## Space Tunnels

Space Tunnels

The mouth of the space tunnel will be higher dimensional in the spatial graph

Causal edges can go through the space tunnel

Can a space tunnel be persistent?

### Our derivation of Einstein equations involves fixed dimension

Our derivation of Einstein equations involves fixed dimension

### We need a dimension tensor [AKA is there isotropy of dimension?]

We need a dimension tensor [AKA is there isotropy of dimension?]

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VectorPlot+,{x,-5,5},{y,-5,5}

{x-1,y}

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Norm[{x-1,y}]

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Analogy with magnetic monopoles

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GridGraph[{3,3,3}]

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The ends of the space tunnel are like a black hole + white hole

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PathGraph[Range[10]]

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Table[{ii+1,ii+100},{i,10}]//Flatten//Graph

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Table[{ii+1,ii+100,ii+200},{i,10}]//Flatten//Graph

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Table[{ii+1,ii+100,ii+200},{i,10}]//Flatten//LayeredGraphPlot

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Table[{ii+1,ii+100,ii+200},{i,10}]//Flatten//ReverseGraph//LayeredGraphPlot

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### Feynman diagrams are the multiway analog of Penrose diagrams

Feynman diagrams are the multiway analog of Penrose diagrams

#### What is a white qubit?

What is a white qubit?

#### Time reversal of measurement

Time reversal of measurement

### Negative mass?

Negative mass?

Requires advanced as opposed to retarded causal edges

Is the positivity of mass derivable thermodynamically?

### Uniqueness of the vacuum?

Uniqueness of the vacuum?

In our models, uniqueness of the vacuum is the direct analog of the uniqueness of the equilibrium state in thermodynamics

#### Is there only one phase of our vacuum?

Is there only one phase of our vacuum?

For our vacuum, temperature is related to energy density, pressure to momentum density

Is one of them always metastable?

The version of space that maintains itself with the lowest number of causal edges is the “true vacuum”

#### Can you create a vacuum cleaner?

Can you create a vacuum cleaner?

#### Can you create a vacuum refrigerator ... which effectively the reduces the energy density of one region of vacuum in favor of another?

Can you create a vacuum refrigerator ... which effectively the reduces the energy density of one region of vacuum in favor of another?

### General case: MW causal graph

General case: MW causal graph

Uniqueness of equilibrium branchial space

Superselection sector where the vacuum energy is different

Say: there are no vacuum fluctuations associated with particles of type X in a particular region

Can you make a generalized Casimir event where some external constraint determines which vacuum fluctuations can exist? [E.g. have a box that is transparent to particle A but not B]

E.g. graph theoretically: obstruction to the presence of topological obstructions

### Between two phases, there will be a domain wall

Between two phases, there will be a domain wall

The notion of having a continuum would fail at the domain wall

Analog of discontinuous cosmological constant

#### Analogous to a fluid shock

Analogous to a fluid shock

No conservation of causal edges

Energy-momentum still conserved because the zero changed

#### Variable dimension fractal curve:

Variable dimension fractal curve:

Construct a graph with geodesic balls

# Black hole searching

Black hole searching