In the previous post, we discussed the “first and second ordering” of the periodic table, as described by physicist Albert Tarantola. The first ordering fits a 4n2 relationship, when the first four elements, hydrogen through beryllium, are placed in the first period, and the total number of elements is extended from 118 elements to 120 elements. Charles Janet proposed this table in 1929.
However, besides adding two additional, unknown, elements to the total of the table, his approach slides the noble elements out of their keystone positions, as especially evident in the Wheel of Motion form of Larson’s table. This is really not a problem, but one hopes it’s not the case intuitively, because it destroys the aesthetics of the wheel.
What’s most interesting about Janet’s analysis is that it agrees with Larson’s in that it places four slots in the first period (4*12 = 4), not two, as in the QM table (2*12 = 2.) However, Larson doesn’t fill these 2 empty slots at the beginning with full-blown elements, as does Janet, but instead he fills them with the proton, and the massless neutron. Thus, helium and deuterium are both in the first period and the “keystone” elements in the Wheel of Motion are the noble gases, completing their respective periods at the 6 and 12 o’clock positions in the concentric circles of the wheel.
Janet – 2,2|8,8|18,18|32,32
Larson – 2,2|8,8|18,18|32,32
QM – 0,2|8,8|18,18|32.32
Meanwhile, Hervé Le Cornec has shown, in what C. K. Whitney calls “a stunning demonstration,” that the atomic ionization potentials exhibit a strikingly simple underlying pattern. The new pattern reveals that, while the elements are indeed grouped into the four 4n2 periods (or eight 2n2 sub-periods) exhibited by all these tables, the s, p, d, and f energy levels of spectroscopy repeat themselves in a different sequence than they do in the quantum mechanics theory. Le Cornec’s empirical pattern is:
s | s-p, s-p | d-s-p, d-s-p | f-d-s-p, (f-d-s-p),
while the theoretical pattern from QM, based on the four quantum numbers, n, l, m, s, and several rules of selection, is:
s | s-p, s-p | s-d-p, s-d-p | s-f-d-p, s-f-d-p.
Janet’s sequential pattern is the same as QM, but the energy levels are grouped differently, requiring the addition of two more elements at the end of the sequence:
s, s | p-s, p-s | d-p-s, d-p-s | f-d-p-s, f-d-p-s.
Tarantola refers to the latter two patterns as a “first ordering, and the Le Cornec pattern as a “second ordering,” of elements, as if the two orderings were not mutually exclusive, but Le Cornec believes that his work, based on the square roots of the ratios of atomic number Z, with the atomic number of hydrogen (1), shows QM to be defective. Interestingly enough, the Le Cornec sequence cannot be regrouped to fit the Janet table, as can the QM sequence.
The reason why is because the Le Cornec sequence places the “s” before the “p” energy level, in all periods, not just in the second, and both the “d” and the “f” levels in the third and fourth periods occur before the “s” and “p” levels, not between them, suggesting that the science of quantum mechanics is still not settled, and that the Schrodinger equation’s complexity hides an unknown, yet simple mathematical structure that organizes all atomic ionization potential (AIP) data.
Of course, this is exactly what we are looking for at the LRC, since, with our new, reciprocal, numbers, based on 1D, 2D and 3D pseudoscalars, and the recent discovery of how they fit so naturally into the tetraktys, giving us a non-pathological, multi-dimensional, algebra, we hope to demonstrate how this pattern of AIPs emerges from the natural sequence of these numbers; that is, we hope to be able to show that the periodicity of the periodic table, and the pattern of energy levels that forms it, are simply the result of nature counting from 1 to 4, using a ratio of pseudoscalars, not scalars.
However, the mathematical pattern of the periods is not the only thing we need to understand. While the right lines and circles inherent in the Euclidean geometry of Larson’s cube provides us with the multidimensional algebra with which to formulate the initial units, combinations of these units and the mathematical relations between them, we still need to quantify these units. We need to assign physical magnitudes to these mathematical units.
