The definition of DM charge is a bit complicated. We have to explain separately with the electron, charge = –1, the d quark charge = –⅓ and the u quark charge = ⅔.
Associated with the key structure of an electron is a three charge-step orbit. Each charge-step takes place in the Na sub-array, and therefore the 3 charge-step orbit takes one full cycle of 6 micro-time steps. The electron’s –1 unit of electrical charge is a consequence of a 3 charge-step per cycle process in the Na sub-array.
A d quark has a similar key structure, also in the Na sub-array. However the d quark completes only 1 charge step per full cycle of 6 micro-time steps. The d quark’s -⅓ electrical charge is a consequence of a 1 charge step per cycle process in the Na sub-array. As should be obvious, there are 3 possible phases for doing 1 step per cycle during even time (in the Na sub-array). Those correspond to the 3 possible colors of the up quark. Of course, an anti-up quark, with its key structure in the Cl sub-array, would have an anti-color. These colors are indicated in the rule table on page 34.
A u quark has a similar key structure which is in the Cl sub-array. The u quark completes 2 charge steps per 6 step cycle which results in an electrical charge of ⅔. As with the up quark, it is obvious that the are 3 possible phases for the u quark, and these again correspond to the quark color.
An anti-particle is the same as a particle but with the key structure in the opposite sub-array. Since the 3 step cycle in the Na sub-array runs in the opposite direction to the 3 step cycle in the Cl sub-array, the handedness of the anti-particle is the opposite of the regular particle. Further, if time is reversed, the 3 step cycles in each sub-array run in the opposite order to the way they do when time runs forwards.
Charge Squared (q2) can be thought of as communication. A digital message is communicated at the speed of light. In ordinary physics the square of the electron charge, e2, is equal to αħc. When 2 charged particles interact, the magnitude of the force is proportional to the product of their charges (q2) divided by the square of the distance. The QED model for such interactions is the exchange of virtual photons between the 2 particles. In DM one interpretation of αBLT-1 (the DM equivalent of αħc) is that information is being communicated at the speed of light. Obviously, the most microscopic act of communication involves the swap of 2 Bits that are spatial neighbors. The kind of communication process that involves longer distances is by a photon traveling from one particle to another. When information leaves a particle, conservation of information mandates that the information in the particle be changed. Similarly, the arrival of information must change the state of a particle. This is a basic aspect of charge interaction in this DM model.
Associated with every cell are P (P=6) different neighborhoods (similar, except for the orientation). An example of a neighborhood is to consider the 8 squares that a king can move to from the middle of a chessboard. Those 8 cells can be thought of as the King neighborhood of the square the king is on. In DM, the cells are organized with parity (each cell being red or black as in checkers, or just plain even or odd). The physics defined by the Rule is Chiral (left-handedness being different that right-handedness). The function of the Rule is to specify how things change. For reasons of economy, we insist that the rule be reversible. It must be universal (the CA must be a UCA, but the logic for DM being a RUCA is overwhelming). A rule is usually defined by a state neighborhood and an input-output neighborhood along with a set of transitions defining how the state neighborhood changes the input state into the output state. At each instant in time (for each successive value of τ), all of the cells are simultaneously involved in executing the neighborhood rules. The system effectively looks at the states of every neighborhood to decide whether or not to change the states of cells in every corresponding result input-output neighborhood. All such systems are called Cellular Automata (CA).
Rules about the Rules; eventually every rule must:
1. Be as isotropic as possible.
2. Be deterministic and reversible.
3. Have chiral spin associated with motion.
4. Have no net effect when applied twice in succession to the same array.
5. Support all aspects of CPT symmetry
6. Have no ambiguities as to what happens to every bit.
7. Be able to be applied in all three planar orientations.
8. Be able to be applied in 4 orientations at once, in a plane, without ambiguity.
9. Be able to advance bits into the vacuum.
10. Be Computation Universal.
11. Conserve all conserved physical quantities.
12. Correspond mathematically to laws of physics.
13. Allow for the creation, annihilation and motions of particles.
14. Support particles and their conjugates properly.
15. Support charge, color charge, energy, linear and angular momentum…
16. Convert the representation of velocity into the appropriate motion.
17. Be consistent with QM, QED, Standard Model, Relativity, Gravity.
18. Implement particle stability and half-life characteristics.
A DM Rule is in the present, is in the past.
Rules A, B, C & D are applied to XY planes as R0, XZ planes as R2 and YZ planes as R4.
Rules F, G, H & I are applied to YZ planes as R1, XZ planes as R3 and XY planes as R5.
Patterns A, B, C, and D are the rule used during even micro-time steps. Patterns F, G, H, and I are the rule used during odd micro-time steps. Rule E (which is similar to rule I) is an example of a pattern that cannot be used during an even micro-time step because it could result in an ambiguity with rule C as the 2 Cl cells (the ±i cells) would each be enabled to swap to 2 different cells at the same time. The same is true for rule J which cannot be used during odd time steps because it could cause an ambiguity with rule F. Each set of 4 patterns is designed so that it is not possible for more than one of the patterns to indicate that a given cell should be swapped. It is easy to see that sub-rules A, B, C and D are the same pattern, each rotated 90° from the previous pattern. Rules F, G, H and I are the mirror images of B, A, D and C respectively, while the present (light gray cells) are in the Cl sub-array ( i and –i) while the past cells are in the Na sub-array ( 1 and –1).
These 8 sub-rules make a Rule that meets the criteria numbered from 1 through 8 inclusive in the table of Rules about the Rules. This Rule was selected solely on the basis that it illustrates what it takes to meet the simplest criteria. Whether or not this Rule meets the other criteria has not yet been investigated. We know that this rule has many fatal flaws. We include it here only to convey the flavor of what a good rule might look like. In all 10 of the diagrams above, the present cells have a light shade and the past cells have a darker shade. The particular neighborhood configurations of cells in the present (the present is always shown as light gray) are the only ones that determine whether or not there will be a swap of the 2 cells in the past (the past is always shown as darker gray). The question as to whether or not to swap is not influenced by the state of the cells being swapped. In the case where the 2 cells being swapped are in the same state, they are still swapped but there is no consequence of the swap. If there is not an exact match to one of the patterns shown above, no swap will occur.
All 4 of the upper set of patterns are applied in every YZ plane, during τ6n 0, to sense all appropriate sets of cells in the present and to swap pairs in the past whenever there is a pattern match in the present. It can be done simultaneously or in any order so long as everything possible is done once and nothing is done more than once.
At time τ 6n 1, Rule R1 is applied next. The situation is similar except the patterns are applied to the YZ planes, and since the present will be the imaginary or Cl sub-array, the cells potentially swapped will be in the real or Na sub-array. The 4 patterns in the lower picture are applied to every appropriate pair in the imaginary or Cl sub-array
(E. g. C2x, 2y, 2z 1, C2x 1, 2y-1, 2z 1 for all x, for all y and for all z such that x y z is odd).
At time τ 6n 2, R2 is then applied in the XZ planes, the upper picture;
At time τ 6n 3, R3 in XZ planes, the lower picture.
At time τ 6n 4, R4 in YZ planes, the upper picture.
At time τ 6n 5, R5 is applied in XY planes, the lower picture, to complete one full cycle of six micro-time steps.
