Quantum Theory from Quantum Gravity

TL;DR

This paper proposes a mechanism where quantum theory emerges from a background-independent model based on an abstract graph, connecting microscopic dynamics to quantum behavior in the low-energy limit.

Contribution

It introduces a novel approach showing how quantum mechanics can arise from a purely geometric, graph-based model of spacetime without initial quantum assumptions.

Findings

Quantum behavior emerges from stochastic dynamics on a microscopic graph.

Distant correlations are mediated by non-local links in the fundamental graph.

The model reproduces the Schrödinger equation in the low-energy limit.

Abstract

We provide a mechanism by which, from a background independent model with no quantum mechanics, quantum theory arises in the same limit in which spatial properties appear. Starting with an arbitrary abstract graph as the microscopic model of spacetime, our ansatz is that the microscopic dynamics can be chosen so that 1) the model has a low low energy limit which reproduces the non-relativistic classical dynamics of a system of N particles in flat spacetime, 2) there is a minimum length, and 3) some of the particles are in a thermal bath or otherwise evolve stochastically. We then construct simple functions of the degrees of freedom of the theory and show that their probability distributions evolve according to the Schroedinger equation. The non-local hidden variables required to satisfy the conditions of Bell's theorem are the links in the fundamental graph that connect nodes adjacent in the graph but distant in the approximate metric of the low energy limit. In the presence of these links, distant stochastic fluctuations are transferred into universal quantum fluctuations.