Conference

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.

In this talk, I will investigate the possibility of time being a fundamental physical entity in quantum gravity. I will briefly review the different notions of time in classical and quantum mechanics and then focus on explaining the fundamental clash that exists between the notions of time in Quantum Field theory and general relativity. This clash, related to the so-called problem of time, is at the core of the fundamental difficulty of quantizing gravity. I will review how recent results in Quantum gravity allow a surprising resolution of this fundamental puzzle through the presence of a quantum anomaly, which promotes time to a fundamental quantum observable in quantum gravity.

Spinfoams define a path integral for quantum gravity based on topological quantum field theory (TQFT). Following Lee’s early intuitions about the implementation of the holographic principle in the formalism, I will explain how the bulk dynamics arises as a network of boundary theories and draw lessons about the bulk-boundary relations. Diving into the example of 3d quantum gravity, this is illustrated by a beautiful holographic-like duality with the 2d inhomogeneous Ising model, with an underlying emergent supersymmetry, opening an intriguing interplay with the world of statistical physics with an elegant geometric formula for the zeroes of the Ising partition function.

I will briefly review an idea spurring from Lee, Stephon and Joao for an action with a varying cosmological constant and at most only three new free parameters, based on a `quasi-topological principle', and show how one can determine its number of degrees of freedom at the non-perturbative level, and some of the interesting features that arise in the analysis.