Discreteness of time in the evolution of the universe

TL;DR

This paper explores how the extended structure of M2-branes limits the resolution of generalized geometries in M-theory, deforming the Wheeler-DeWitt equation and potentially solving the problem of time through spontaneous time re-parametrization breaking.

Contribution

It introduces a deformation of the Wheeler-DeWitt equation caused by M2-branes, linking extended structures to the emergence of time crystals and addressing the problem of time in quantum gravity.

Findings

Deformation of Wheeler-DeWitt equation due to M2-branes

Emergence of time crystals from spontaneous symmetry breaking

Potential resolution of the problem of time in quantum cosmology

Abstract

In this paper, we will first derive the Wheeler-DeWitt equation for the generalized geometry which occurs in M-theory. Then we will observe that M2-branes act as probes for this generalized geometry, and as M2-branes have an extended structure, their extended structure will limits the resolution to which this generalized geometry can be defined. We will demonstrate that this will deform the Wheeler-DeWitt equation for the generalized geometry. We analyze such a deformed Wheeler-DeWitt equation in the minisuperspace approximation and observe that this deformation can be used as a solution to the problem of time. This is because this deformation gives rise to time crystals in our universe due to the spontaneous breaking of time re-parametrization invariance.