The Other Half
Doug
4 Comments
The 3D model of the S|T unit is a composite of two 3D oscillations, the space oscillation, the SUDR, and the time oscillation, the TUDR. Since they are the inverse of each other, the SUDR is 27 times smaller than the TUDR. We can therefore use the SUDR volume, surface or radius to express the relationship numerically. For example, let’s use the volume:
54(1/27)/(27), (27(1/27)/(27), (27(1/27)/2(27), or(54/27)/27, 27/27, 27/54
As explained in the previous entry, only the unit measure of 3 volumes out of the lower 27, actually cube to an integer. 9, 18 and 27, which enables us to use them as 1/3, 2/3 and 3/3 of the whole, in 3D terms. Interestingly enough, however, in 1D terms, the numbers are different. Only three SUDR radii fit in a TUDR radius (i.e. 3 * (1/31/2) = 31/2), so the volume sum in which the SUDR radius is 1/3, 2/3 and 3/3 of the TUDR radius is 1, 8 and 27, respectively. I will defer the discussion of the ramifications of this fact until later. Right now I want to complete the other half of the numeric system, where the SUDR is larger than the TUDR, what we can refer to as the upper half of the number system, which terminates at 54/27.
Figure 1 below shows the chart of the upper half that corresponds to the chart of the lower half provided in the previous entry.
Figure 1. Chart of 27 SUDR Volumes Summing to Two TUDR Volumes
The concepts being introduced here are somewhat subtle. First, we assume that our universe is nothing but motion, with two reciprocal aspects, space and time, existing in discrete units. Since nothing is perfect, we must introduce a deviation into the perfect, one for one, expansion of space and time. The only deviation possible is a “direction” reversal in one of the two aspects, which produces a unit displacement in the otherwise perfect expansion.
We label the unit space displacement, SUDR, for space unit displacement ratio, and the unit time displacement, TUDR, for time unit displacement ratio. In simple terms the SUDR is a 3D space oscillation, while the TUDR is the inverse of this, a 3D time oscillation.
These two fundamental units progress, or increase, in their respective non-oscillating aspects. For the SUDR, this means that for each half of its oscillation, time continues to expand, and for the TUDR, space continues to expand, during each half of its oscillation. If we chart these motions we see that they are perpendicularly oriented, because they are reciprocals. Hence, it is possible that the time expansion of a space oscillation (SUDR) could bring it into contact with the space expansion of a time oscillation (TUDR).
A combination of these two fundamental entities constitutes a new ratio of space and time, a SUDR|TUDR (S|T) unit. A little consideration will show that an S|T unit is an oscillating combination that propagates in both space and time, and therefore can come into contact with other instances of S|T units, forming compound units. Consequently, we need to calculate the properties of this fundamental scalar motion combo in order to explore the possible combinations that might occur and then compare them to observations.
From simple geometric and mathematical properties, we deduce that the radius of the smallest TUDR is the square root of 3, and that the radius of the largest SUDR is the inverse of this, which means that, while it is three times smaller than the radius of the TUDR, its volume is exactly 27 times smaller than the volume of the TUDR.
Of course, these sizes are all relative until we choose a unit for the scale, which undoubtedly must be based on the speed of light.
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Reader Comments (4)
I wonder if it would come out to integers in 4D too.
If not, it would be a neat explanation why the universe is 3-dimensional...
Horace
P.S.
You did not answer some of my earlier questions in the previous posts
Doug wrote:
"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"
I suppose, but it's giving me a headache. Maybe all the those sums that don't form integers end up being dark matter, but it gets worse, because the volume sums equating to 1/3, 2/3, 3/3 radii (diameters), which are the 1D (electrical differentials needed for the standard model particles, are, 1, 8 and 27 respectively!
I'm sure the answers are lurking in here somewhere, but it's not easy teasing them out.
What IF we have a cycling universe? Then S/T expansion is changing its acceleration during the cycle, and even stopping and reversing twice during a complete cycle. It follows that 'light speed' and the gravitational 'constant' would also change in an inverse manner, right? My thought experiment on this is are frightening, having to imagine a contraction cycle of no light. A cosmic night of renewal awaiting for the dawn of a new creation cycle. If these cycles are on the order of billions of years, we might not even be able to detect changes in gravitation or light speed. Can you think of a way to detect these minute changes if they in fact exist? Thanks for the work you guys do at Larson. You and a few others may be our only hope in this era of scientific authoritarianism to bring down the current house of cards that is modern physics and start to build a more worthy foundation. Replys greatly appreciated.
Louis, please see my previous replies on this. The RST is highly inflexible and does not permit us to introduce "what if" scenarios that are not possible consequences of its fundamental postulates.
Certain things can be safely extrapolated from observations, but they are quite limited. See, for instance, Arnold D. Studtmann, "Toward a Unified Cosmological Physics: The Reciprocal System of D.B. Larson," PhD Dissertation. It's available here.