is proportional to the spatial frequency of bits. Given a momentum wave in a DM model, we can identify certain qualities of that wave: the wavelength and the orientation. However momentum is a signed quantity, so that a given orientation of the wave must be able to exist in 2 phases. All of this is extraordinarily simple in a DM model. The beauty of DP is that it lets us understand exactly, the nature of a smallest part of a momentum wave; a kind of momentum atom. It must be 2 spatially adjacent cells that are, at the same point in time, in different states. This is nice because in the DM RUCA each cell has 12 spatial nearest neighbors at the same point in time. When we use the time subscript “2t”, it means that τ is an even number. We use a subscript of “2t 1” or “2t ”(any odd integer) to indicate that τ is an odd number. The subscript t is used when it does not matter whether or not τ is even or odd.
E.g. S2x-1, 2y, 2z, 2t 1 = –1 and S2x, 2y 1, 2z, 2t 1 = 1
That combination represents the greatest possible momentum density. The combined space and state parities of the two cells determines the sign of the momentum vector, which, in this case is (1, 1, 0).
For S2x, 2y 1, 2z, 2t 1= 1 and S2x 1, 2y 1, 2z 1, 2t 1= –1 it would be (–1, –1, 0).
We have now given an unambiguous and exact definition of the DM representation of an atom of momentum. This is what was promised. While this may not be the best definition of momentum, there is no doubt that it is a possible definition given the general power of a RUCA. However what is very likely is that there will be found a set of different definitions that, overall, make for a better model.
At this point, we are going to go into depth on the exact meaning of DP “momentum.” We know that the momentum of a composite thing is the vector sum of the momenta of its parts. The converse argument is that every non-atomic object with momentum is the composite of parts where the vector sum of the momenta of the parts equals the momentum of the object. In a finite world, this kind of argument leads to atoms of momentum. In DP we have atoms of both angular momentum and of linear momentum. Such atoms of momentum are found in particles.
There is also something we must think of as momentum information. These are bits and if they could be examined and decoded, they would give us information as to an amount of momentum. They can be thought of as instructions for some computer program. What a particle has to do, in some sense, is to interpret (execute) the momentum instructions and then move the whole particle itself, along with the instructions, accordingly. Programmers understand the concepts of instructions and of data and this is very similar. It is very easy to write a block of computer code that has in it some vector to a new location in the memory where the block moves itself to, including the code, if it is executed.
We are not going to worry about the details, such as the mass or velocity of what is moved, but rather just concentrate on the most microscopic aspects of the process. The momentum information must also get moved because we expect it to stay in the vicinity of the thing being moved. An approximate statement about DP momentum is: “An atom of momentum ought to, every so often, move itself and an atom of energy one unit of space in one unit of time.” It’s actually more complicated but that’s the general idea. The fundamental atom of motion is a swap the states of 2 nearby cells. It may seem that DM momentum is doomed to always be zero if whenever something moves to the right, something else moves to the left. But even that will soon make sense. To understand all of this you need to understand the DP vacuum.
The DP vacuum contains bits and particles made of bits, 1’s and –1’s (or i’s and –i’s). Nothing is ever empty. There are no 0’s. Matter and energy, the vacuum and all else are full of bits. Particles are little machines that have particular patterns of design. In this model of DM, in a region with no particles, all of the bits are in the vacuum state. We assume that the vacuum state is the same for an ordinary particle and for an antimatter particle. This implies that, in a 2 state DM model, empty space must be some kind of pattern that is symmetrical with respect to matter and antimatter. This particular problem is considerably simpler in the case of a 3 state system, where the states could be 1, 0 and -1. It is somewhat unclear at this time as to the advantages and disadvantages of 2 state versus 3 state, but it is certain that either can be Universal so either can be forced into being a correct model. We expect that one or the other will be a better model.
When a particle moves, it doesn’t move into a completely empty vacuum, it moves through the bits of the vacuum or the bits of parts of particles. It might do so by somehow shoving aside the bits it encounters, as happens when a body moves through a fluid. This poses a number of problems for DP models. It can’t do so by ordinary superposition because everything is 2 state. Everything that moves in this DP model does so by a method called “Earthworm Motion” or EM. As the leading cells of a particle move forwards into the vacuum or parts of other particles, the particle’s bits are swapped ahead. Of course the vacuum bits or other particle bits are swapped into the particle! In fact a particle can be thought of as mostly vacuum! The vacuum states are transported through the particle as the particle inches forward. The trail behind the moving particle contains vacuum bits that have been displaced back along the path the particle is taking. Thus EM implements a different kind of superposition process than occurs in ordinary physics. EM is different than any kind of classical motion, although it bears some kind of resemblance to the way a jet engine transports itself through the air.
What must happen is that the existence of the pattern of bits that our DM model calls “momentum” must be interpreted by the DM rule in such a way as to cause the swapping of bits that in turn causes some fermion to end up as a quantity of mass moving at a speed proportional to what is indicated by the momentum information. On page 38 there is an example of a DM rule that makes it clear how it is that momentum information might be interpreted in order to cause causes the appropriate motion.
The definition of momentum must also take into account the implication of CPT that the signs of momentum are complemented when time is reversed. This poses an interesting problem for DM models in that momentum is represented by a purely spatial wave (with no explicit temporal information), yet the sign of the momentum must change under time reversal. In this DM model, that happens because the sign of B changes under time reversal. The sign of B changes because the 6 rules (if P=6) are executed in the opposite order when time is reversed.
We generalize the concept of a momentum wave to define the total momentum of a particle in a region of DM space-time; it is the vector sum of all the momentum atoms associated and traveling with that particle. The sum must include both of the time states: past and present. We require of the DM Rule, R, that the evolution of state conserve momentum.
