What is a black hole?

1. Split in a causal graph

1. Split in a causal graph

Progressively, the pieces of the causal graph will split

Meanwhile, the branchial will become disconnected.....

Meanwhile, the branchial will become disconnected.....

SubstitutionSystemCausalGraph[{"A""ABA"},"A",4]//LayeredGraphPlot

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SubstitutionSystemCausalGraph[{"A""ABA"},"AAA",4]//LayeredGraphPlot

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“Superluminally expanding universe”

causals=Import["/Users/sw/Dropbox/Physics/Data/MWCausalInvariantSamples/samples-01.wxf"];

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causals[[3]]

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{{AAA},{AAB},{ABB},{AAA},{ABA}}

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causals[[4]]

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MultiwaySystem[{"A""ABA"},"A",5,"CausalGraphStructure"]

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MultiwaySystem[{"A""ABA"},"A",5,"BranchialGraphStructure"]

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causals[[5]]

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MultiwaySystem[{"A""AABA"},"A",4,"BranchialGraphStructure"]

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MultiwaySystem[{"A""AABA"},"AA",4,"BranchialGraphStructure"]

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If they are pure spacelike branchial connections, then they must have common past light cones....

If they have pure-branchlike branchial connections, then they have common past entanglement cones

If they have pure-branchlike branchial connections, then they have common past entanglement cones

causals[[6]]

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SubstitutionSystemCausalGraph[{"AB""AABA"},"ABAAB",4]//LayeredGraphPlot

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25 signature needed....

Select[causals[[7]],(StringLength/@First[#])===25&]

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{}

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r25={{"AA""AAAAA"},{"AA""AAABA"},{"AA""AABAA"},{"AA""AABBA"},{"AA""ABABA"},{"AA""ABBBA"},{"AB""AAAAA"},{"AB""AAAAB"},{"AB""AAABA"},{"AB""AAABB"},{"AB""AABAA"},{"AB""AABAB"},{"AB""AABBA"},{"AB""ABAAA"},{"AB""ABAAB"},{"AB""ABABA"},{"AB""ABBAA"},{"AB""ABBBA"},{"AB""BAAAA"},{"AB""BAABA"},{"AB""BABAA"},{"AB""BBAAA"}};

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InteractiveListSelectorSW[ParallelMapMonitored[{SubstitutionSystemCausalGraph[#,#[[1,1]],4]//LayeredGraphPlot,MultiwaySystem[#,#[[1,1]],4,"BranchialGraphStructure"]}#&,r25]]

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InteractiveListSelectorSW[ParallelMapMonitored[{SubstitutionSystemCausalGraph[#,#[[1,1]],4]//LayeredGraphPlot,TimeConstrained[MultiwaySystem[#,#[[1,1]],6,"BranchialGraphStructure"],5]}#&,r25]]

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RuleVelocity[rule_]:=Max[(StringLength[#[[2]]]-StringLength[#[[1]]])&/@rule]/Max[StringLength[#[[1]]]&/@rule]

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Select[causals[[7]],RuleVelocity[#]>1&]

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InteractiveListSelectorSW[ParallelMapMonitored[TimeConstrained[Show[#,ImageSizeTiny]&/@{SubstitutionSystemCausalGraph[#,#[[1,1]],4]//LayeredGraphPlot,TimeConstrained[MultiwaySystem[#,#[[1,1]],5,"BranchialGraphStructure"],2]},3]#&,%]]

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SubstitutionSystemCausalGraph[{"A""AA","A""BAB"},"A",5]//LayeredGraphPlot

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Table[MultiwaySystem[{"A""AA","A""BAB"},"A",t,"BranchialGraphStructure"],{t,5}]

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Table[MultiwaySystem[{"A""AA","A""BAB"},"A",t,"BranchialGraphStructure"],{t,7}]

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LayeredGraphPlot[MultiwaySystem[{"A""AA","A""BAB"},"A",5,"StatesGraphStructure"],AspectRatio1/2]

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CausalInvariantQ[{"A""AA","A""BAB"},"A",2]

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False

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CausalInvariantQ[{"A""AA","A""BAB"},{"A"},2]

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False

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CausalInvariantQ[{"A""AA","A""BAB"},"A",5]

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False

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CausalInvariantQ[{"A""AA","A""BAB"},"A",6]

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True

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We will get disconnection in the branchial graph when the thickness of a branchial slice is less than the resolution time for branch pairs.

