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....