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I present a cosmological toy model of the resolution of the problem of time based on the Page-Wootters formalism but written in terms of evolving constants of motion. The use of these quantities resolves the issues, e.g., the incorrect propagators, etc., of the Page-Wootters formalism, and points to some interesting preliminary results.

If you can control a wormhole, you can time-travel. The issue is whether they can exist at all. Wormhole solutions in general relativity have spectacular local and global features. Invariantly, a wormhole throat is an outer marginally trapped surface satisfying additional constraints. Some of its properties — like violation of the energy conditions — it shares with black holes that are required to trap light in finite time for a distant observer. This condition may be contentious for black and white holes, but it is the essential part of what “traversable” means. Standard traversable wormholes, such as those described by the Ellis-Morris-Thorne or Simpson-Visser metrics, are static and spherically symmetric. We show that no dynamical solution of the semiclassical Einstein equations can asymptote to these geometries. Conversely, dynamical solutions that do exist either fail to yield a traversable static limit, or breach quantum energy inequalities that bound violations of the null energy condition, or lead to divergent tidal forces. These conclusions hold independently of the choice of quantum fields. Such symmetric wormholes, therefore, are ruled out in semiclassical gravity — making time travel a costlier proposition.

Lee Smolin is fully aware that quantum physics has deep philosophical implications (about the nature of reality, time and space, observation, etc.). However, when philosophers engage in quantum theories, they often succumb to idealist temptations (consciousness creates reality, etc.). My aim as a philosopher is to bring out and clarify these implications which often appear inconsistent

I will present three results: 1. Violation of positivity of energy in the extension of classical General Relativity provided by Ashtekar's polynomial formulation by virtue of its admittance of initial data with degenerate (densitized) triads. 2. Consistency of Propagation in the sense articulated by Lee with the apparent ``ultralocal'' action of the Hamiltonian constraint in LQG. 3. An explicit demonstration of the consistency of area discreteness with Lorentz Invariance for an LQG type quantization of free scalar field theory on 1+1 flat spacetime formulated in a diffeomorphism invariant disguise. The first two results were obtained as answers to direct questions from Lee, the third is a new result and all three are motivated by issues connected with Dynamics, and hence, Time in LQG.