Another Inter-regional Ratio
One of the most important, and most mysterious, elements of the Reciprocal System of Physical Theory is what Larson called the "inter-regional ratio." Evidently, it was the subject of some conversation at the 1984 ISUS conference, in Salt Lake City, because afterwards, each ISUS member was invited to "write a statement of his ideas on the subject for publication in Reciprocity." In Larson's statement he writes:
The first point that should be noted in connection with this ratio is that it is a basic physical constant, like the gas constant, the gravitational constant, etc. Conventional physical theory has no explanation for any of these constants. It simply uses the, measured values, without attempting to explain where they come from, or what they mean, or even if they have any meaning. If anyone has difficulty in following the theoretical derivation of the inter-regional ratio, I would suggest following this prevailing scientific practice for the present, and accepting this ratio as a measured value, leaving its theoretical status to be considered later, after more familiarity with the theory has been gained. This ratio can, of course, be measured in the same way that the other fundamental constants are measured; that is, by applying one of the relations in which it participates. This is how I obtained it originally. I measured it and used it in my studies long before I formulated the Reciprocal System of theory and found a theoretical explanation for the measured value. In order to appreciate the significance of the ratio, it is necessary to have a reasonably good understanding of the basic features of scalar motion. The existence of this type of motion is not recognized by conventional science, but this is an obvious oversight, as scalar motion can be observed.
It would be very useful, I think, to be able to measure the IRR, as Larson did, but as far as I know, no one knows how he did it, or what exactly he was measuring when he measured it. The only thing we have in Larson's formal works is his theoretical explanation of the constant, which is based on numbers, the numbers entering into the combinations of compound scalar motions, from which he builds the particles and the subsequent atoms of the material elements into the periodic table.
However, his explanation in the above statement is another elaboration on his thinking that provides us with some additional insight. In it, he defines what he calls "scalar dimensions," as opposed to the "vector dimensions," the dimensions of space that we are accustomed to:
In order to grasp the significance of the expression “three dimensions of motion,” the term “dimensions” has to be interpreted in the mathematical sense; that is, the foregoing expression refers to a motion that requires three independent quantities for a complete definition. To distinguish these dimensions of motion from the dimensions of space, or of time, that can be represented in the conventional three-dimensional reference system, I am calling them scalar dimensions.
Once this distinction between scalar vs. vector dimensions is made, Larson proceeds to derive the IRR, which, numerically, comes down to 128(1.22...):1, or 156.44..... Not only does Larson use this ratio in his development of RST theory, including the theoretical derivation of commonly known physical constants, such as the gravitational constant and Planck's constant, but Nehru and Satz also use it in their updated derivations of these constants.
Hence, it would be very interesting to know how to measure it, but, for all I know, this knowledge died with Larson. In the meantime, however, another inter-regional ratio has come to light that might end up shedding some light on Larson's IRR someday. The new ratio is not an observed quantity, nor a theoretical one, but a mathematical one. It comes from the numbers of the periodic table, the 4n2 numbers that determine the periods of the table, in Larson's RST-based theory.
I won't attempt to give a full explanation here, but I will try to summarize the idea. Recall that the periods of the periodic table are 2(2n2), where 2n2 is the quantum mechanical formula and n is 1, 2, 3, and 4, successively. Thus, the first period is 4, the second is 16, then 36, and finally 64.
However, the elements in the period are linear combinations of scalar motion, so that each one is, ideally, one unit of mass greater than the previous element (Larson uses a double-unit unit), thus the first element in the second period is a sum of 4 + 1 = 5 units, the first unit in the third period is a sum of (4+16) + 1 = 21 units, and the first element in the fourth period is a sum of (4 + 16 + 36) + 1 = 57 units of mass.
Although no one (as far as I know) has treated it quantitatively, the inverse of the material periodic table, the cosmic periodic table, is clearly an important part of the theoretical development. As it turns out, though, we can mathematically define the inverse of the table quite easily, if we square the table and take the inverse of it.
For example, there are 120 elements in the table, where the word "elements" is defined to include the three "pre-elements" of the first period; that is, 4+16+36+64 = 120. If we include the 8 subparticles, we have Larson's number of 128, which we should do, but I will not for now. The square of the 120 figure is 14,400, but as we build each element from the beginning, as shown in the link below, we get a number that results from the discrete steps:
http://www.lrcphysics.com/storage/images/periodic%20element%20steps.jpg
Notice that, just like an ADC converter, the diagonal of the square must be discretized, as each successive element is one discrete unit greater than the previous. This is actually a fundamental mathematical result. You can see it very clearly in the first period, but it holds in each of the successive periods, and is modified by their cumulative effect; that is, in the first period, 4x4 = 16, but the first element is one, the second is two, the third is three, and the last element in the period is four units of magnitude. 1+2+3+4 = 10, the magical numbers of the tetraktys. But the important part is that this number is not half of 16, the square, but more than half!
If we consider the inverse of the table, over on the upper half of the diagonal, we start with the same numbers, but we are at the upper right hand corner of the square, where the same numerical relationship holds: 1+2+3+4 =10, coming down the diagonal!
Thus, a non-unit ratio exist between these scalar numbers and their inverses: In the first period, the ratio is 10:6, but building on into the second period, the accumulative ratio is 210:190, then 1596:1540, and, finally, it ends up at 7260:7140. In other words, the differences between the number of units on the lower side of the diagonal, and the number of units on the upper side of it, are the numbers of the accumulating periods: 4, 20, 56, 120.
