An Adynamical, Graphical Approach to Quantum Gravity and Unification

TL;DR

This paper introduces a novel graphical, adynamical framework for quantum gravity and unification, modifying existing theories to reconcile general relativity with quantum field theory without relying on dynamical evolution.

Contribution

It proposes a new approach using graphical field gradients and a spacetimesource element to unify quantum mechanics and gravity in a background-independent manner.

Findings

Corrects proper distance in cosmology, fitting supernova data without dark energy.

Provides an adynamical account of quantum interference.

Reconciles general relativity and quantum field theory through graphical modifications.

Abstract

We use graphical field gradients in an adynamical, background independent fashion to propose a new approach to quantum gravity and unification. Our proposed reconciliation of general relativity and quantum field theory is based on a modification of their graphical instantiations, i.e., Regge calculus and lattice gauge theory, respectively, which we assume are fundamental to their continuum counterparts. Accordingly, the fundamental structure is a graphical amalgam of space, time, and sources (in parlance of quantum field theory) called a "spacetimesource element." These are fundamental elements of space, time, and sources, not source elements in space and time. The transition amplitude for a spacetimesource element is computed using a path integral with discrete graphical action. The action for a spacetimesource element is constructed from a difference matrix K and source vector J on the graph, as in lattice gauge theory. K is constructed from graphical field gradients so that it contains a non-trivial null space and J is then restricted to the row space of K, so that it is divergence-free and represents a conserved exchange of energy-momentum. This construct of K and J represents an adynamical global constraint between sources, the spacetime metric, and the energy-momentum content of the element, rather than a dynamical law for time-evolved entities. We use this approach via modified Regge calculus to correct proper distance in the Einstein-deSitter cosmology model yielding a fit of the Union2 Compilation supernova data that matches LambdaCDM without having to invoke accelerating expansion or dark energy. A similar modification to lattice gauge theory results in an adynamical account of quantum interference.