ER = EPR and non-perturbative action integrals for quantum gravity

Abstract

International audienceIn this paper, we construct and calculate non-perturbative path integrals in a multiply-connected spacetime. This is done by summing over homotopy classes of paths. The topology of the spacetime 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 are connected by Planckian ERBs because of the ER = EPR conjecture. Hence, the spacetime will possess a large first Betti number B1. For any compact 2-surface in the spacetime, the topology (in particular the homotopy) of that surface is non-trivial due to the large number of Planckian ERBs that define homotopy through this surface. The quantization of spacetime with this topology — along with the proper choice of the 2-surfaces — is conjectured to allow non-perturbative path integrals of quantum gravity theory over the spacetime manifold

Quantum Gravity Emergence from Entanglement in a Multi-Fold Universe

“…De facto, we have shown that our model for UMF is background independent [25,249,248], i.e. it does not assume a fixed background (see how we can change the conditions) and by definition is built by the sum of the contributions of all the entities and so dynamic by nature at all time; something believed by many to be key to ensure correct modelling / avoidance of graviton selfinteractions 88 [248] and essential to align with GR that we need to recover at semi classical and classical scales.…”

“…Typically, this includes adding dimensions to spacetime and modifying the Hilbert-Einstein Action to achieve such cancellation at higher orders. 88 Because of the need to model through them the back reaction when the background is fixed as in QFT and superstring theory.…”

“…[86] refers to non-traversable wormholes. Some follow-up work looked at some consequences of ER=EPR approach [87,88,50]. If wormholes are not traversable, then they cannot satisfy the required features for folds in U M F as paths cannot be added.…”