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

Abstract

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.

Scale-invariant gravity: geometrodynamics

“…We hope to use a 'top-down' approach: to start from firm classical theory and deduce features of the quantum universe. However, we start from space rather than spacetime for relational reasons [13,47,11,9] and to illustrate the potential naivety of presupposing and extending spacetime structure. The great problems of quantizing gravity are hopelessly interrelated, so that adding to a partial resolution to tackle further problems can spoil that partial resolution [48].…”

Symplectic Reduction and the Problem of Time in Nonrelativistic Mechanics

“…That the Hamiltonian constraint in reparameterization invariant theories should be thought of as generating genuine change is a position that has been notably defended by Kuchař [1991] and Barbour [1994]; more recently it has been outlined explicitly in Barbour and Foster [2009]. We shall call it the Kuchař-Barbour-Foster position with regard to change.…”

“…In particular, Kuchař ([1992]) and Barbour ([1994]) have argued that there are characteristics peculiar to the Hamiltonian constraint which mean we should not follow the standard procedure and treat it as gauge generating. On a similar note, Pons and Salisbury ([2005]) argue that Dirac's analysis is incomplete (Pons [2005]) since gauge symmetry groups should be more properly thought of as acting on the space of entire solutions rather than, as Dirac assumes, at a given time.…”

Open Questions Regarding the Arrow of Time

“…Julian Barbour has called states that contain consistent documents (regardless of their causal origin) "time capsules". 7 Since conventional concepts of physical entropy are local (based on an entropy density), they cannot distinguish between consistent and inconsistent documents. An evolved ("historical") state has much lower statistical probability than indicated by its physical entropy, and this fact may rule out Boltzmann brains for being "statistically unreasonable" (see Sect.…”