Conference

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.

The original spinfoam model, the Ponzano-Regge spinfoam model of 3D Euclidean gravity with zero cosmological constant, has two properties in seeming contradiction: (1.) Its connection formulation consists in the imposition of exact flatness, and (2.) Its sum-over-spins formulation has, as its leading order large spin asymptotics, Regge calculus, modified to include an additional local discrete orientation variable for each tetrahedron, which, when fixed inhomogeneously, leads to critical point equations for the edge lengths which do not imply flatness, but rather allow spikes. We explore possible resolutions to this paradox which may also have relevance for the semiclassical regime of both Euclidean and Lorentzian 4D spinfoams, with both zero and non-zero cosmological constant, in which a similar sum over local orientations appears.

What if the cosmic clock actually ticks? In this talk, I will explore growing evidence—from the structure of the cosmos to the frontiers of quantum gravity—that time may not be continuous, but fundamentally discrete. By rethinking the flow of time as a sequence of quantized events, we uncover surprising connections that challenge our classical intuitions and open new paths in fundamental physics.

If the Hamiltonian constraint were ever violated (in the early Universe, at high energies, etc), its subsequent restoration could never erase a memory effect of the original violation. Depending on the technicalities of restoration, the memory effect may be as boring as something which mimics standard dark matter, or an anisotropic extension of dark matter... Or, as crazy as something that acts like a dust fluid capable of attracting other matter but being attracted to nothing. Attracting without being attracted: we discuss how it might be possible in a relativistic theory of gravity, its implications to the foundations of physics (specifically Dirac's algebra of constraints underpinning relativistic physics), and what its observational hallmarks might be.

I report on recent progress of investigations of in-vacuo dispersion for GRB neutrinos, also highlighting the connection with a previous study done in collaboration with Lee Smolin investigating in-vacuo dispersion for GRB photons. The present status of IceCube neutrino observations provides preliminary encouragement for a scenario based on in-vacuo dispersion and the KM3-230213A neutrino recently annouced by KM3NeT fits rather naturally within the in-vacuo-dispersion scenario motivated by IceCube data.