Wow, it is hard to believe that I started this idea of a photon as a quaternion 7 years ago (first post:
Photon model as a quaternion, posted: 15-Feb-2012) and it has taken all that time and dozens of dead-ends to get where it is now. It is interesting to review how I get from one idea to another.
I have been looking for a way to convert the color quaternion to a conventional representation of frequency and ended up building a spreadsheet of the known frequency bands. One of the things that has always bothered me was the sheer number of "natural units" (Larson's "direction reversals") that must be packed together to get to the extremely low frequency band (ELF), the bottom of which--the longest wavelength--being some 2,194,763,294,778,660 "units" -- that's TWO QUADRILLION UNITS. Given that all the other displacements in the Reciprocal System don't get higher than ±16, I cannot see how this can be a viable structure, or a "natural consequence."
Last night I realized that the frequency spectrum is a logarithmic scale (base 10 log) and the log of this ELF frequency is only about 15. Now THAT makes more sense... then I realized that, as an angular velocity,
frequency is a recursion. What I mean by that is that angular velocity, like speeds in the time region, is a growth measure--layers of skin on an onion, and only the
outer skin is the one that matters for interaction.
We see this structure already in Larson's atomic model, as well as conventional science. Take, for example, gold (AU), atomic number 79. With displacements of 4-4-(7), it
does not have 79 units of anything, because we don't count the inner layers (4-3, 3-3, 3-2, 2-2, 2-1) unless we want to get the atomic number. Conventional science does the same, by references to the prior noble gas: [Xe] 6s
1 4f
14 5d
10--it does not include all the inner electron orbitals.
The center of this "onion" appears to be on the green/magenta rotation, at 12 natural units. Visible light runs from 8 (410nm) to 16 natural units of space (729 nm), an
octave. Octaves are common in Nature, so this makes sense (conventional spectrum is based on powers of the meter).
The next layer out runs from 4 (UV-A, 364 nm) to 32 (IR-A, 1458 nm) natural units. Now this seems like a big spread--but we did not remove the visible part from 8-16 units, upon which it is built.
- Angular recursion
- Angular-Recursion.png (14.34 KiB) Viewed 21537 times
As a consequence of this recursion, the "A" band is split into two halves, UV-A (ultraviolet) and IR-A (infrared),
which is observed. The next layer is the UV-B:IR-B, then UV-C:IR-C.
What is not accounted for in the conventional frequency model is the reciprocal relation. We have the spatial displacements well documented (from red down to ELF), because the frequency distribution is exponential--the further you go from red, the larger the spatial gap (wavelength).
However, in the opposite direction, all we have is blue, UV, EUV (extreme UV), SX (soft X-rays), HX (hard X-rays) and gamma rays. Space seems to have been "compressed out"... because on this side, it isn't a
wavelength, but a
waveduration... the displacement is in time and "more time = less space." If one were to look from the temporal aspect, then we'd see dozens of bands, rather than just four of them.
This recursion model of the frequency spectrum also parallels
Nehru's concept of "electric folds" that he once presented to explain atomic orbitals. It also makes the photon behave in the same manner as other rotating systems, both magnetic and electric. However, it also proves that Larson's model of the "direction reversal" is wrong (only applicable to low displacements in the visible light region).