Of course, the same ratio holds coming down the diagonal from the upper right, only in reverse, which shows a most perfect example of hidden symmetry that appears broken, when we are only viewing it from a limiting perspective. The figure below shows this graphically:
http://www.lrcphysics.com/storage/images/periodic%20element%20squaes.jpg
Of course, we are not taking into account here the "scalar dimensions," so these numbers are not likely to play into the theoretical development directly, but since this "inter-regional ratio" is an indisputable fact, it may serve as a starting point to mathematically derive the measured constant someday, from the periodic table.
That would really be something, I think.
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The IRR as described by KVK Nehru
You may want to read Nehru's paper "The Inter-Regional Ratio", which describes its derivation in detail. It's just a measure of degrees of freedom.
Larson's Inter-regional Ratio
In the entry above, I was explaining another "inter-regional ratio" that I put in quotes to indicate that it was not Larson's inter-regional ratio. However, apparently some readers didn't understand the difference, and have expressed doubts as to whether I understand Larson's inter-regional ratio. I don't see how that conclusion could be reached on the basis of the post above, but I will take it as a convenient seque into the subject.
As I mentioned above, Larson's ratio is a measured physical constant, but no one knows, as far as I can tell, what was measured or how it was measured. Yet, his theoretical explanation was so little understood by members of ISUS that, in their attempt to grasp it, they decided to challenge each attendee at the 1984 conference, including Larson, to explain their understanding in writing, after the meeting.
I quoted passages from Larson's published response to this challenge in the post, but there may have been other responses published. If so, I don't have any knowledge of them. Peret recommended a paper by Nehru, which may be a response, entitled "Inter-Regional Ratio," but, if it is, there's no indication that this is the case in the paper itself.
In his paper, Nehru treats the inter-regional ratio's "scalar dimensions" as an abstract space with a certain number of "degrees of freedom." Since there are three, independent, scalar dimensions in Larson's development, his view is that each one of these three scalar dimensions has (2/9 * (8 * 4 * 4)) + 128 = 155.444 possibilities, or degrees of freedom, when manifest in the three-dimensions of vector time.
This would be true for any of the three scalar dimensions, but only one of them can be represented in a 3D temporal reference system, as shown in the figure below copied from Nehru's paper:
Figure 1. Illustration from Nehru's Paper
In the illustration above, the 8 degrees of freedom in the 3D time region are explained on the basis that only one of the three scalar dimensions is representable in a 3D temporal reference system (the circle in the illustration.) Nehru explains that, "if the three dimensions are interrelated, the total number of degrees of freedom, as given by equation [f = pn] is:
I'm not sure what he means by "interrelated," but if he means orthogonal, which is really another way of saying independent, then we can picture the two interpenetrated disks that Larson uses to illustrate the scalar rotations of the atom in his works. Only in our picture, we initially have three interpenetrated disks, one for each "interrelated" axis.
Since each rotation can be + or -, which is tantamount to space or time "directions" in the RST, then there are 23 = 8 possibilities, or degrees of freedom, which the 1D rotations (the three disks) can take (+++, ---, +--, ++-, -++, --+, -+-, +-+). So now, with the three interpenetrated disks whirling away, we can flip them as well, flipping the horizontal disk around either the x or z axis, and one of the two vertical disks around either the y or z, or the y or x axis.
However, since a flipping of one of these two vertical disks is always going to be indistinguishable from the flipping of either the horizontal or the other, vertical, disk, it's only possible to effectively flip two of them, one horizontal and one vertical (that is, there is a degeneracy), so we end up with four flipping possibilities (++, --, +-, -+) in each case (rotating space/time and filipping space/time for each of two, interpenetrated, disks.)
All this is easy enough to understand, but then, in Larson's model of the atom, the degenerate disk is removed and we have two interpentrated disks that are rotating and flipping. The total number of degrees of freedom for this set then, would be 8 * 4 * 4 = 128 degrees of freedom, but, in Larson's atomic model, there are two LVs that are being rotated and flipped, which can be oriented along any of the 3 axes, and, since the atoms are rotations of two LV+ vibrations, this adds 2/9 more degrees of freedom per unit of motion, which gives us a grand total of (2/9 * 128) + 128 = 156.444 degrees of freedom for each atom.
Now, if you have difficulty following or visualizing this logical development, don't worry, you can actually build a physical and/or computer model of it. I have done both. You might have questions about how to merge a physical model of two rotating systems together, or how to align the axes of the two systems in a computer model, but you will at least understand the 156.444... possibilities for configuring the model's state (even though you might wonder why, if there are two systems, there are not 2*(128 + (1/9 *128)) possibilities, but should you decide to ask, you would be the first to do so, as far as I know.)
In my case, it is not a question of following the logic of Larson's explanation, or even questioning it, but it is a more fundamental issue of accepting the prior assumption that a linear, point-to-point, vibration can be regarded as a 1D, scalar, magnitude in a 3D system and how it can then be rotated in two "directions" and yet still be regarded as a scalar magnitude, a magnitude without direction. To my way of thinking, a scalar magnitude cannot vibrate back and forth in two directions, or rotate clockwise or counter-clockwise. Of course, that leaves me with a much more difficult challenge of finding an alternative theoretical explanation for this empirical constant.
In the meantime, though, as I stated in the post, there is another inter-regional ratio that may end up shedding light on Larson's. Only time will tell.