Reducing Spacetime to Binary Information

TL;DR

This paper introduces a binary encoding framework for discrete 1+1 dimensional space-time, enabling classical and quantum analysis of gravitational fluctuations through a lattice gas model.

Contribution

It presents a novel binary encoding of space-time that respects general relativity invariances and allows classical and quantum simulations of quantum gravity.

Findings

Able to compute Ricci curvature tensor and Einstein equations

Constructed a path integral for discrete gravity

Proposed a quantum simulation approach for fluctuating space-time

Abstract

We present a new description of discrete space-time in 1+1 dimensions in terms of a set of elementary geometrical units that represent its independent classical degrees of freedom. This is achieved by means of a binary encoding that is ergodic in the class of space-time manifolds respecting coordinate invariance of general relativity. Space-time fluctuations can be represented in a classical lattice gas model whose Boltzmann weights are constructed with the discretized form of the Einstein-Hilbert action. Within this framework, it is possible to compute basic quantities such as the Ricci curvature tensor and the Einstein equations, and to evaluate the path integral of discrete gravity. The description as a lattice gas model also provides a novel way of quantization and, at the same time, to quantum simulation of fluctuating space-time.