In writing the essay for the latest FQXi Contest, “Is Reality Digital or Analog?” I argued for the necessity of 3D time on the basis of space/time conservation; that is, space can’t increase, in the observed 3D spatial expansion, outside gravitational limits, without violating the law of conservation.
In the case of the postulated 3D space/time oscillation, we face double jeopardy from this law, as the volume of space, created during the expansion, disappears upon contraction to zero. “Where did it come from? Where did it go?”
Of course, the immediate conclusion is that it is transformed into its inverse, 3D time. This would not be surprising to students of the RST, but it must be startling to the LST community, who never seem to contemplate the possibility, even though it is a perfectly reasonable extrapolation from what we know about space and the laws of symmetry, which, after all, are laws of conservation, as Noether’s theorem proves.
However, what is surprising to me is that I realized that even I hadn’t thought about it before. The realization of its necessity didn’t strike me until I wrote the FQXI essay. I remember Larson saying something similar in the Preliminary version of The Physical Structure, but I have never spent the time to look for it.
Regardless, it appears to me that it is a significant insight that ought to play a central role in getting the RST comimunity more up to speed with the LST community, who, while theoretically challenged, is way ahead of us analytically.
The advantage they possess comes, in large part, from the physics of vector motion. When they faced the quantum mechanics challenge in the 20th century, they met it by finding ways to adapt the principles of vector motion to solve problems of scalar motion, something that they don’t recognize even to this day.
They are not happy with the QM situation, and they have tried many ways to correct the confusion that has resulted from it, but in the meantime we haven’t been of much help, unfortunately. Now, though, I think I see the way we can lead them to consider the physics of scalar motion, because the parallel between the two systems can be exploited in a way that was not possible before the change to Larson’s development of his RSt, which we introduced by taking exception to his concept of 1D “directiion” reversals, insisting that they had to be 3D.
This change, though so disruptive to ISUS, has lead to the conclusion that “scalar rotation” is an oxymoron. Physical entities rotate, translate and vibrate, but scalar ratios of space and time, which form physical entities, in the universe of motion, do not. They expand and they contract, or oscillate, like the zooming in and out in one, two or three dimensions, but that’s it. The elementary space/time entity, in the LRC’s development of RST theory, is a 3D oscillation that is a composite of 1D, 2D and 3D scalar motion.
Since unit speed is the datum of the universe of motion, the 3D oscillations are on either side of this speed, like the two sidebands of RF modulation. Taking the unit speed as s/t = 2/2, then the slower side is s/t = 1/2, while the faster side is s/t = 2/1. We have dubbed the slower one, the Space Unit Displacement Ratio, or SUDR, and the faster one the Time Unit Displacement Ratio, or TUDR.
By displacement, we mean that the oscillation of one aspect of the unit motion confines its magnitude to one unit of space or time, causing its reciprocal aspect to move forward two units for every cycle, thus displacing the unit ratio by one unit, in the appropriate “direction” (the same thing happens in rotation - it takes two units of time for every 360 degrees of rotation, a 1/2 ratio, even though we double the unit so we can speak in terms of cycles per unit of time).
However, until the composing of the essay, the oscillation of the SUDR (TUDR) was confined to space (time), with no consideration given to a law of space (time) conservation. It was in composing the essay, and thinking about the definition of a point of no extent, and an instant of no duration, a concept used in the LST community, but inconsistently, that the concept became clear: The 3D oscillation must transform into its inverse, just as the 2D vectorial oscillation does (see the FQXI paper here.)
What is clear now is that the 3D oscillation, when the inverse volume is included, can be described in the same way traditional oscillation is described, with something similar to the sine and cosine, or the ratio of orthogonal dimensions with the radius. The difference is that the magnitudes that constitute the sine and cosine, which are projections of the moving radius upon the two, inverse, dimensions, in the vectorial rotation, as the radius moves along the circumference, are changed to two actual magnitudes: The ratio of the these two, inverse, radii, the spatial and the temporal radii, the sum of which always equals 1, just as the familiar,
sin2Θ + cos2Θ = 1,
have the same relation, but just as they are, without the need to employ the Pythagorean theorem.
Indeed, we can say that, while the radius of rotation oscillation is fixed, but its angle changes, the radii of the expansion/contraction oscillation change, but their angle is fixed. As the angle of rotation increases from 0 to 360, the sine and cosine vary inversely:
Sine: 0 <—> 1 <—> 0
Cosine: 1 <—> 0 <—> 1
and as the progression of the 3D oscillation increases from 0 to 2, the temporal and spatial radii vary inversely, in exactly the same way:
Temporal radius: 0 <—> 1 <—> 0
Spatial radius: 1 <—> 0 <—> 1
The great thing about this is that there is no need to square anything to get the result, but that is not all. With this in hand, we can describe the 1D, 2D and 3D oscillations mathematically, together, or separately, and the 4π change (called “quantum spin”) per cycle falls out naturally (see table 1 in FQXI paper for details.) In addition, the 1D time/space oscillation, t/s, corresponds to the dimensions of electrical charge, the 2D oscillation, t2/s2, to the dimensions of magnetic flux, and the 3D oscillation, t3/s3 to the dimensions of mass.
Certainly, there is a mighty long way to go, but what a wonderfully simple, if prospective, solution it is.