An update rule is like a quantum operator: at least the time evolution operator

Each branch of the multiway system is like a classical evolution

I.e. each branch represent a basis state

The whole MW is like a superposition of these states (and we assume it’s a pure state)

Amplitudes are weights in the MW system

The whole MW is like a superposition of these states (and we assume it’s a pure state)

Amplitudes are weights in the MW system

Causal invariance is saying that there is a unified thread of behavior (wrt equivalence classes)

Critical pair represents branch-like separated events.

Divergence between MW causal networks

Divergence between MW causal networks

#### MW geometry is like Hilbert space geometry

MW geometry is like Hilbert space geometry

But it is Hilbert space geometry for an interacting field theory

Free field theory => causal graph branches at each step

#### We have a time-evolving Hilbert space

We have a time-evolving Hilbert space

#### You can poke the system by do a random update, and that’s like applying an operator

You can poke the system by do a random update, and that’s like applying an operator

#### Consider poking the MW system

Consider poking the MW system

When the poke leads to a critical pair, it causes the system to branch

Two pokes are noncommuting if the branch doesn’t resolve

#### The hyperedges are in Planck units

The hyperedges are in Planck units

(((A single hyperedge))) relates space and time using the speed of light

? Also related through ℏ

? Also related through ℏ

#### In one “update event” information can propagate by the diameter of the rule

In one “update event” information can propagate by the diameter of the rule

Claim is made that “edges are mass/energy”

The steeper the spacelike hypersurface .... the more edges, the more mass.....

### Source of fundamental constants

Source of fundamental constants

#### spatial graph

causal graph

multiway graph

spatial graph

causal graph

multiway graph

causal graph

multiway graph

Speed of light: spatial graph [spacelike separation] vs causal graph [timelike separation]

Planck’s constant / G : multiway graph vs. causal graph

multiway vs spatial

Planck’s constant / G : multiway graph vs. causal graph

multiway vs spatial

### Bizarre claim: degree of a node in the spatial hypergraph is energy

Bizarre claim: degree of a node in the spatial hypergraph is energy

Mass per unit ball = degree of node

#### Edges to nodes ratio

Edges to nodes ratio

#### The reason our “vacuum energy” doesn’t curl spacetime up into a ball is because it is spacetime

The reason our “vacuum energy” doesn’t curl spacetime up into a ball is because it is spacetime

Is the energy linear wrt degree

### Light cones vs. branch cones

Light cones vs. branch cones

Both involve passage of time; in a light cone you are going a certain spatial distance

#### Moving in space is like applying an operator that rearranges the hypergraph

Moving in space is like applying an operator that rearranges the hypergraph

Value of an elementary commutator in the causal graph is basically c

Value of an elementary commutator in the multiway graph it is ℏ

Value of an elementary commutator in the multiway graph it is ℏ

Sqrt[ℏG/c^3]

Planck area:

Is it c^3

Is it c^3

Volume of an elementary light cone: time t : volume is c^3 t^3

#### What are the units of G? G’s units are dimension dependent. So the Planck area in dimension d is:

What are the units of G? G’s units are dimension dependent. So the Planck area in dimension d is:

ℏ G/c^d ~ elementary area

### Superposition principle of model

Superposition principle of model

Model can pick up hyperedges from a node independent of other hyperedges there....

Does this imply linear superposition in QM?

#### Claim is that the independence of rule application between different edges at a node is like separability of states ????

Claim is that the independence of rule application between different edges at a node is like separability of states ????

#### Nodes shared between hyperedges correspond to non-separately evolvable things (cf critical pairs)

Nodes shared between hyperedges correspond to non-separately evolvable things (cf critical pairs)

### [Gauge theories renormalizable in 4D only ..... maybe that is why these emerge as the theories ]

[Gauge theories renormalizable in 4D only ..... maybe that is why these emerge as the theories ]

There might be many other kinds of fields, but gauge theories might be the only ones that survive in the effectively 4D case....