Energy, B/T, is the temporal frequency of bits. An atom of energy is 2 cells that are:
1. co-located spatially,
2. temporal neighbors,
3. have different states.
The 2 cells need to have the same spatial coordinates but different temporal coordinates. The consequence is that the 2 cells must be separated by 2 units of time (in this case 2τ, 2 micro-time steps). Notice that energy is not explicitly present if you stop the DM model, since it requires 2 cells that are separated by 2 units of time. The Salt Array consists of 2 sub-arrays separated by 1 unit of time. Energy is implicitly present since by looking at the Rule, we can tell what the next state will be. One atom of energy exists in every location where a rule has caused 2 neighboring cells that differ in state to swap. It exists nowhere else. Unlike charge, energy has the same value going forwards and in reverse. This means that energy does not need a second-order representation in 2 adjacent time steps! CPT requires that the sign of energy be not affected by the direction of time. The definition of energy must take into account the Rule and the time phase, α Modulo 6.
E.g. S2x, 2y, 2z, t= 1 and S2x, 2y, 2z, t 2= –1 give ½ unit of energy, B/2τ.
That combination represents the greatest possible energy density. Since we are supposing that the basic atom of motion is a swap, then units of energy must be created in pairs. That means that the atom of energy is B/τ, B/2τ B/2τ.
It should be obvious that anytime a swap occurs, where the pair of swapped states are not identical, the result will be energy. Thus energy is present whenever temporal change occurs.
In this DM model, all energy is found in particles. It may not be true that all particles carry appreciable energy. What we know about the vacuum of ordinary physics makes it clear that there has to be a background flux of essentially random particles in the vacuum. Of course that apparent randomness is the result of a deterministic computational process that conserves information. Nothing is actually random, but it can be orthogonal to local phenomena. Cellular Automata are wonderful mechanisms for producing endless apparent randomness from simple initial states. [1] In DP we confine that behavior to the trajectories of the particles. In a way similar to kinetic theory, the apparent randomness is in the deterministic microscopic motion and interactions of the particles. In general, the DM equivalents to randomness are processes that are usually orthogonal to most other things. As with momentum, we require of the DM Rule, R, that the evolution of state conserves energy.
Energy is a conserved quantity based on nothing other than the Rule. As we shall see, many of the observed symmetries of physics can be consequences of the more primitive conservation laws. Since the DM model has energy conservation, it is natural to expect that asymptotic continuous time reversal symmetry will be a consequence.
It should be clear that energy and momentum are intimately connected in this DM model. When some structure moves, the configurations of bits that represent its momentum are both the generators of its motion and the producers of energy. The microscopic discrete representation of energy and momentum in DP do not depend on the reference frame chosen by an observer; they are absolute and are based on a common fixed reference frame. Nevertheless, the mathematics of energy and momentum allow the use of arbitrary translational reference frames for processes above the most microscopic.
[1] Stephen Wolfram: go to http:/www.stephenwolfram.com/publications/articles/ca/ for references on 20 articles about Cellular Automata written from 1982 to 1988. A New Kind of Science, Wolfram’s monumental book, should be published in 2001 or 2002.
