Since I keep getting asked on how the RS2 differs from the RS, and what are the points of departure, commonality and contention, I thought it wise to summarize the process of how this re-evaluation got to where it is, from Larson's RS starting point.
The actual process over the last 5 years was far more haphazard and random, because it was basically "trial and error", but now that we can see the "long run", here are the stages that RS2 has gone thru from Larson's RS starting point:
1) First on the list is the addition of reciprocity to geometry, such that when one crosses a unit boundary, not only do the aspects of space and time invert, but so does the geometry.
It does make sense that if you have a "reciprocal" theory, that everything should be subject to a reciprocal relationship. There is nothing in Larson's work that imply that Larson was aware of geometric inverses, since they did not become popular until the advent of computers and CGI some 40 years later. Not having know of it, he never considered the idea.
2) The reciprocal of rectangular geometry is polar geometry, most commonly understood as "imaginary numbers". We've seen this reference frequently in atomic physics, where atoms are best described by imaginary numbers or quaternions.
The realm of polar geometry is called "counterspace", and by including geometric inverses, it is necessary to also include the concepts of counterspace in the RS2 in order to deal with polar spaces.
3) There is no direct representation of a polar space in our Euclidean thinking, so the inclusion of counterspace brought with it the study of "Projective Geometry", a way to represent various types of geometry such that our consciousness can perceive and communicate it.
4) Projective geometry has, by necessity, a need to define the perspective from which a geometric system is examined, and thus by inclusion of Projective Geometry in RS2, the "observer principle" had to become well defined and could no longer be assumed (as in the case of Euclidean geometry).
5) This necessitated the inclusion of just how our consciousness perceives the "reality" around us, thru the physical senses. This revealed the assumptions we were taking for granted in how we perceive the "reality" around us; such concepts of "center", "infinity", projective cones, eye triangulation and vanishing points were now explicitly defined, and attached to specific types of geometry, based on the Projective Geometry model.
6) From this, it became apparent that observed or consensus "reality" was actually an illusion; just a shadow cast on the projective screen of Euclid. But the RS2 model showed where the projector was located, and the various filters used to make the image on Euclid's screen.
Larson recognized that there were two different "reference systems", one he called "scalar" and the other "coordinate" or "extension space", but never actually defined the connection between them, leaving them disjoint, randomly or statistically connected.
RS2, in identifing the filters, approaches the connection between scalar and coordinate reference systems as a projective transformation, the same process that computer modeling programs use to render a 3-d object on the computer screen.
7) By backstepping thru the assumptions that built the illusion of reality, we were able to get to the source of what Larson refers to as "scalar motion"--the first invariant property outside of unity, which is defined as the cross-ratio.
8) The cross-ratio has no named aspects; it is the generic form of motion, speed and energy, and is the "light" that comes out of the projector before it gets filtered. This is where the RS2 bases its idea of "scalar motion", outside all geometric projections.
Cross-ratio, in the projective stratum of geometry, then becomes the starting point for RS2.
Developmental Summary of RS2
Developmental Summary of RS2
Every dogma has its day...
Developmental Summary of RS2
Now that we have defined how RS2 differs conceptually from Larson's RS, we can examine some of the consequences that the addition of Projective geometry and counterspace have on the model.
Both systems start with Uniform Motion -- unity. Since Larson postulates Euclidean space, that translates to an outward motion in all directions; a linear, scalar expansion of space and time.
RS2 postulates an inverse geometric relationship between space and time, as well as a mathematical one. From the "local" view of the material sector, RS2 then views "space" the same way as Larson, moving in a linear, scalar expansion.
Since each absolute location on this grid is a potential location for atomic motion of some kind, it can be viewed as a scalar expansion of "time regions". Since the time region is across a unit boundary from the region of the observer, the geometry of the time region is polar, aka "counterspace." Motion inside the time region is therefore a rotational, scalar expansion--a "rotational base" on which other rotations can be built--and because it is rotating at unit speed, it is precisely the "rotational equivalent of nothing."
This is a major conceptual difference from Larson, who requires the presence of a "direction reversal" to occur before he can build a rotational base. Direction reversals are not required in RS2, because of the polar nature of counterspace constructs a "rotational base" at every absolute location in the natural reference system.
Larson then creates a random "direction reversal", such that the outward progression is reversed to an inward motion, creating a linear vibration identified as the "photon." (Many undisclosed assumptions are needed to make this work, and it has a lot of problems). This creates a "sea of photons", all progressing outward at absolute locations and not interacting with each other.
RS2 does not require the concept of a "direction reversal" to create inward motion, since the rotational bases already exist. All it requires is an increase of temporal magnitude at a location, such that the aspect of time is larger than unity. This produces a unit temporal ROTATION, in Larson's notation, M 0-0-1 -- the positron. (Switch "time" with "space" to get the cosmic viewpoint; I am sticking with the material viewpoint for simplicity in these examples). RS2 creates a "sea of positrons", the building blocks of matter, crashing into each other forming more complex structures.
