Arithmetic Quantum Gravity

Abstract

The arithmetic chaos of classical (super)gravity near a spacelike singularity is elevated to the quantum level via the construction of a cosmological quantum billiard system. Its precise formulation, together with its underlying algebraic structure, allows for a general analysis of the wavefunction of the universe near the singularity. We argue that the extension of these results beyond the billiard approximation may provide a concrete mechanism for emergent space as well as new perspectives on several long-standing issues in canonical quantum gravity. The exponentially growing complexity of the underlying symmetry structure could introduce an element of non-computability that effectively "screens" the cosmological singularity from a complete resolution.

Eisenstein series for infinite-dimensional U-duality groups

“…Finally, we note that automorphic forms for E 10 (Z) and for the Weyl group of E 10 have appeared in different conjectures concerning M-theory [75,76] and quantum gravity [47,48] and we hope that our investigations can prove useful for these ideas. It would also be interesting to see how much can be learned about curvature correction terms with more space-time derivatives, starting from ∂ 6 R 6 where the automorphic function is not expected to be a pure Eisenstein series since the Laplace equation is inhomogeneous [27,28,29].…”

“…We use the incorrect terminology 'plane wave' with an application to quantum gravity in mind, where the Eisenstein series should describe wavefunctions[47,48].…”

This Year's Nobel Prize (2022) in Physics for Entanglement and Quantum Information: the New Revolution in Quantum Mechanics and Science

“…Further, but without being necessary, the same unification can be continued to quantum gravity even in an abstract mathematical sense (e,g. Sorkin, Yazdi 2018;Kleinschmidt, Hermann 2010;Baianu, Brown, Glazebrook 2007;El Naschie 2008;: an approach comparable with that of the present paper. 15 In fact, many papers (e.g.…”