The timelessness of quantum gravity: II. The appearance of dynamics in static configurations

Abstract

A strategy for quantization of general relativity is considered in the context of the `timelessness' of classical general relativity discussed in the preceding companion paper. The Wheeler--DeWitt equation (WDE) of canonical quantum gravity is interpreted as being like a time-independent Schrödinger equation for one fixed energy, the solution of which simply gives, once and for all, relative probabilities for each possible static relative configuration of the complete universe. Each such configuration is identified with a possible instant of experienced time. These instants are not embedded in any kind of external or internal time and, if experienced, exist in their own right. The central question is then: Whence comes the appearance of the passage of time, dynamics, and history? The answer proposed here is that these must all be `coded', in the form of what appear to be mutually consistent `records', in the individual static configurations of the universe that are actually experienced. Such configurations are called time capsules and suggest a new, many-instants, interpretation of quantum mechanics. Mott's explanation of why -particles make straight tracks in Wilson cloud chambers shows that the time-independent Schrödinger equation can concentrate its solution on time capsules. This demonstrates how the appearance of dynamics and history can arise in a static situation. If it can be shown that solutions of the Wheeler--DeWitt equation are spontaneously and generically concentrated on time capsules, this opens up the possibility of an explanation of time at a very deep level: the timeless wavefunction of the universe concentrates the quantum mechanical probability on static configurations that are time capsules, so that the situations which have the highest probability of being experienced carry within them the appearance of time and history. It is suggested that the inescapable asymmetry of the configuration space of the universe could play an important role in bringing about such concentration on time capsules and be the ultimate origin of the arrow of time.

Triangleland: II. Quantum mechanics of pure shape

“…3) There are also timeless records strategies [21,38,2,24,3,39,40]. Here, the primary objects are records -informationcontaining subconfigurations of a single instant that are localized in both space and configuration space.…”

Trajectories for the wave function of the universe from a simple detector model

“…Most importantly, Kiefer and Zeh [20] and Barbour [21,22,4] have devoted much effort to elucidating the emergence of trajectories and of time from the timeless Wheeler-DeWitt equation.…”

“…The approach we adopt here stems from Barbour's observation [22] that a substantial insight into the Wheeler-DeWitt equation may be found in Mott's 1929 analysis of alphaparticle tracks in a Wilson cloud chamber [23]. Mott's paper concerned the question of how the alpha-particle's outgoing spherical wave state, e ikR /R, could lead to straight line tracks in a cloud chamber.…”

Machian classical and semiclassical emergent time

“…Nor does Quantum Cosmology possess "pure incoming wave laboratory set-up". Moreover, not being able to justify the WKB ansatz in the Semiclassical Approach to the Problem of Time is a particular problem [74,44,45,18,46,19,75,7]. This is since its its trick by which the chroniferous cross-term becomes the time-derivative part of a TDSE is exclusive to WKB ansatz wavefunctions.…”