Resolving Fundamental Issues
In discussing the RST model with Sam, I referred him to the FQXI paper that I wrote entitled “What is the Point of Reality?” which takes on the enigma and the fundamental issue of the point concept, at the heart of all physics.
The LST community covers the enigma up with “Poincaré stresses,” but truth be told, it was the reason the LHC was built: They want to resolve the issue, not just cover it up. The RST community is still striving to resolve it, as well. K.V.K. Nehru challenged Larson’s concept of “simple harmonic motion,” which Larson described as “…a motion in which there is a continuous and uniform change from outward to inward and vice versa.”
Nehru objected to the validity of this conclusion, based on the fact that scalar “directions,” inward and outward, are discrete. There is no scalar “direction” that is partly outward or partly inward. He writes:
Since there is nothing like more outward (inward) or less outward (inward) the question arises as to the meaning of the statement “a continuous and uniform change from outward to inward”? Outward and inward, as applied to scalar motion, are discrete directions: the scalar motion could be either outward or inward. There are no intermediate possibilities.
In the LRC RSTbased theory (RSt), the periodic “direction” reversals are 3D, thus avoiding the sawtooth vs. sinewave dilemma that plagued Larson and that drove him to positing his concept of simple harmonic motion. The reversal from a 3D expansion to a 3D contraction, and viceversa, clearly has the gradual change, to which Nehru objected, built right into it: As the expanding volume grows toward unit size, its outward rate of spherical expansion slows, even while the radius’ rate of expansion remains constant. At the point of reversal, the decrease of the volume in the inward “direction” is again gradual at first, even though the radius’ change of “direction” is instantaneous.
At the zero point (3D origin), however, this is not the case, unless we recognize the nature of the point described in the FQXI paper: In that case, the gradual change in “direction” of the spatial sphere, at one end, is matched by the gradual change in “direction” of the temporal sphere, at the other end, and, thus, it is perfectly analogous to the concept of the interchange of inverses that is inherent in rotation and also in simple harmonic motion.
Nevertheless, while 3D oscillation solves the enigma of the point, it introduces another one, an enigma that is uniquely ours: If the 3D space (time) unit oscillates by changing into its inverse, isn’t that tantamount to the numerator changing into the denominator, in the case of the SUDR, and viceversa, in the case of the TUDR?
This question has gnawed at me ever since I wrote the FQXI paper. The tentative conclusion that I have been forced to come to is that it’s a matter of accounting. If 8 units of space are converted into 8 units of time, during an expansion to 64 units of space and 64 units of time, then the net balance is 64  8 = 56 units of space and 64 + 8 = 72 units of time, an 8 unit deficit of space and an 8 unit surplus of time.
During the next step, when 8 units of time are transformed into 8 units of space, the space deficit is made up from the time surplus. This is not unlike the swinging pendulum, when the potential energy is max, it’s all on one side of zero, and this surplus is transferred back to the reciprocal side, from which it came, before the cycle repeats itself.
If it works for mass, momentum and vector motion, why not for space, time and scalar motion? Maybe Ted’s quantum wave equation would be applicable after all.
:)
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What is the measure of this "spherical expansion" ?
 sphere's area
 sphere's volume
 sth else...?
Sphere's area.
Ball's volume.
The growth of the radius is uniform, but not the volume or area.
I'm just going to think aloud here using 3D cartesian functions, and see if it gets anywhere. Still trying to figure out this sinewave/sawwave dilemma in terms I can understand (ie. mathematical functions).
So the radius is progressing uniformly, and motion is conserved because as the radius grows in space it diminishes in time. In which case the length of the radius does produce a saw wave.
But the growth of the area and volume produces something even further from a cosine wave. As the radius increases uniformly, the growth of the SA and V accelerates, not decelerates, producing a "choppy wave" / "loopy saw wave" graph (think 3yearold's drawing of waves in the sea).
Starting from (0,0) for the part of the sphere in time (and ignoring the 4pi and 4pi/3 constants):
y = x^2 [1<x<1, periodic along x axis]
or
y = x^3 [1<x<1, periodic along x axis]
And starting from (0,1) for the part of the sphere in space:
y = (x  1)^2 [0<x<2, periodic along x axis]
or
y = (x  1)^3 [0<x<2, periodic along x axis]
Superimposing the waves for the surface area gives:
y = x^2 + (x^2  2x + 1)
y = 2x^2  2x + 1 [0<x<1, periodic along x axis]
... which is another choppy wave, but closer to what you'd get if you took a sine wave and made all the negative regions positive  ie. sin(x).
Illustration: http://millar153.wordpress.com/?attachment_id=1211
Of course you have to add an infinite progression of successively higher powers to get a perfect sine/cos wave as can be seen in Maclaurin's series, and since we only have three dimensions that's not going to happen.
So methinks I'm wasting my time going down this rabbit hole, bacause you simply can't produce a perfect sine wave using only polynomial functions in Cartesian geometry if you're limited to the third power.
So either:
(a) I'm coming at this from the wrong angle and missing something
(b) we need polar geometry (Nehru's solution)
(c) what we observe in nature isn't actually a perfect sine wave, just a polynomial function very close to it (ie. I'm asking, do we really need to produce a sine wave?)
To me, Nehru's birotation (b) makes more sense, but do want to see whether we still can get the photon wave just with the LRC expanding/collapsing spheres. Unless event (a) is true (which is likely), I'm can't really see how we can. And then there's option (c), which on gut instinct I think is almost certainly wrong!
Does that make sense?
Sam
Hi Sam,
You have to keep in mind that using a quadrantal function isn't appropriate for what we are analyzing here. Recall that we are necessarily dealing with a binary rotation, not a quadrantal rotation.
This was discussed here.
It's been six years since I tackled this challenge, and I will have to go back and review it in order to discuss it intelligently.
It's not complete by any means. There are conclusions to revisit, given the progress we've made since then, but it should help you understand that it's not as straight forward as you might think.
Hi Doug,
Thanks for your reply. I can see I've a long way to go  I'll keep reading!
No problem.
Keep in mind though, blogging on ongoing research does not provide text book like material for learning. A lot of conclusions turn out to be wrong and we have to backtrack, and the topics are not organized in any way, but chronologically.
The Structure of the Physical Universe Document (SPUD) was the document that we intended on providing for newcomers so that they could learn/study/discuss/challenge the LRC's development of its RSTbased theory.
However, it has been sorely neglected, I'm afraid. We hope to remedy that this year.