Interpretation of Momentum?
Interpretation of Momentum?
Index position by a grid of light cones , which is effectively the causal graph [ “grid of elementary light cones” ]
Any effect propagates through spacetime on the edges of these light cones.... (everything is at least locally going on a null geodesic) [cf refractive index of water, etc.]
Possible claim: more energy, more nodes
Effective dimension of spacetime cones....
What Spacelike Hypersurfaces Correspond to an Inertial Frame?
What Spacelike Hypersurfaces Correspond to an Inertial Frame?
The surface must always be spacelike... can we enumerate all spacelike surfaces through a point?
Out[]=
Given an event, find the spacelike separated events
Can we find a sequence of surfaces that fill the spacetime, but are always spacelike?
The foliations correspond to layerings of the causal graph
In[]:=
LayeredGraphPlot
Out[]=
Claim is that a hypersurface is a collection of edges (i.e. a bunch of pieces of elementary light cones)
Foliation is a parametrized enumeration of edges
Layering defines the observer’s frame
Does following the elementary light cones propagate you smoothly from one hypersurface to the next?
Jonathan’s claim: density of edges defines momentum; complete graph is maximum density