It’s been so long since I’ve posted anything on research, I’m afraid people will think I’ve abandoned the work. However, the truth is, I’ve had to turn my attention to practical matters, leading to a neglect of the theoretical.
But I have some unpublished articles that have lain around for sometime, because I haven’t been able to get up enough momentum to finish them, or think them out completely. I think I will go ahead and post them anyway, though, just to get something out there to think about. Maybe that will help me get going again, even if it might be embarassing. Here’s the first one:
In our virtual lab in Second Life, we’ve been playing with SUDRs and TUDRs and their combinations, S|T units. Here is a short video of three S|T units combined as a neutrino triplet from our toy model of standard model entities:
The animation of the SUDR (red pseudoscalar) is driven by the changing diameter generated by the difference between the sine and -sine function, while the TUDR (blue pseudoscalar) is driven by the changing diameter generated by the difference between the cosine and -cosine functions.
In essence, this means that the expansion/contraction of the pseudoscalars is a function of two, counter-rotating, rotations, as shown in figure 1 below:
Figure 1. Two Counter Sine Functions (left), and Two Counter Cosine Functions (right), Define Inverse Diameters of Oscillating Pseudoscalars (not synchronized)
Consequently, with these two functions, we can analyze the pseudoscalar oscillations, and their combinations as S|T units. The first thought was to plot the changing 1D, 2D and 3D pseudoscalars in terms of π, which produced some interesting wave forms, but then the idea ocurred to us to take a point on the surface of the pseudoscalars as a zero reference. This means that the origin “moves” with respect to the reference point and gives us a way to compare the n-dimensional magnitudes as a function of time (space); that is, the 20 point increases from 0 to 1 * 10 , and back to 0, while the 21 function changes from 0 to 6 * 11, during the same time, while the 22 function changes from 0 to 12 * 12, and the 23 function changes from 0 to 8 * 13 and back, during one cycle.
In this way, everything is positive, and never negative, just as the magnitude of the diameter is always positive and never negative. While this is interesting, the big challenge is to capture the inverse relationship. In what way is the TUDR oscillation the inverse of the SUDR? From the standpoint of the expanding/contracting diameter, there is no difference between the two oscillations of figure 1. The oscillation on the left is the +/- cosine projected on the horizontal diameter, while the oscillation on the right is the +/- sine projected on the vertical diameter, but the geometric inverse of the unit diameter is twice its size.
If this were not bad enough, how do we represent the temporal diameter with a spatial diameter? The answer, I believe, is to follow the math. As far as the math is concerned, the inverse of 1/2, is 2/1, and this is simply a doubling of the numerator, from 1 to 2, and a halving of the denominator, from 2 to 1, the mediato/duplacio math of the ancients.
Another way to express the same result is to keep the size of the diameter the same, but to quadruple the frequency of the TUDR, with respect to the SUDR. Figure 2 incorporates this idea.
Figure 2. Normalized SUDR and TUDR Oscillations
Of course, this is tantamount to assuming that the relative frequencies of the oscillating pseudoscalars is a valid comparison, but I don’t see any other way of comparing them. If this works, we can leverage the knowledge of hetrodyning and harmonics. Something we’ve already explored to some extent.