Conference

Ordered structures that tile the plane in an aperiodic fashion - thus lacking translational symmetry - have long been considered in the mathematical literature. A general method for the construction of quasicrystals is known as *cut-and-project* ($\mathsf{CNP}$ for short), where an irrational slice "cuts" a higher-dimensional space endowed with a lattice and suitably chosen lattice points are further "projected down" onto the subspace to form the vertices of the quasicrystal. However, most of the known examples of $\mathsf{CNP}$ quasi-tilings are Euclidean. In this talk, after presenting the main ingredients of the Euclidean prescription, we will extend it to Lorentzian spacetimes and develop Lorentzian $\mathsf{CNP}$. This will allow us to discuss the first ever examples of Lorentzian quasicrystals, one in $(1+1)$- and another in $(1+3)$-dimensional spacetime. Finally, we will argue why the latter construction might be relevant for *our Lorentzian spacetime*. In particular, we shall appreciate how the picture of a quasi-crystalline spacetime could provide a potentially new string-compactification scheme that can naturally accommodate for the hierarchy problem and the smallness of our cosmological constant. Lastly, we will comment on its relevance to quantum geometry and quantum gravity; first, as a conformal Lorentzian structure of no intrinsic scale, and second through the connection of quasicrystals to quantum error-correcting codes.

Modern quantum simulations methods often use a fictitious imaginary time introduced by Feynman to exactly transform static quantum problems to dynamic imaginary time classical ones [1]. In addition to imaginary time simulation methods such as centroid molecular dynamics and path integral Monte Carlo, one can apply this quantum-classical isomorphism to self-consistent field theory (SCFT). An advantage of the field-theoretic perspective is that it can be exactly transformed into quantum density functional theory (DFT), meaning that the theorems of DFT (Hohenberg-Kohn and Mermin theorems) prove an equivalence between classical imaginary time SCFT dynamics and static quantum results [2]. Since imaginary time is assigned the same properties as regular time, one can replace the imaginary time in the SCFT equations with real time (a Wick rotation), which gives the equations of time-dependent DFT. The time-dependent DFT theorem (Runge-Gross theorem) then proves that one obtains all results of standard quantum mechanics from this imaginary time classical starting point. These results make it very tempting to consider treating imaginary time as an element of reality. This quantum reconstruction from imaginary time will be discussed, including a speculative look at treating imaginary time in the context of special relativity, with a preliminary comparison to the deformed special relativity of Magueijo and Smolin. [1] D. M. Ceperely, Reviews of Modern Physics 67, 279 (1995) [2] R. B. Thompson, Journal of Chemical Physics 150, 204109 (2019) [3] J. Magueijo and L. Smolin, Physical Review D 67, 044017 (2003)

Based on a previously published model of a quantum gravity path integral, expressed in spectral-geometric variables (Phys. Rev. Lett. 131, 211501), co-authored with M. Reitz and A. Kempf, I study the emergence of Lorentzian signature and time dimension from quantum fluctuations, and argue the physical intuition behind it via a known condensed matter phenomenon.

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