Discrete quantum gravity in the framework of Regge calculus formalism

TL;DR

This paper discusses a discrete quantum gravity approach using Regge calculus, where spacetime is modeled as a piecewise flat manifold with quantum length expectations at the Planck scale, bridging discrete and continuous general relativity.

Contribution

It introduces a quantum gravity framework based on Regge calculus with nonzero quantum length expectations at the Planck scale, connecting discrete and classical gravity.

Findings

Quantum length expectations are nonzero at Planck scale.

Discrete spacetime structure emerges at very small scales.

Regge calculus provides a viable formalism for quantum gravity.

Abstract

An approach to the discrete quantum gravity based on the Regge calculus is discussed which was developed in a number of our papers. Regge calculus is general relativity for the subclass of general Riemannian manifolds called piecewise flat ones. Regge calculus deals with the discrete set of variables, triangulation lengths, and contains continuous general relativity as a particular limiting case when the lengths tend to zero. In our approach the quantum length expectations are nonzero and of the order of Plank scale $10^{-33}cm$. This means the discrete spacetime structure on these scales.