K. Thébault- 'On the emergence of temporal structure in Wheeler-DeWitt Cosmology' (BS AS, Feb. 2023)

"Workshop on The Arrow of Time: From Local Systems to the Whole Universe" held in Buenos Aires (Argentina), February 20-23, 2023.

Nick Huggett and Karim Thébault (University of Illinois Chicago/University of Bristol)
- "On the emergence of temporal structure in Wheeler-DeWitt Cosmology"

Abstract: Wheerler-DeWitt cosmologies are quantum models of the universe in which the wavefunction obeys a time independent equation. The standard approach to the recovery of a minimal notion of temporal structure from such an equation is through appeal to a relational concept of evolution that can be formally implemented via the process of de-parametrization. In de-parametrization, a sub-set of the physical degrees of freedom of the model play the role of `clocks' that parametrize the evolution of other degrees of freedom.
A specific approach to the recovery of temporal structure in Wheeler-DeWitt cosmology is due to Kiefer and Zeh. This approach implements a de-parametrization scheme whereby the gravitational degrees of freedom are used as a clock for the matter degrees of freedom. Remarkably, under this de-parametrization scheme and a particular choice of boundary conditions, the gravitational degrees of freedom can be argued to play the role not only of a time parameter, but also of a directed temporal structure.
Time and its arrow can thus be understood to emerge from a quantum dynamics without any extrinsic temporal structure.
The success of the Kiefer and Zeh approach depends upon two crucial assumptions. First, in order for the gravitational degrees of freedom to play the role of internal clocks their coupling to the matter degrees of freedom must be neglected to first order under a Born-Oppenheimer type approximation. Second, the boundary condition applied must be isolated as an “initial”' condition. In this paper we will evaluate to cogency of each of these assumptions in the context of critical arguments relating to ``temporal double standards" due to Price (1997) and Chua and Callender (2021).