8.3 Potential Basic Translations

As a guide to the potential application of our models to physics, we list here some current expectations about possible translations between features of physics and features of our models. This should be considered a rough summary, with every item requiring significant explanation and qualification. In addition, it should be noted that in an effort to clarify presentation, many highly abstract concepts have been indicated here by more mechanistic analogies.

Basic Physics Concepts

space: general limiting structure of basic hypergraph

time: index of causal foliations of hypergraph rewriting

matter (in bulk): local fluctuations of features of basic hypergraph

energy: flux of edges in the multiway causal graph through spacelike (or branchlike) hypersurfaces

momentum: flux of edges in the multiway causal graph through timelike hypersurfaces

(rest) mass: numbers of nodes in the hypergraph being reused in updating events

motion: possible because of causal invariance; associated with change of causal foliations

particles: locally stable configurations in the hypergraph

charge, spin, etc.: associated with local configurations of hyperedges

quantum indeterminacy: different foliations (of branchlike hypersurfaces) in the
multiway graph

quantum effects: associated with locally unresolved branching in the multiway graph

quantum states: (instantaneously) nodes in the branchial graph

quantum entanglement: shared ancestry in the multiway graph / distance in branchial graph

quantum amplitudes: path counting and branchial directions in the multiway graph

quantum action density (Lagrangian): total flux (divergence) of multiway causal
graph edges

Physical Theories & Principles

special relativity: global consequence of causal invariance in hypergraph rewriting

general relativity / general covariance: effect of causal invariance in the causal graph

locality / causality: consequence of locality of hypergraph rewriting and causal invariance

rotational invariance: limiting homogeneity of the hypergraph

Lorentz invariance: consequence of causal invariance in the causal graph

time dilation: effect of different foliations of the causal graph

relativistic mass increase: effect of different foliations of the causal graph

local gauge invariance: consequence of causal invariance in the multiway graph

lack of quantum cosmological constant: space is effectively created by quantum fluctuations

cosmological homogeneity: early universe can have higher effective spatial dimension

expansion of universe: growth of hypergraph

conservation of energy: equilibrium in the causal graph

conservation of momentum: balance of different hyperedges during rewritings

principle of equivalence: gravitational and inertial mass both arise from features
of the hypergraph

discrete conservation laws: features of the ways local hypergraph structures can combine

microscopic reversibility: limiting equilibrium of hypergraph rewriting processes

quantum mechanics: consequence of branching in the multiway system

observer in quantum mechanics: branchlike hypersurface foliation

quantum objective reality: equivalence of quantum observation frames in the multiway graph

quantum measurements: updating events with choice of outcomes, that can be frozen
by a foliation

quantum eigenstates: branches in multiway system

quantum linear superposition: additivity of path counts in the multiway graph

uncertainty principle: non-commutation of update events in the multiway graph

wave-particle duality: relation between spacelike and branchlike projections of the
multiway causal graph

operator-state correspondence: states in the multiway graph are generated by
events (operators)

path integral: turning of paths in the multiway graph is proportional to causal edge density

violation of Bell’s inequalities, etc.: existence of causal connections in the multiway graph

quantum numbers: associated with discrete local properties of the hypergraph

quantization of charge, etc.: consequence of the discrete hypergraph structure

black holes / singularities: causal disconnection in the causal graph

dark matter: (possibly) relic oligons / dimension changes in of space

virtual particles: local structures continually generated in the spatial and multiway graphs

black hole radiation / information: causal disconnection of branch pairs

holographic principle: correspondence between spatial and branchial structure

Physical Quantities & Constructs

dimension of space: growth rate exponent in hypergraph / causal cones

curvature of space: polynomial part of growth rate in hypergraph / causal cones

local gauge group: limiting automorphisms of local hypergraph configurations

speed of light (c): measure of edges in spatial graph vs. causal graph

light cones: causal cones in the causal graph

unit of energy: count of edges in the causal graph

momentum space: limiting structure of causal graph in terms of edges

gravitational constant: proportionality between node counts and spatial volume

quantum parameter (ℏ): measure of edges in the branchial graph (maximum speed
of measurement)

elementary unit of entanglement: branching of single branch pair

electric/gauge charges: counts of local hyperedge configurations

spectrum of particles: spectrum of locally stable configurations in the hypergraph

Idealizations, etc. Used in Physics

inertial frame: parallel foliation of causal graph

rest frame of universe: geodesically layered foliation of causal graph

flat space: uniform hypergraph (typically not maintained by rules)

Minkowski space: effectively uniform causal graph

cosmological constant: uniform curvature in the hypergraph

de Sitter space: cyclically connected hypergraph

closed timelike curves: loops in the causal graph (only possible in some rules)

point particle: a persistent structure in the hypergraph involving comparatively few nodes

purely empty space: not possible in our models (space is maintained by rule evolution)

vacuum: statistically uniform regions of the spatial hypergraph

vacuum energy: causal connections attributed purely to establishing the structure of space

isolated quantum system: disconnected part of the branchial/multiway graph

collapse of the wave function: degenerate foliation that infinitely retards
branchlike entanglement

non-interacting observer in quantum mechanics: “parallel” foliation of multiway graph

free field theory: e.g. pure branching in the multiway system

quantum computation: following multiple branches in multiway system (limited by causal invariance)

string field theory: (potentially) continuous analog of the multiway causal graph for string substitutions