## Minimal model of multiway causal graphs

Minimal model of multiway causal graphs

Minimal model of a causal invariant multiway graph is also a grid graph.

Graph3D[GeneralizedGridGraph[{4"Directed",4"Directed",4"Directed"}]]

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Out[]=

Two kinds of nodes, and two kinds of edges.

State nodes: they are on grid graph

Event nodes: they are on a grid graph, and they are the intermediate nodes on every state edge

Branchial graph for this minimal model is also a grid graph.

What is a “tipped foliation” in the MW graph? [Different foliations are different choices of measurements to make]

Analog of inertial is non-interacting observers (as in: the observers affect the system, but the system does not affect the observers)

Nearby events in branchial space are the most entangled....

Basic claim: Moving faster in branchial space just means you’re doing more uncorrelated measurements per unit time..... <quantum Zeno paradox>

https://en.wikipedia.org/wiki/Quantum_Zeno_effect : preventing E^I H t by repeated measurement

[What is the analog of length contraction?]

The geodesic in multiway space is your path to what sequence of measurements you want....

Analog of inertial is non-interacting observers (as in: the observers affect the system, but the system does not affect the observers)

Nearby events in branchial space are the most entangled....

Basic claim: Moving faster in branchial space just means you’re doing more uncorrelated measurements per unit time..... <quantum Zeno paradox>

https://en.wikipedia.org/wiki/Quantum_Zeno_effect : preventing E^I H t by repeated measurement

[What is the analog of length contraction?]

The geodesic in multiway space is your path to what sequence of measurements you want....

#### Wave packets are like geodesic bundles in multiway space....

Wave packets are like geodesic bundles in multiway space....

#### Analog of finite speed of light is finite speed of measurement

Analog of finite speed of light is finite speed of measurement

You can’t do measurements too quickly or you don’t know their results [because your brain hasn’t had time to get entangled]

~ maximum rate of entanglement

~ maximum rate of entanglement

As you approach the maximum rate of measurement, you are seeing more multiway states; i.e. more possible outcomes of measurement

[more critical pairs]. [Analog of an analog-to-digital converter : needs a tree of a certain size ]

I.e. it is harder and harder to resolve the results of the measurement [standard version: because the energy levels get closer together]

[more critical pairs]. [Analog of an analog-to-digital converter : needs a tree of a certain size ]

I.e. it is harder and harder to resolve the results of the measurement [standard version: because the energy levels get closer together]

####

Time dilation: analog is quantum Zeno's paradox

Time dilation: analog is quantum Zeno's paradox

Time dilation: analog is quantum Zeno's paradox

Things you are observing are evolving slower in time than your hyperactive measurement is happening << maybe ordinary time dilation >>

To go faster in doing measurements [you need more rapid communication of the outside world with your quantum system], you allow a faster decoherence time << moving into new degrees of freedom instead of new pieces of space >>

Claim: sufficiently rapid measurement entangles you with everything so you effectively thermalize

To go faster in doing measurements [you need more rapid communication of the outside world with your quantum system], you allow a faster decoherence time << moving into new degrees of freedom instead of new pieces of space >>

Claim: sufficiently rapid measurement entangles you with everything so you effectively thermalize

#### Event horizon also disconnects in the multiway graph

Event horizon also disconnects in the multiway graph

<Therefore there is a dual in the relativistic vs. quantum behavior>

They both redshift in spatial relativity, and they measure out in branchial relativity...

[[Is the connection between multiway relativity and spacetime relativity like holography]]

#### Twin paradox

Twin paradox

The faster-measuring twin entangles more;

#### Bigger bundle of geodesics in MW graph more confused/thermalized

Bigger bundle of geodesics in MW graph more confused/thermalized

#### Observer is family of branchlike hypersurfaces

Observer is family of branchlike hypersurfaces

Making those more tipped implies a high speed of measurement

[Cosmological reference frame is the minimal rate of observing]

Exploring more in branchial space is what you get by having higher speed of measurement

[Cosmological reference frame is the minimal rate of observing]

Exploring more in branchial space is what you get by having higher speed of measurement

[[[ What does distance in branchial space mean? ]]]

[ I.e. what are the edges in the branchial graph ]

[ I.e. what are the edges in the branchial graph ]

How do you measure the speed of measurement?

[ something ] / time

[ something ] / time

- ρ log ρ : von Neumann entanglement entropy

After tracing out some branches...

[[ Classical entropy: how many bits (aka discrete classical dof) are needed to describe the system ]]

[[ Entanglement entropy: how many discrete quantum dof are needed to describe the system ]]

After tracing out some branches...

[[ Classical entropy: how many bits (aka discrete classical dof) are needed to describe the system ]]

[[ Entanglement entropy: how many discrete quantum dof are needed to describe the system ]]

e^(iHt/ℏ)

L = c t

#### What is branchial space?

What is branchial space?

Dof are laid out in branchial space [a bit like phase space]

Distances in branchial space characterize [[the amount of entanglement entropy]]

Distance between dofs might be a bit like edit distance aka how many operations in our lexicon do you have do to get from one to other

(KC entropy)

What is the metric in state space? < Minimum number of events to get from one to the other >

Distance between dofs might be a bit like edit distance aka how many operations in our lexicon do you have do to get from one to other

(KC entropy)

What is the metric in state space? < Minimum number of events to get from one to the other >

#### Speed of measurement is measured relative to the maximum speed which is determined by the minimum number of events to get from one state to another

Speed of measurement is measured relative to the maximum speed which is determined by the minimum number of events to get from one state to another

#### Which gives the slope of the elementary entanglement cone

Which gives the slope of the elementary entanglement cone

#### Units

Units

Branchlike separated points : [ spin ] * time

#### Relation to path integrals

Relation to path integrals

Multiway graph: each square in the grid graph might correspond to a unit of action * time

#### Classical limit (?)

Classical limit (?)

1. 1/ℏ : it takes longer to get entanglement (i.e. classical limit is a single branch, because it never reaches entanglement)

2. ℏ: it takes less time to get entangled, and then everything is entangled, and the “higher inertia blob” behaves classically

2. ℏ: it takes less time to get entangled, and then everything is entangled, and the “higher inertia blob” behaves classically

This is a better theory if the observer is normally a multi-branch branchlike hypersurface

## Inertial vs. gravitational mass

Inertial vs. gravitational mass

## Energy in spacetime vs. energy in QM

Energy in spacetime vs. energy in QM