are addressed in a following companion paper.