Combining branchial space with ordinary space....

Foliating the MWCG

Wave-particle duality
Image you started a geodesic bundle in the MWCG. The bundle will spread in both spacelike (light cone) and branchlike (entanglement cone) directions.... In the MWCG, can mix spacelike/branchlike according to foliation
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In spacetime, it follows a standard geodesic path
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In branchtime, the thing may spread out
Wave of a certain frequency vs. particle of a certain energy....
Particle with given energy: flux of causal edges through spacelike surfaces
Frequency is associated with rate of phase change of e^(i H t) : its version of energy....
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Wavepacket in space: has a spatial falloff; in branchial space, also has a falloff...

Scaling all cross-section of bundles

Look at all path counts reaching a certain slice; now consider what fraction are the ones you care about....
(  solid angle)

Uncertainty Principle

Rotation in spacetime (going from measuring position to measuring timelike flux)
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Claim: rotation in spacetime involves rotation in branchtime
x, p uncertainty relation
First this, then that. How do you operationally go from one to the other?
Rotating an apparatus with n gradations takes O(n^2) operations [[ takes n time steps ]]
At each step, there is an x-direction update, and a p-direction update that could be done....,
The x, p measurement sequence induces dispersion in branch space....
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​Measured x using a fine toothed comb.... (with O(n) teeth)
Now measure p by having transported their comb, but actually their comb fuzzed out in branchial space..... ​
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Commutator failure might be thought of as an angle mismatch

Propagation of wave packets

Measure branchial dispersion : angle ℏ/τ
If there is a bundle of MW geodesics, some fraction of them will get “dispersed”... Assume they are all branched.
Number of geodesics for energy E is essentially E/(branchial area)
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Transition amplitude is the overall measure of the beginning and end of the geodesic bundle onto their states....
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If they are zero distance apart the amplitude will be 1
As they go further, there is more dispersion....
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Event density aka causal edges determines number of branches
Measuring the dispersion going down the MWCG. Look at an angle because it doesn’t depend on the foliation....
[ Angles are complicated because of metric on branchial space ;;; and increasing dimension of branchial graph with time ]

Correspondence between conformal structure [ cones ... ]

Quantum Hamiltonian : defines flux of edges across branchlike hypersurfaces in the multiway causal graph

Lagrangian: not measuring flux across timelike-transverse hypersurfaces, but instead measuring overall flux in any direction.....
global hypersurface [[[ from a given point ]]]
Lagrangian : flux of edges in the multiway graph
Action is the multiway volume integral of the Lagrangian .... ​Lagrangian is like the Ricci scalar......Integrating to get the action is ∫L
g
​Transporting around a loop the change in angle is R area....

Lagrangian relative to the “vacuum Lagrangian”

If you didn’t prepare the quantum state ..... there will be some behavior.
Now include your preparation....
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?? normalization of states in Hilbert space .......
<Refractive index for geodesics>

Single path going through region of changed Ricci scalar

Density of alternate branches.....
In[]:=
Graphics[Line[AnglePath[RandomReal[{0,2Pi},20]]]]
Out[]=
Angle affects the probability of hitting the right spot to contribute to the measure of a particular outcome....
[[In high-dimensional space, probably only the angle matters....]]
In a changing of dimensions, need to use angles.....
“Hitting the target” is simply the projection of its angle on the final surface / aka sin/cos