### Two possible reconstructions of space:

Two possible reconstructions of space:

#### From knitting of hyperedges by elements

From knitting of hyperedges by elements

[ The reconstructed object is the dual of the spatial hypergraph ... i.e. its nodes are the hyperedges of the spatial hypergraph, and each hyperedge is associated with a single space atom ]

#### Knitting of hyperedges by events

Knitting of hyperedges by events

Not the same because of the flow of elements through hyperedges

## Inequalities

Inequalities

#### Speed in space is less than c

Speed in space is less than c

There exist rules that make one be able to go further in the reconstructed spatial ball vs. the causal ball.

[Happens when expressions with shared elements are not both matched]

[Happens when expressions with shared elements are not both matched]

#### Speed in space is greater than c

Speed in space is greater than c

Rule could disconnect its input which would limit how far the spatial ball could extend, but the causal ball would extend. I.e. you can causally reach more places in space than you can geometrically reach if space is broken by event horizons....

This is analogous to having a temporary wormhole, that then disappears, but leaves the results of its communication....

This is analogous to having a temporary wormhole, that then disappears, but leaves the results of its communication....

### Claim: want both the past and future causal balls to be bigger than the geodesic ball.

Claim: want both the past and future causal balls to be bigger than the geodesic ball.

## Future Causal Ball ?

Future Causal Ball ?

I.e. something that will reach a particular expression in the future....

#### Possible claim:

Possible claim:

There is a constant (say c) for which the future causal ball for an expression t steps in the future is always smaller than the c t step geodesic ball......

#### A rule that matches any collection of hyperedges out to a certain geodesic distance will simply reconstruct a geodesic ball....

A rule that matches any collection of hyperedges out to a certain geodesic distance will simply reconstruct a geodesic ball....

[Assuming the rule is connected]

#### (Geodesic ball: generated by “anything goes” rule of a given diameter)

(Geodesic ball: generated by “anything goes” rule of a given diameter)

#### [ I.e. “geodesic speed” is the absolute upper limit ] [[ not obviously correct: the rule makes extra space ... ]]

[ I.e. “geodesic speed” is the absolute upper limit ] [[ not obviously correct: the rule makes extra space ... ]]

## Cases

Cases

#### Pre-existing network of wormholes

Pre-existing network of wormholes

#### Wormhole network one can pre-construct

Wormhole network one can pre-construct

#### [Dynamic case]

[Dynamic case]

#### [Manipulate update order so that the space around where you are is updated faster than space further away]

[Manipulate update order so that the space around where you are is updated faster than space further away]

## “Creating Space”

“Creating Space”

If there is a higher density of nodes than usual created in a fixed number of steps ... that is effectively negative relative energy

## Einstein Equations

Einstein Equations

Given a metric, there exists a that gives that metric .... the issue is whether the is realizable with matter...

T

μν

T

μ⋁

[For Newton’s equations: given a trajectory, deduce a force that will give that]

## Alcubierre Metric

Alcubierre Metric

What happens to time for people moving inside the bubble?

<Analogous to expansion of universe, where effectively space is being created by expansion>

## Universe Expansion

Universe Expansion

Formation of cosmological event horizon is simply a disconnection in the causal graph

[[ Hitchhiking on the expansion of the universe ]]