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