One of the most important and immediate objectives of our research here at the LRC is to address the “glaring lacuna” in Larson’s work, the inability to calculate the atomic spectra. Larson tried to work it out, but temporarily gave it up, when it appeared so complex and obtuse a subject that it became apparent that it would drain his resources and slow his progress in developing his RST-based theory, what we call his Reciprocal System theory (RSt).
It was Nehru who gave it the label with which we still refer to it today. While noting this great contrast with the success of the LST’s wave mechanics in explaining the “vast wealth of spectroscopic data,” he goes on to elaborate on the much heralded success of the LST theory:
The several quantum numbers, n, l, m, etc. come out in a natural way in the theory. Even the “selection rules” that govern the transitions from one energy state to another could be derived. The fine and the hyperfine structures of the spectra, the breadth and intensity of the lines, the effects of electric and magnetic forces on the spectra could all be derived with great accuracy. In addition, it predicts many non-classical phenomena, such as the tunneling through potential barriers or the phenomena connected with the phase, which found experimental verification.
Of course, all of this began with Heisenberg’s great discovery of the non-commutative multiplication in the first mathematical structure of quantum mechanics. As Bohr wrote Rutherford:
Heisenberg is a young German of gifts and achievement. In fact, because of his last work, prospects have at one stroke been realized, which, although only vaguely grasped, have for a long time been the center of our wishes. We now see the possibility of developing a quantitative theory of atomic structure.
In developing an RST-based theory, however, the second postulate limits us to an algebra of magnitudes that is ordered (absolute), commutative and associative (meaning its geometry is Euclidean). Nehru’s approach, an attempt to clarify the physical concepts of quantum mechanics, while keeping the mathematics, is therefore problematic, unless we drop the second fundamental postulate of the RST.
Fortunately, as described in the previous post, the new mathematics developed at the LRC, based on reciprocal numbers as analogs of the scalar/pseudoscalar ratios, maintains these essential algebraic properties. Using this algebra, we have been able to build a simple toy model of the motions and combinations of motions that is consistent with the second postulate and that contains the bosons and fermions (both quarks and leptons) of the standard model of particle physics and the baryons of the periodic table based on Larson’s 4n2 concept, as opposed to the 2n2 concept of quantum mechanics.
The challenge, however, has, again, been to identify the quantitative relations between these bosons, quarks and leptons, as observed in the experimental energy levels of the baryons. In short, we need the RST breakthrough that corresponds to Heisenberg’s quantum mechanical breakthrough.
Well, I’m happy to announce today that the needed breakthrough has arrived; at least it has as far as the toy model is concerned. Recall that our RST-based model, unlike the LST model and Nehru’s model, is not based on rotation, but rather the vibrations of the pseudoscalars, which we call S|T units, the SUDRs and TUDRs, which are inverse pseudoscalar/scalar oscillations. Figure 1 shows how these combine to form the entities of the standard model.
Figure 1. Scalar Motion Combinations
The middle colors, green, red and blue are used to indicate the relative balance of red SUDRs and blue TUDRs in a given combination. A green circle in the middle of a combo indicates an even number of each. A red color indicates more SUDRs than TUDRs, while a blue color indicates the reverse. We assume an initial value of one SUDR and one TUDR in the green balanced combo, and an excess of one kind of unit in the unbalanced combos.
This works out perfectly in terms of combining protons, neutrons and electrons, but the question has been how to fit the photons into these combos. In the quantum mechanical model, the electron is regarded as orbiting the nucleus (Bohr’s model), even though this was modified (the cloud model) to fit Heisenberg’s mathematical structure, wherein no definite orbital path could be identified.
In the S|T model, the electron doesn’t rotate around the nucleus, but becomes an integral part of the atomic structure, as shown in figure 2 below:
Electron
Figure 2. Combining Quarks and Leptons into Baryons
Even though the standard model is empirical, the mathematical relations of its entities are described by Heisenberg’s fundamental mathematical structure developed in two theories: The first theory is quantum electro dynamics (QED), and the second theory is quantum chromo dynamics (QCD). Both of these theories are based on rotations and suffer from the algebraic pathology of higher dimensional numbers, as explained in previous posts. The underlying mathematical structure is described as based upon the principles of symmetry in U(1)xSU(2)xSU(3) groups, but these groups are formed from numbers derived from rotations.
In our theory, there are no rotations, so the challenge has been how to show the different energy levels of the atomic spectra in the new model, which has no orbits or electron shells. The breakthrough has come by realizing that the combinations of motions in the S|T combos, while numerically balanced and accurate in the baryons and their combos are nevertheless what we might call internally polarized. This was understood by simply tabulating the SUDR|TUDR counts at the nodes of the combos. For instance, tabulating the S|T nodes in the combination of a proton, neutron and electron, as shown in figure 3a below, results in a polarized triangle, representing the deuterium atom, as shown in figure 3b.
Figure 3. The Polarization of Non-Ionized Deuterium
This is a remarkable and fortuitous result, since it permits the binding of a boson to the atom, as shown in figure 4 below, without changing anything, but the energy of the combo:
Figure 4. Combining Photons with Baryons
On this basis, we may now begin to develop a quantitative relation between photons and atoms in our model – the atomic spectra! Indeed, we might say that, perhaps, the prospects at one stroke have been realized, which have, for a long time, been the center of our wishes!