If the branchial graph is disconnected, you can never measure the disconectee....

With C.I., thicker branchial foliation [[ lower and lower time resolution ]]

With C.I., thicker branchial foliation [[ lower and lower time resolution ]]

#### Uncertainty from foliations?

Uncertainty from foliations?

Entanglement distance :

(The more finely foliated in time, the less you can tell what the direction of a causal edge is)

Select[causals[[8]],RuleVelocity[#]>1&]

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InteractiveListSelectorSW[ParallelMapMonitored[TimeConstrained[Show[#,ImageSizeTiny]&/@{SubstitutionSystemCausalGraph[#,#[[1,1]],4]//LayeredGraphPlot,TimeConstrained[MultiwaySystem[#,#[[1,1]],5,"BranchialGraphStructure"],2]},3]#&,%]]

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Union[{{"A""AA","A""BABB"},{"A""AA","A""BABB"},{"A""BAAB","AA""A"},{"A""BAAB","AA""A"},{"A""BABB","BB""A"},{"A""BABB","BB""A"},{"A""AAB","A""BAB"},{"A""AAB","A""BAB"},{"A""ABA","A""BAB"},{"A""ABA","A""BAB"},{"A""ABA","A""BAB"}}]

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{SubstitutionSystemCausalGraph[#,#[[1,1]],5]//LayeredGraphPlot,TimeConstrained[MultiwaySystem[#,#[[1,1]],5,"BranchialGraphStructure"],2]}&/@{{"A""AA","A""BABB"},{"A""AAB","A""BAB"},{"A""ABA","A""BAB"},{"A""BAAB","AA""A"},{"A""BABB","BB""A"}}

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## Max entanglement rate

Max entanglement rate

Can’t make a condensate quickly enough.... [[ freezing to a ground state ]] < forces it to be polycrystalline > <e.g. domains in early universe>

[[[ Frame dependence is a feature of singularities in GR too .... ]]] [ Can no longer fix it after it separates ]

Smallness of branchial black holes is a consequence of υ being large (and branchial space being compact) ...... [[[ what is the value of υ for this system ]]]

## Singularities

Singularities

“Physical singularity”

Setup of a qubit: “temporary black hole” [[ which unwinds probably due an analog of Hawking radiation ]]

What is the analog of gravity? There does not appear to be a runaway mechanism....

Singularity theorem: inevitability

Singularity theorem: inevitability

2 G m / c^2

What is the source of curvature in branchial space? Energy.

When a large number of branch pairs resolve, that brings together geodesics....

Possibly: with isolation, resolution could be achieved more quickly

E.g. in the black hole case, have to have infalling matter to offset radiation

When a large number of branch pairs resolve, that brings together geodesics....

Possibly: with isolation, resolution could be achieved more quickly

E.g. in the black hole case, have to have infalling matter to offset radiation

Branchial singularity vs branchial event horizon:

if all geodesics to one state, that has to disconnect [?] (weak cosmic censorship)

if all geodesics to one state, that has to disconnect [?] (weak cosmic censorship)

All causal disconnections aren’t if you go back to the beginning......

#### Should be possible to have branchial disconnection without causal disconnection

Should be possible to have branchial disconnection without causal disconnection

[ if one is going to have a permanent measurement ]

#### Can you have temporary disconnection in the branchial graph? [ Probably yes ]

Can you have temporary disconnection in the branchial graph? [ Probably yes ]

The branchial graph is a shadow of a bunch of entanglement cones...

υ T

υ T

Estimate for υ is based on average for geodesics

Stripping all branchlike connections .... leaves only the spacelike connections ..... which is basically a shadow of the spatial hypergraph

Matching its underlying speed with actual units

Stripping all branchlike connections .... leaves only the spacelike connections ..... which is basically a shadow of the spatial hypergraph

Matching its underlying speed with actual units

Is maintaining a qubit like holding an object at the event horizon?

#### One case of time freezing is termination.

Another case is causal disconnection

One case of time freezing is termination.

Another case is causal disconnection

Another case is causal disconnection

If there are multiple normal forms, you clearly get causal disconnection

You can have causal disconnection without termination, just like you can have event horizons without singularities

#### Hawking radiation comes from entanglement horizons [ which is not spatially localized ]

Hawking radiation comes from entanglement horizons [ which is not spatially localized ]

MultiwaySystem[{"AA""ABABA"},"AAAAAA",6,"StatesGraph"]

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