Conjugate variables are associated with orthogonal directions in multiway space
Conjugate variables are associated with orthogonal directions in multiway space
If operators O1, O2 correspond to conjugate variables, then O1, O2 yield a nontrivial branch pair
And by virtue of their branch, they are orthogonal
Position is a feature that is visible in the MW CG...
In MW CG, every event has a {t, x, b} coordinate
1/Δx elements in the x measuring device; reconfiguring these for momentum leads to O(1/Δx) dispersion in the branchial direction [ which leads to a spread of everything ]
Everything turns into a ball in multiway space; of a certain size....
1/Δx elements in the x measuring device; reconfiguring these for momentum leads to O(1/Δx) dispersion in the branchial direction [ which leads to a spread of everything ]
Everything turns into a ball in multiway space; of a certain size....
Everything turns into a ball in multiway space; of a certain size....
Local similarities
Entanglement monotone
Entanglement monotone
https://en.wikipedia.org/wiki/Entanglement_monotone
Manifold of manifolds
Manifold of manifolds
( Like fiber bundle ? )
Branching and merging of multiway edges ↔ string field theory
AdS/CFT
AdS/CFT
Boundary of region in MW CG
Units
Units
Causal edge:
time extent : τ
spatial extent : c τ
energy : [ ϵ : unit of energy ]
time extent : τ
spatial extent : c τ
energy : [ ϵ : unit of energy ]
Node of hypergraph:
Edge of hypergraph:
Edge of hypergraph:
Contribution of a single edge to energy:
Minimum energy ~ h c / radius of universe
In[]:=
Out[]=
In[]:=
energyunit=UnitConvert[%147,"ElectronVolt"]
Out[]=
Contribution of single edge to curvature:
1 + r^2 R
In[]:=
ΔR==1^2
Out[]=
ΔR
Gravitational constant is a scaling between spatial curvature and energy density
Energy density of a single edge : ϵ/(c^3 τ^4)
G / c^4 ϵ/(c^3 τ^3) ==
1/Ru^2
In[]:=
G/c^4*hc/Ru/(c^3τ^3)1/Ru^2
Out[]=
Gh
6
c
3
τ
1
2
Ru
In[]:=
Solve[%,τ]
Out[]=
τ,τ-,τ
1/3
G
1/3
h
1/3
Ru
2
c
1/3
(-1)
1/3
G
1/3
h
1/3
Ru
2
c
2/3
(-1)
1/3
G
1/3
h
1/3
Ru
2
c
In[]:=
1/3
G
1/3
h
1/3
Ru
2
c
Out[]=
Take 2 : use (c τ) as the curvature scale
Take 2 : use (c τ) as the curvature scale
Planck units: take 2
Planck units: take 2
What is an energy h c / Ru in Planck units?
Using Planck units
Using Planck units
Alternative derivation (black hole based)
Alternative derivation (black hole based)
Spacetime energy density per causal edge : ϵ /
energy of universe =
Previous version
Previous version
spacetime energy density associated with causal edge : ϵ / (τ ( c τ)^d)
G t t T ~ L L R : both dimensionless
T ~ (energy / unit volume)
Imagine the contribution of a single edge to
(1 +
R ~ 1/( macrolength^2 )
Ru size of universe
G τ^2 T / c^4 == (c τ)^2 / Ru^2
Is it c^4 or c^(d+1) ???