Stochastic Emergent Quantum Gravity

TL;DR

This paper introduces a stochastic framework for emergent quantum gravity that links stochasticity in clock and ruler fields to the emergence of quantum probabilistic behavior and general relativity, applicable to standard Lorentz-invariant theories.

Contribution

It proposes a novel stochastic approach to emergent quantum gravity, connecting clock and ruler field critical points to quantum and gravitational phenomena, and outlines embedding standard field theories within this framework.

Findings

Stochasticity in clock and ruler fields relates to quantum probabilistic behavior.

Emergent gravity described by general relativity arises at long distances.

Framework can embed the Standard Model and Lorentz-invariant extensions.

Abstract

We present a stochastic framework for emergent quantum gravity coupled to matter. The Hamiltonian constraint in diffeomorphism-invariant theories demands the identification of a clock relative to which dynamics may be defined, and other degrees of freedom can play the role of rulers. However, a global system of clock and rulers is generally not available. We provide evidence that stochasticity associated with critical points of clock and ruler fields can be related to the emergence of both a probabilistic description consistent with ordinary quantum theory, and gravitation described by general relativity at long distances. We propose a procedure for embedding any Lorentz-invariant field theory, including the Standard Model and its Lorentz-invariant extensions, in this framework.