Mr. Wolfram describes energy as "energy: flux of edges in the multiway causal graph through spacelike (or branchlike) hypersurfaces". Take this idea of flux seriously and assign energy to be directly proportional to the quantity of edge changes on a particular vertices. For the purposes of conservation, we may set the proportionally constant to one and simply allow the energy to be the number of edges changed per update. Now, say that the unit energy will be the planck energy and that we may set that equal to one change per update. Now, let us look at any two updates A, and B. Count the total number of edges changed during A and again for B. The total for A will be the total energy content of the universe at that point in 'time'. The same will be true for B.
What energy conservation tells us is that we can not destroy or create energy, which in this model translates to the number of changes of edges each update will not change. Because if A and B were to have different numbers of edge changes or energy contents, then the universe would have changed its energy content. So, if we are to keep energy conservation within this model, then it seems clear that we must do one of two things:
Assume that every update contains the same number of edge changes. Which would put a hard criteria upon the replacement rules since we have seen through the registry of notable universes that a conservation of edges changes seems a rare creature.
That the hypergraph splits in such a way to causally begin with some net energy, but end with a tilted scale in each of the splits without violating conservation on the whole. Which also seems like an incredible claim to force upon whatever replacement rule that generates the whole structure.
Both of these paths of criteria for replacement rules provides very strict rules directly from energy conservation and the concept that energy may be a flux of edges. My question here is whether this very brief analysis seems valid and if so, does it in fact provide a strict limitation for replacement rules?
Furthermore, if such a criteria be accepted, there is one interesting application that emerges quite immediately: Take the concept of energy as edge flux or edges changing upon update. Then say that a particle is some persistent and stable subset of the hypergraph that seems relatively invariant under hypergraph transformation up to isomorphism. Then, imagine the situation of a particle with some rest mass m which is really some energy content E. By forcing said particle to be stationary, one then sees that the there still exists an energy content of the particle despite a lack of motion. The only way in which this particle may contain energy, i.e. have edge changes without moving and changing its vertices, is some form of internal change of edges between the vertices that construct the particle. This internal change of edges may, potentially, be thought of as intrinsic spin or perhaps some other intrinsic property of the particle which is directly related to the fact that there is no situation where this particle may be without an intrinsic energy content.
