The 3D Preon Model
Doug
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As I have already admitted, to my chagrin, I was trying to build the LRC’s preon model using the 2D square root of 2-based number system, but I couldn’t get there. When I realized my mistake, I started over, using the correct 3D square root of 3-based number system, but now I had to deal with a very disconcerting challenge: Whereas the volume of the incorrect 2D TUDR was eight times the volume of the incorrect 2D SUDR, the volume of the correct 3D TUDR is 27 times the volume of the correct 3D SUDR!
True, the preon model was doable with these numbers (based on 3), but only if certain volumes were selected, the volumes of 9, 18 and 27 SUDR sums. While this meant that the radius of the TUDR (31/2) was three times the radius of the SUDR (1/31/2), so that the color charges of the quarks and the electrical charges of the electron and positron and the neutrality of the neutrinos worked out, as they should, the thirds were divided up into 3*9=27 increments of volume, each additional SUDR adding only a fraction of the required third!
For a day or two, this seemed to me to be a fatal flaw, but today I’m happy to report the discovery of what surely must be the answer: If we divide each increment of volume by its inverse and then cube that value, the only increments that come out as integers are 9, 18 and 27! All other volume increments are not integers. They are all irrational numbers. What this means, I believe, is that all volume increments except these three are excluded from forming combinations with their reciprocal counterparts by the discrete postulate of the RST. Happy day!
Readers can test this assertion themselves using the chart in figure 1 below:
Figure 1. Chart of 27 SUDR Volumes Summing to One TUDR Volume.
The values in the volume, area and radii columns are mostly rounded off irrational numbers, so the respective ratios must be used to get the actual numbers. This is done by multiplying the indicated ratio by its respective value in the column of the initial SUDR (row 1). The rounded off values in each row can then be used as an approximate value to check to ensure that the correct value has been calculated.
For example, for the ninth volume, we multiply the cube root of 9 by the inverse of the square root of 3, which gives us the radius for the ninth volume. Then, squaring the radius and cubing it, gives us the integer 3. Doing the same thing for number 18 yields the integer 12, while it yields the number 27 for n = 27.
As far as I can tell, no other n than these three meets the requirement.
Whew!!
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Response: 3d logo makerThe 3d model that you are trying to design seems to be great and maybe it will work good but still in case not you should keep trying. -
Response: ij.start.canonThanks for sharing wonderful and informative blogs.
Reader Comments (7)
And that begs the question whether the directional reversals must happen simultaneously in all three dimensions, or can they happen only in some dimensions?
Of course the word "simultaneously" is very icky in RST...
Nevertheless, the question if there is some kind of mechanism that mandates reversals in all dimensions, warrants consideration, ...especially that by definition, the word "dimension" denotes independent phenomena/quantitites
Doug wrote:
"Hence, the 3D system is a composite of 0D, 1D, 2D and 3D numbers"
...also that bears resemblance to the trivectors (k-blades) of the Geometric Algebra...
Doug wrote:
"Hence, the 3D system is a composite of 0D, 1D, 2D and 3D numbers"
That's right, it does, but they use unit trivectors as unit 3D rotations.
You forgot to answer the first question in the first comment above :(
"...whether the directional reversals must happen simultaneously in all three dimensions, or can they happen only in some dimensions?"
Larson's view was that one of the three dimensions must be reversing, which gave him his model of the photon. My conclusion was that he was wrong. It's either all or none. All three dimensions reverse as a unit, simultaneously.
But why? What is the mechanism that mandates reversals in all dimensions? Even if you're right you must answer this question.
...especially that this is inconsistent with the meaning of the word "dimension", which denotes independent phenomena/quantities
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Doug wrote:
"All three dimensions reverse as a unit, simultaneously."
It was sort of a backdoor conclusion for me. Larson needed rotation of the 1D vibration in his development, which he called "scalar rotation." But I realized that such a rotation had to be vectorial, not scalar, and I believed that this was the root cause of the widely acknowledged problems with his photon model.
It occurred to me that a reversal of scalar "direction" would have to be three-dimensional in a three-dimensional system, at least initially, because it was the only alternative that could lead to the propagation of the S|T combo.
The SUDR space progression is confined to one unit of space, while the TUDR time progression is confined to one unit of time. When they combine, they expand in both space and time, but the combo is oscillating in three dimensions, while progressing in only one of three dimensions, because otherwise it couldn't remain intact.
So, Larson killed the progression of the three dimensional expansion by an initial vibration, which subsequently rotates in the remaining two dimensions, to form a non-progressing entity, whereas I kill the progression in all three dimensions and then build a progressing combo, which continues to combine to form a non-progressing entity.
It's two different ways of logically developing the consequences of the fundamental postulates, but in both cases it's a matter of assumption. There is no mechanism to select a dimension for reversal and there is no mechanism to force a dimension reversal. It's simply a matter of exploring what will work to get the observed consequence.
In this case, the observed consequence is the existence of non-propagating matter that emits propagating non-matter, each with all its observed properties.