An Adynamical, Graphical Approach to Quantum Gravity and Unification

We propose an adynamical, background independent approach to quantum gravity and unification whereby the fundamental elements of Nature are graphical units of space, time and sources. The transition amplitude for these elements of “spacetimesource” is computed using a path integral with discrete Gaussian graphical action. The unit of 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 relations so that it contains a non-trivial null space, and J is then restricted to the column space of K which ensures it is distributed in a divergence-free fashion over the spacetime defined by the element. This rule for the relational construct of K and J is our proposed fundamental axiom of physics and results in a self-consistency relationship between sources, the spacetime metric, and the stress-energy-momentum content of the element, rather than a dynamical law for time-evolved entities. In its most general form, the set of fundamental elements employed by lattice gauge theory contains scalar fields on nodes and links, and vector fields on nodes. To complete the fundamental set, we propose the addition of scalar fields on plaquettes and vector fields on links. 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 ɅCDM without having to invoke accelerating expansion or dark energy.