I didn't present part 3, because it's supposed to show the actual calculations of the spectra of a given element. The group was surprised to learn that the LST's wave equation can only be used to calculate the Hydrogen and Helium spectra, since it cannot be solved for three or more electrons. However, the LST community says it works "in principle" for the others (see here.)

Of course, our new scalar-motion model is not based on the principles of vector motion associated with orbiting electrons. In fact, if we go all the way back to the fundamental basis of the LST's quantum mechanics, the de Broglie equation, where the idea of wave/particle duality started ( λ = h/mv), we have to take issue with the whole concept, because our model is only a combo of oscillating space (time) and time (space), but more on that later.

The most immediate challenge is to account for the line spectra of the elements in our new model. Though the complete answer is not yet available, the beginning point is the scalar motion equation, where the middle term equals the inner portion of the space and time oscillations:

S|T = 1/2 + 1/1 + 2/1 = 4|4

This is the LRC's scalar motion equation of the photon, combinations of which, as we've shown, lead to our standard model of particles and, most recently, the periodic table of elements. In the process, we've discovered the reciprocal nature of the eight sub-periods of the table, making up its four periods. Now we want to be able to take a given element of the table and calculate its line spectra, something the LST community can't do with their quantum mechanics and its wave equation.

Nevertheless, the accomplishments of their vector-motion based model are quite impressive. They use the four so-called quantum numbers in their wave equation to model the empirical data, even though they can't solve that wave equation for many body calculations. However, the concepts of mass, energy, angular momentum and quantum spin, together with Planck's constant have enabled them to move forward, in spite of the mysterious quantum mysteries that emerge from the little understood concept of quantum spin and the de Broglie equation.

Coming up with a whole new model that can replace this LST model of spinning, orbiting electrons, the binding energy of which counteracts and balances the energy of the angular momentum produced by the moving masses, even though that energy gets shielded by the electrons in the closest orbits to the nucleus, until the outward energy of the momentum overcomes the energy of the inward electrical attraction, ionizing the atom, is a tremendous challenge.

Fortunately, we too have an outward versus inward force, which models the same behavior, where, as the outward force increases, with each new photon absorbed, the inward force is eventually overcome and the atom is ionized. To understand this model, we need to examine the middle term of our scalar motion equation. Recall that the equation for the positively charged proton is:

S|T = 10/20 + 10/13 + 26/13 = 46|46 num, and for the negatively charged electron, it is:

S|T = 6/12 + 6/3 + 6/3 = 18|18 num.

The value for the middle s/t term of the proton, the inward portion, which is the motion corresponding to the LST concept of electrical charge, is 13-10 = 3, while for the electron, it is 3-6 = -3, so they normally balance out each other for a total of 16/16, or unity. This would be equivalent to what is termed the "ground state of Hydrogen," in the LST model. Since the displacement from unity of the inner term is greater to the time side (> 1/1) of the unit progression in the proton, we label its "charge" as "positive," and since it is greater to the space side (< 1/1) in the electron, we label its "charge" as "negative."

Now, if we add a photon to the electron, it adds a 1/1 balanced unit to the total s/t of its inner term:

S|T = (6/12 +

**6/3**+ 6/3) + (1/2 +

**1/1**+ 2/1) = 7/14 +

**7/4**+ 8/4 = 22|22

So the space displacement of the electron (4-7 = -3) remains unchanged, but the "strength" or energy of the atom, as a combination of the proton and electron, has increased to 17/17, from 16/16. It's important to note that this 1-unit increment in the inner term of the atom is due to the addition of the photon's 4|4 num, which reminds us of the unexplained number 4 in Balmer's equation, and the constant in Rydberg's equation, obtained when Balmer's constant is divided by 4 and inverted from wavelength (λ) to wave number (1/λ).

What happened (as we've explained previously) is that Balmer discovered that, if he multiplied his constant times the ratio of n/(n - 4), where n = (m

^{2}) and m => 3, he could calculate the observed wavelengths of the line spectra of Hydrogen. However, this limited the range of the calculations to the third quantum level and above, because 1

^{2}- 4 = -3 and 2

^{2}- 4 = 0. Rydberg solved this problem later, simply by rearranging the terms. He divided Balmer's constant by 4 and inverted his equation for wavelength to an equation of wave number, obtaining:

1/λ = R(1/n

_{1}

^{2}- 1/n

_{2}

^{2}), n

_{1}> n

_{2}

which enabled the calculation to start from the ground state and increase from there.

On this basis, Neils Bohr proposed his atomic model, which worked well for Hydrogen's single electron, but failed for the other elements, with multiple electrons. We were able to also calculate Hydrogen's line spectra, based on the scalar motion equation, but we were not prepared to follow the LST into the world of the wave equation solution, since it is based on the dimensional character of the 3d coordinate system and it was difficult to see how a combination of space and time oscillations had the necessary dimensional characteristics.

However, now that we have overcome that challenge, we are faced with finding the equivalent of the LST community's outward centrifugal force of angular momentum versus the inward centripetal force of electrical charge concept, in the context of 1d, 2d and 3d orbitals, which constitutes their accepted vector motion model.

In the next post, I will outline our approach to that challenge.