Causal set approach to discrete quantum gravity

TL;DR

This paper develops a quantum sequential growth model of causal sets to explore discrete quantum gravity, deriving a discrete Einstein equation, defining geodesics, and analyzing a complex percolation process that respects causality and covariance.

Contribution

It introduces a quantum dynamics framework for causal sets, including a quantum sequential growth process and a complex percolation model, advancing discrete quantum gravity research.

Findings

Derived a discrete Einstein field equation.

Proposed a definition for discrete geodesics.

Analyzed a complex percolation process consistent with causality.

Abstract

We begin by describing a sequential growth model in which the universe grows one element at a time in discrete time steps. At each step, the process has the form of a causal set and the "completed" universe is given by a path consisting of a discretely growing chain of causal sets. We then introduce a quantum dynamics to obtain a quantum sequential growth process (QSGP) which may lead to a viable model for discrete quantum gravity. A discrete version of Einstein's field equation is derived and a definition for discrete geodesics is proposed. A type of QSGP called an amplitude process is introduced. An example of an amplitude process called a complex percolation process is studied. This process conforms with general principles of causality and covariance. We end with some detailed quantum measure calculations for a specific percolation constant.