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?]

Edges slicing a hypersurface

time vector : lapse function + shift vector
t
μ
(indexes leaves in the foliation)
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)
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]
C
t
(X)
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
C
t
behavior

If increasing faster than t^d, effectively speed of light increases
Things get more connected; independent experiments get harder
If
C
t
approaches t^d .... but there could still be a “dimension wave”
If there is a lump of increased dimension, what are its equations of motion?

Speed of light change

Multiplies C(X) by a constant

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]

Dimension vs. scale

At a small scale, dimension is not defined
Looking at small scale, there are plenty of dimension fluctuations

Dimensionons

Can a lump of higher connectivity in the causal graph just dissipate? [Has to follow underlying rule]

Thermal conductivity

How does this vary with dimension?
3/2kTKE1/2mv^2