Conference

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.

The covariant dynamics of Loop Quantum Gravity answers the question of what we can in principle predict and observe in quantum gravity. It features a characteristic discrete quantum evolution, as proposed in a seminal paper by Smolin and Markoupoulou in 1997. Spinfoam transition amplitudes are local exactly thanks to this form of discreteness. Another property of the amplitudes is to be exactly finite when their formulation includes a cosmological constant: this adds further to the fundamental discreteness of spacetime quanta, and again it is a feature rooted in Lee’s Smolin seminal works.

I will examine a foundational assumption in quantum probability assignments, that experimental data arise from an identically and independently distributed (i.i.d.) ensemble. However, this assumption becomes problematic in the regime of quantum gravity. I will outline a proposal to resolve this issue by leveraging the tool of quantum reference frames in the measurement context.

In a series of papers [Phys. Rev. D 102, 124027 (2020)], [Phys. Rev. D 102, 124028 (2020)] I had the pleasure to explore with Cortês, Elitzur and Smolin realist formulations of quantum theory which obey either retrocausality or disordered causality. After briefly presenting these works, I will attempt to extend them by addressing time as a quantum observable using the Page-Wootters formalism. Within this framework, the clock is treated as a quantum subsystem, endowing the remainder of the system with a notion of time through entanglement. I will show the fruitfulness of this approach by deriving new time-energy uncertainty relations [Quantum 6, 683 (2022)] and by elucidating aspects of dynamical nonlocality [Phys. Rev. A 105, 042207 (2022)]. Furthermore, I will demonstrate that in the post-Newtonian regime, perspective-dependent non-unitarity and a distinct form of time–asymmetry naturally emerge when the clocks experience acceleration or gravitational effects [Commun. Phys. 5, 298 (2022)]. Finally, I will discuss the more recent works viewing all the above as spatiotemporal quantum reference frames [Phys. Rev. A 109, 032205 (2024)], [arXiv:2503.20090].

Lee’s most philosophical work is a probing challenge to the "timeless" view prevailing in much of physics. I’’ll say why I think he is right that the idea of the universe as a fixed totality of events is a mirage, and one that arises– as he argued – from extending techniques appropriate for open subsystems to the universe as a whole. Time (for any system in the universe) is irresolubly open-ended, ongoing, and incomplete.