ER= EPR and Non-Perturbative Action Integrals for Quantum Gravity

TL;DR

This paper develops a non-perturbative path integral approach to quantum gravity by summing over homotopy classes of paths in a multiply-connected spacetime influenced by ER=EPR conjecture, linking topology and entanglement.

Contribution

It introduces a novel method for constructing non-perturbative quantum gravity path integrals using spacetime topology defined by Einstein-Rosen bridges and quantum entanglement.

Findings

Topologically non-trivial spacetime due to ER bridges.

Path integrals over homotopy classes in multiply-connected spacetime.

Potential for non-perturbative quantum gravity quantization.

Abstract

In this paper, we construct and calculate a non-perturbative path integrals in a multiply-connected space-time. This is done by by summing over homotopy classes of paths. The topology of the space-time is defined by Einstein-Rosen bridges (ERB) forming from the entanglement of quantum foam described by virtual black holes. As these `bubbles' are entangled, they ar econnected by Plankian ERB's because of the $ER=EPR$ conjecture. Hence the space-time will possess a large first Betti number $B1$. For any compact 2-surface in the space-time, the topology (in particular the homotopy) of that surface is not-trivial, due to the large number of Plankian ERB's that define homotopy though this surface. The quantisation of space-time with this topology - along with the proper choice of the 2-surfaces - is conjectured to allow anon-perturbative path integrals of quantum gravity theory over the space-time manifold.