The primary difference between RS and RS2 is the inclusion of various strata of geometry, and their polar inverses. This has a number of consequences that lead to a slightly different set of conclusions than Larson’s original statements in the Reciprocal System of physical theory.
One must understand that geometry is based upon perception—how we view things with our senses. With normal, binocular vision, we see a Euclidean world, one in which we can tell that “1 meter” in length is “1 meter” in length, regardless of where it is placed in relation to us (providing it is within the tolerance of our vision to perceive it). This gives us the absolute measures we need to function in this world. This is why Euclidean geometry is scale invariant (a fixed unchanging scale).
Close one eye, and the Euclidean world vanishes, becoming a Metric world, where only relative measurements exist. If one were to place a yardstick in an otherwise featureless room, you would only know it was a yard long because you would recognize the yardstick. If someone placed a 6-inch long yardstick in the room, that looked exactly like a regular yardstick, you would still perceive it to be a yard long, except at a further distance away, since you lost the triangulation that binocular vision provides. Metric geometry is scale variant—in other words, the scale of an object can change, resulting in a perceived change in location. Under metric perception, you could not tell the difference if a yardstick shrunk to half size, or moved it twice as far away. It would look exactly the same in both cases (geometrically, a case of “similar triangles” in the field of monocular perception).
With that understanding, one realizes that once we leave the Euclidean realm of “coordinate time-space” (what Larson calls “extension space”), we have lost absolute measurements, and only have measurements that make sense relative to each other. Therefore, we can conclude that:
Larson identified the natural datum of scalar speed to be Unity, 1 unit of space per 1 unit of time being the reference point for speed. This is known as a “unit boundary” (“unit” meaning “1”). (See the article on Scalar Motion for more information).
When we move from the time-space of the material sector into the space-time of the cosmic sector, the aspects of space and time invert. A material speed of s/t becomes a cosmic speed of t/s, perceived in the material sector as “energy”.
Likewise, the geometry of the “other side” becomes the polar inverse of the geometry we are measuring with. In our normal, Euclidean realm of extension space, the cosmic sector appears as polar-Euclidean — what we would describe mathematically with “imaginary” numbers (complex numbers and quaternions). Our translational motion in space appears as rotational motion in the cosmic sector. The same holds true for the time and space regions.
The time region is the region within 1 unit of space. The magnitude of motion in the spatial aspect of motion is fixed at unity. In other words, 1/t. Only “time” can increase, not space. The boundary of the time region is therefore 1/1—a unit boundary, so we also see the configuration space of the atom as polar-Euclidean to our perception, which is known as counterspace.
All measurements in counterspace are based in rotation. Translation does not exist in counterspace, except as a result of the dimensional reduction of compound rotation, as in the photon.
In normal, extension space, we see rotation as a shear in two dimensions. Move something in one direction (translation); push it in another direction at the same time, and it follows a curve. In counterspace, the principle is the same… rotate something in one direction, push it again in another, and it follows a straight line. We see all motion in both the cosmic sector, and the time region as having a primary motion of rotation, whereas in the material sector, the primary motion is translation.
This brings us back to the natural datum of unity. In the material sector, we see outward translational motion in 3 dimensions, which results in the progression of the natural reference system—everything moving away from everything else.
But, when we view the time region that defines atoms, we see an outward rotational motion in 3 dimensions, which results in Larson’s “rotational base” with nothing rotating, because rotation occurs naturally in the region.
The natural consequence of this is that “linear vibration”, upon which Larsonbuilds the photon, does not occur, because you cannot have “linear” motion in a polar region, unless there are two dimensions involved—just as it requires two translations to rotate an object in “normal” space.