In the previous post, I explained what is meant by a system of theory, as opposed to a theory based on that system. I also explained that the RST is a new, deductive, system of physical theory that I have exploited to develop a new theory of the standard model of particle physics. Accordingly, it is referred to as an RST-based physical theory and denoted as RSt, with the lower-case t indicating the difference, thereby distinguishing the theory from the system, or program of research, it is based on.
The RST is a deceptively simple system of research. It begins with two postulates from which a universe consisting of nothing but motion is deduced, by developing the consequences of the postulates (speculations). These two postulates are:
1) The universe is composed entirely of one component, motion, existing in three dimensions, in discrete units, with two reciprocal aspects, space and time.
2) The physical universe conforms to the relations of ordinary commutative mathematics, its magnitudes are absolute and its geometry is Euclidean (i.e. flat).
Now, the moderators of this forum want me to lay out the evidence in one post that this is a valid, scientific, system for developing physical theory. I really don't understand the reasoning behind this requirement, but as a new-comer I want to comply, even though to me it's folly to think it can be done in one post. Nevertheless, assuming the reader understands what the evidence is actually establishing (i.e. the validity & usefulness of the system), here is what I will start with:
Quantum spin and spin states: We all know how Pauli was unable to make the wave equation relativistic, if it were to incorporate quantum spin, yet Dirac not only achieved it, but his relativistic wave equation actually required it, astonishing the world even to this day. Nevertheless, as Bruce Schumm explains in his book Deep Down Things (page 187), physicists don't have "a clue about the physical origin of spin." It truly is a vexing enigma, because quantum theory would not be possible without this mysterious observable, and yet no one knows where it comes from, or even how it can exist (what cycle of rotation only completes in two, 2pi, rotations?).
Happily, the RSt that I am developing explains quantum spin in terms of its discrete units of motion (more detail on these to come.) These units are actually discrete, oscillating, volumes (3d space/time ratios), which combine and interact according to varying degrees of freedom in the theory. A given degree of freedom determines how the units can possibly combine and begins with 1, then doubles to 2, then to 4 and finally to 8 unique combinations, as dimensions increase from 0 to 3. It's important to note that these four powers of 2 are inherent in the numbers of the first four levels of Pascal's triangle, which also happens to be isometric to the number of "directions" (poles) possible in each of the three known physical dimensions (four counting zero):
1st dimension = 20 = 1 (a mathematical monopole, analogous to a geometric point)
2nd dimension = 21 = 2 (a mathematical dipole, analogous to a geometric line)
3rd dimension = 22 = 4 (a mathematical quadrupole, analogous to a geometric area)
4th dimension = 23 = 8 (a mathematical octupole, analogous to a geometric volume)
In QM, the possible spin states of the standard model particles are calculated by multiplying the spin of a particle type by 2 and adding 1:
As it turns out, the combinations of the RSt's units of motion follow the same pattern of quantum spin and number of spin states, as shown above, indicating that these motion combinations follow the QM rules of quantum spin, as observed in physical observations. This is a good start to finding evidence that the system works , but many questions remain, which unfortunately can't all be addressed in one post. In the next post, I'll show how the existence of the theory's units of motion and their properties (including 4pi spin) are derived, leading inevitably to combined entities of these units that can be identified with the bosons and fermions of the standard model, having these identical spin states, if it's ok with the moderators to proceed.