They say that the standard model of particle interactions (SM) is the greatest intellectual achievement of the 20th Century. It stands as something the LST community can point to that explains the structure of the physical universe. Of course, they confess at the same time that it’s far from perfect or even complete, but many books are written every year extolling its virtues. Certainly, no one in the LST community believes that future physical theory won’t contain the SM in some form or another.
However, when we view the SM from the perspective of the chart of motions, we see a great simplification. In the chart of motions, there are simply four degrees of magnitude in four bases of motion, but in the SM four types of forces, based on only one type of motion, are used to classify four elementary types of entities in each of three categories (disregarding anti-matter particles). The four entity types classified by the four forces are divided into two sets: the quark type form one set, constituting the heavy particles of the atom, the protons and neutrons (nucleons), and the lepton type form a second set, constituting the light particles of the atom, the electrons and neutrinos. The interactions of these four types of atomic entities are characterized as governed by the four forces of the SM, three of which are understood fairly well by the LST community, while the fourth is not.
The three forces that are understood are the so-called electromagnetic, the weak, and the strong force. The force that is not understood is the gravitational force. However, when the SM is expounded by LST teachers and authors, the concept of force itself, or of a force field, upon which the SM’s classification scheme depends, is seldom explained in detail. Yet it is important to recognize that the force field concept is treated as an autonomous concept in LST physics, as if it were something that has an independent existence like acorns or automobiles.
For instance, the theoretical strong force arises from the concept of a field quantum that is thought to bind three quarks as one, called a gluon. The theoretical weak force is thought to be a property of another field quantum, called an intermediate vector boson (IVB), that transforms one lepton, or quark, into another lepton, or quark, while the theoretical electromagnetic force is thought to be a property of a third field quantum, the photon, that transforms the charges of quarks and leptons. The theoretical field quantum of the gravitational force is thought to be the Higgs boson, but the interaction it is supposed to catalyze hasn’t been observed yet.
Of course, energy conservation is the governing principle of all these interactions, but it’s energy in the form of charge conservation that is the key to understanding the SM. The idea is that anything that happens in the physical universe is caused by these four force interactions, and they are regarded as properties of charges, not electrical, magnetic, and gravitational charges, but electrical and color charges. The color charges are the charge of the strong force, the electrical force is the charge of the electromagnetic and weak force, called the electroweak force.
Quarks have fractional electrical charges and one fractional charge is twice as great as the other, so two of one, when combined with one of the other, either totals one whole electrical charge, or eliminates it, depending upon the configuration (2(2/3) - 1/3 = 4/3 - 1/3 = 3/3, or 2(-1/3) + 2/3 = -2/3 + 2/3 = 0). The gluon quanta of the strong force carries the color charge of quark interaction. They are called red, green, and blue, and any three bound quarks are associated with one of the three color charges, so that their combined color charge is always white, or neutral (zero).
Both energy and net electric charge must be conserved in all force interactions. No matter what, when physical entities interact, energy must be conserved and the net charge must be the same after as before the interaction. However, if we regard force as a quantity of charge, whether color charge, or electric charge, the question that really needs to be answered is, what is charge?
In the case of the EM charge, the force quanta, the photon, is not a charge carrier, but in the case of the weak charge, the force quanta, the IVB, is the charge carrier. In the case of the strong charge, the force quanta, the gluon, is the color charge carrier. Whether the force quanta, called bosons, are charge carriers, or not, depends on the particulars of the gauge principle that applies in each case. So, what are gauge principles, and how do they relate to these four “fundamental” forces? The short answer is that they are principles of symmetry that relate to energy/charge conservation, or invariance, but that doesn’t tell us much.
Gauge theory is the underlying principle of the SM. It was used to modify the initial quantum electrodynamics (QED) theory of the SM, and it is the basis of the SM’s quantum chromodynamics (QCD), often referred to as a “pure gauge theory.” In order to understand the underlying symmetries of the SM, it’s necessary to understand Lie groups and Lie algebras and how they contain elements of rotations expressed as products of multi-dimensional complex numbers. These abstract concepts express magnitudes of “spin” and “isospin” that enable LST physicists to “renormalize” their calculations of wave equation solutions, predicting the outcome of particle interactions. Without this capability to renormalize the calculations, the interaction theories give nonsensical results, but with it, the theories are quite successful, and it is the identification of the appropriate Lie group, in which the pattern of the charge properties is revealed as a specific mathematical structure, that makes renormalization possible. In other words, given the mathematical structure of this pattern, and the observed strength of the relevant charge (coupling constant), the calculations give the accurate predictions of the LST’s SM.
Given the nuclear model of the atom then, each force of the SM exhibits an underlying mathematical structure that forms a unique Lie group that pertains to the domain of the relevant charges, revealed through the pattern of their properties. Thus, the EM force pertains to the electrically charged Coulomb forces of interaction between atomic constituents, binding electrons and protons together for instance, and it always involves the bosons of radiation, or photons. This pattern of charge properties exhibits the mathematical structure of the Lie group known as U(1), described by the single dimensional value of a complex number in the unit circle. The pattern of charge properties exhibited by the weak force, binding nucleons into nuclei, always involving IVB bosons, is described by the two-dimensional Lie group known as SU(2). Finally, the pattern of (color) charge properties exhibited by the strong force, binding quarks into nucleons, always involving gluon bosons, is described by the three-dimensional Lie group known as SU(3).
Hence, mapping these Lie groups to the chart of motions suggest a correlation, as shown below:
However, the fact that, in the SM, the charge of gluons comes in the form of the three primary colors, to convey the concept of color charge, with the net charge of the three combined charges equaling zero, analogous to the white result of combining red, blue, and green colors, and the use of the same analogy, in the base 4 motion of scalar motion, is purely coincidental. Nevertheless, it shows a close connection between the central concept of n-dimensional force, used in the SM, and the central concept of n-dimensional motion, used in the motion chart.
Hence, while the difference between the two approaches of classification is conceptually divergent, the intimation is that there is an underlying commonality. One that we clearly expect and need to clearly understand, but which must be understood in terms of motion, not force, since in the RST, force is a property of motion, a quantity of acceleration, which is energy per unit time.