Lorentzian Quasicrystals and the Irrationality of SpacetimeConfirmed

by Sotirios Mygdalas (Perimeter Institute for Theoretical Physics)

Monday May 26, 2025, 2:00 p.m. → 3:00 p.m. America/Toronto

PI/4-400 - Space Room (Perimeter Institute for Theoretical Physics)

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 \textit{cut-and-project} (\textsf{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 \textsf{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 \textsf{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 \textit{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.