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WOLFRAM NOTEBOOK
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}
3
Norm[{x-1,y}]
-1{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