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 RST-based theory (RSt), the periodic “direction” reversals are 3D, thus avoiding the saw-tooth vs. sine-wave 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 vice-versa, 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 vice-versa, 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.
:)