The magnitude of the RST’s universal motion, relative to its matter, depends upon the magnitude of the discrete space and time units that we select. Larson’s approach was to use the Rydberg frequency, R, and the speed of light, c, for this purpose. Since the constant speed of light plays such a central role in physical phenomena, it is reasonable to assume that the magnitude of the unit ratio, ds/dt = 1/1, is equal to c. This means that, if we can find the correct magnitude of either the space unit, or the time unit, we can easily calculate the magnitude of the reciprocal aspect.
Larson selected the Rydberg constant for this purpose, since it also seems to play a central role in the spectral phenomena of the hydrogen atom. The Rydberg frequency is 3.2899 x 1015 Hertz, so the reciprocal of this frequency is a time unit equal to 3.03961 x 10-16 seconds. The accepted value of the Rydberg constant has changed slightly since Larson’s day, so this figure differs slightly from his.
Since the units are vibrational, the actual unit of time, which Larson called the natural unit of time, that enters into the unit progression ratio, is half of this value (1/2 cycle), which he calculated as 1.520655 x 10-16 seconds, as found in his publications. Hence, the natural unit of space is then calculated as c divided by this quantity of time, or 4.558816 x 10-6 cm. So, the physical situation, at this point, is a constant increase of space/time, in three dimensions, the magnitude of which is 2.997930 x 1010 cm/sec, the speed of light, measured relative to matter (here, I use the figures in Larson’s publications, which, again, have been slightly modified since his day.)
While this seems to be a reasonable approach for deriving the magnitude of the discrete units, it’s never been directly substantiated, as far as I know. What’s more, at first blush, if the speed of light, s/t = 2.997930 x 1010 cm/sec, is the unit speed of the 3D expansion, as measured by the increase of its spatial radius, the RST’s inverse of this, t/s = 3.335635 x 10-11 sec/cm, would be its unit inverse-speed, as measured by the increase of the radius of its temporal expansion.
Now, if we take Larson’s view of the radiation energy equation, E = hv, where the frequency term 1/t is cast as a velocity, with dimensions s/t, instead of 1/t, forcing the dimensions of Planck’s constant, h, to be t2/s2, as a consequence, then we have a velocity to work with, and the task to explain the meaning of the new dimensions.
One view we can take is that Larson’s modifications of the dimensions of frequency and Planck’s constant gives us a new understanding of the relationship of what we might call Einstein’s constant, s2/t2, and its inverse, what we will now call Larson’s constant, t2/s2.
Since the dimensions of mass, t3/s3, are related to energy, t/s, by Einstein’s constant, then it’s a logical conclusion that the dimensions of inverse mass, s3/t3, are related to velocity, s/t, by Larson’s constant.
This is tantamount to asserting that Einstein’s mass-energy equation, E = mc2, is just the reciprocal of an inverse-mass-energy equation, 1/E = (1/m)(1/c)2, even though Larson never really wrote this equation down, as far as I know. In other words, 1D energy is equal to 3D energy (mass) times Einstein’s constant, while 1D “velocity” (radiation) is equal to 3D velocity (inverse mass) times Larson’s constant.
However, the fact that, in the development of the theory, we have to convert the 1D velocity, s/t, into a frequency, 1/t, via “directional” reversals, in order to transform it into a quantum unit, while we don’t have to convert the 1D energy, t/s, into a frequency, 1/s, in order to transform it into a quantum unit, causes us to wonder why. Could it be that the dimensions, t/s, can be expressed as a spatial frequency, 1/s, with a temporal wavelength, analogous to the spatial wavelength of the 1/t temporal frequency?
If the answer to this question is yes, as the RST strongly implies, then the spatial-radiation energy equation 1/E = (1/h)(1/v) —> s/t = s2/t * 1/s, the inverse of the temporal-radiation energy equation, E = hv —> t/s = t2/s * 1/t, would also hold.
But even if the mathematical operations make sense, that fact doesn’t necessarily mean that the physical operation makes sense. Even if we can make sense of a conversion from frequency to velocity, and vice-versa, what is inverse energy? We know dimensionally, this term is velocity, but the LST community’s question would be, “Velocity of what?”
For the RST community, however, a quantity of s/t motion is just as viable as a quantity of t/s inverse-motion. When Einstein’s equation was discovered, it didn’t take long to find a way to transform mass into energy and check it, but how do we find a way to check the inverse equation? I have some ideas.