Claim about mass
Claim about mass
The mass is some function of the number of elements
[But if you break the object in 2, how do you up with half the mass?]
[But if you break the object in 2, how do you up with half the mass?]
Edges slicing a hypersurface
Edges slicing a hypersurface
time vector : lapse function + shift vector (indexes leaves in the foliation)
t
μ
Volume of cone is number of events contained in a cone with a certain length of time vector
(Growth rate [i.e. coefficient of t^2] is being interpreted as curvature)
(Growth rate [i.e. coefficient of t^2] is being interpreted as curvature)
Pick a hyperslice: then there a particular space graph
Now evolve to the next hyperslice. We could count the number of edges in the causal graph getting to the next hyperslice. [Which is comparable to the number of elements changed between hyperslices]
Now evolve to the next hyperslice. We could count the number of edges in the causal graph getting to the next hyperslice. [Which is comparable to the number of elements changed between hyperslices]
C
t
Gets a contribution from whatever put edges in the causal graph at a certain density
C(t)~t^d ( 1 + a t^2 )
Out[]=
How do you add nodes without increasing the dimension?
Action: volume average of subleading terms of
C
t
Consequences of Ct behavior
Consequences of behavior
C
t
If increasing faster than t^d, effectively speed of light increases
Things get more connected; independent experiments get harder
Things get more connected; independent experiments get harder
If approaches t^d .... but there could still be a “dimension wave”
C
t
If there is a lump of increased dimension, what are its equations of motion?
Speed of light change
Speed of light change
Multiplies C(X) by a constant
Momentum conservation
Momentum conservation
Continuity equation on nodes of the causal graph
[aggregate has a certain form; therefore individual piece of C(X) have to compensate each other]
[aggregate has a certain form; therefore individual piece of C(X) have to compensate each other]
Dimension vs. scale
Dimension vs. scale
At a small scale, dimension is not defined
Looking at small scale, there are plenty of dimension fluctuations
Dimensionons
Dimensionons
Can a lump of higher connectivity in the causal graph just dissipate? [Has to follow underlying rule]
Thermal conductivity
Thermal conductivity
How does this vary with dimension?
3/2kTKE1/2mv^2