RS2 is a far simpler system at this point; speed changing from 1/1 to 1/2 to produce a positron. Nothing else involved. Larson, however, needs to randomly reverse the direction and create secondary reference points to produce a linear vibration at the absolute location -- which, from a scalar direction viewpoint is a non-linear square wave (a random direction reversal does not create a regular wavepattern), and from a conventional reference system is a triangle wave (inside the time region) and a tangent wave (in equivalent space). But Larson concludes it is a sine wave; a conclusion I have yet to understand.
Now that Larson has "something to rotate", though he didn't need anything to "vibrate", he rotates the photon, producing a "rotational base", the "rotational equivalent of nothing."
He then takes the rotational base, and increases its speed, as RS2 did from uniform motion, to produce the positron. The systems are conceptually in agreement here; increasing the speed of a rotational base produces the positron.
RS2, on the other hand, already has a universe full of positrons, which are NOT fixed at absolute locations, because unlike linear vibration, rotation carries torque--they jump locations and collide with each other. The result is speed changes in the positrons, building other particles, including photons.
In RS2, the photon is a bi-rotation; two counter-rotating systems that manifest as a linear vibration. (See topic on photons for details). The positron is basically a "special case" photon, where one half of the bi-rotation is at unit speed.
At this point, both systems have created photons and positrons thru the application of motion:
RS: unit speed -> direction reversal -> photon -> rotation -> rotational base -> rotation -> positron.
RS2: unit speed -> speed increase -> positron -> interaction -> photon.
Both systems start with Uniform Motion -- unity. Since Larson postulates Euclidean space, that translates to an outward motion in all directions; a linear, scalar expansion of space and time.
RS2 postulates an inverse geometric relationship between space and time, as well as a mathematical one. From the "local" view of the material sector, RS2 then views "space" the same way as Larson, moving in a linear, scalar expansion.
Since each absolute location on this grid is a potential location for atomic motion of some kind, it can be viewed as a scalar expansion of "time regions". Since the time region is across a unit boundary from the region of the observer, the geometry of the time region is polar, aka "counterspace." Motion inside the time region is therefore a rotational, scalar expansion--a "rotational base" on which other rotations can be built--and because it is rotating at unit speed, it is precisely the "rotational equivalent of nothing."
This is a major conceptual difference from Larson, who requires the presence of a "direction reversal" to occur before he can build a rotational base. Direction reversals are not required in RS2, because of the polar nature of counterspace constructs a "rotational base" at every absolute location in the natural reference system.
Larson then creates a random "direction reversal", such that the outward progression is reversed to an inward motion, creating a linear vibration identified as the "photon." (Many undisclosed assumptions are needed to make this work, and it has a lot of problems). This creates a "sea of photons", all progressing outward at absolute locations and not interacting with each other.
RS2 does not require the concept of a "direction reversal" to create inward motion, since the rotational bases already exist. All it requires is an increase of temporal magnitude at a location, such that the aspect of time is larger than unity. This produces a unit temporal ROTATION, in Larson's notation, M 0-0-1 -- the positron. (Switch "time" with "space" to get the cosmic viewpoint; I am sticking with the material viewpoint for simplicity in these examples). RS2 creates a "sea of positrons", the building blocks of matter, crashing into each other forming more complex structures.
RS2 is a far simpler system at this point; speed changing from 1/1 to 1/2 to produce a positron. Nothing else involved. Larson, however, needs to randomly reverse the direction and create secondary reference points to produce a linear vibration at the absolute location -- which, from a scalar direction viewpoint is a non-linear square wave (a random direction reversal does not create a regular wavepattern), and from a conventional reference system is a triangle wave (inside the time region) and a tangent wave (in equivalent space). But Larson concludes it is a sine wave; a conclusion I have yet to understand.
Now that Larson has "something to rotate", though he didn't need anything to "vibrate", he rotates the photon, producing a "rotational base", the "rotational equivalent of nothing."
He then takes the rotational base, and increases its speed, as RS2 did from uniform motion, to produce the positron. The systems are conceptually in agreement here; increasing the speed of a rotational base produces the positron.
RS2, on the other hand, already has a universe full of positrons, which are NOT fixed at absolute locations, because unlike linear vibration, rotation carries torque--they jump locations and collide with each other. The result is speed changes in the positrons, building other particles, including photons.
In RS2, the photon is a bi-rotation; two counter-rotating systems that manifest as a linear vibration. (See topic on photons for details). The positron is basically a "special case" photon, where one half of the bi-rotation is at unit speed.
At this point, both systems have created photons and positrons thru the application of motion:
RS: unit speed -> direction reversal -> photon -> rotation -> rotational base -> rotation -> positron.
RS2: unit speed -> speed increase -> positron -> interaction -> photon.
Every dogma has its day...