I discussed in detail (RE: my article, "On the Nature of Rotation and Birotation," Reciprocity, XX (1), Spring 1991, p. 8), that space has two intrinsic traits, linear and rotational. These are respectively the spatial aspects of linear motion and rotational motion. They could be measured in, say, centimeters and radians.
Note that these two are mutually exclusive: there is no angle in linear space, and there is no linear space in angle.
(A) In the Outside Region (that is, the conventional three-dimensional spatial frame), there is no upper bound for linear space though there exists a lower bound (what we call the quantum of linear space). On the other hand, in the case of the rotational trait, the angle, there is an upper bound (of 2 PI radians).
Now since experiments seem to point out (RE: Bhandari) that in the Inside Region there is no upper bound for angle, let us re-write the paragraph (A) above interchanging corresponding words like "linear" and "rotational".
(B)"In the Inside Region there is no upper bound for rotational space though there exists a lower bound (what we might call the quantum of rotational space or angle). On the other hand, in the case of the linear trait, the length, there is an upper bound (of the quantum of space)."
We summarize these ideas in the Table below, showing the minimum and maximum quantities of linear and rotational space respectively.
|Sizes of the Spatial Quanta|
|Inside Region||Outside Region|
Lnat is the Natural Unit of Linear Space (quantum of space) and
Rnat is the Natural Unit of Rotation (pi radians).
Some observations follow:
(1) In both the cases of Rotation and Linear Motion, the Inside Region quantity equals the INVERSE of the corresponding Outside Region quantity. The inverse of 1 is 1 and the inverse of infinity is 0. So much so, the Max. in the Inside Region equals the Min. in Outside Region and vice versa (in natural units).
(2) Now, in order to find out what types of PRIMARY Motions are possible we need to inquire what the MINIMUM quantities happen to be in the Region.
(2 a) The minimum quantities of Linear space, that is, 1 Lnat in the Outside Region and 0 (zero) in the Inside Region, always occur.
(2 b) Similarly the minimum quantities of Rotational space, namely, 0 (zero) in the Outside Region and 1 revolution (or "solid revolution" as the case may be) in the Inside Region, always occur.
(3) Because of (2 b), especially that the minimum possible rotation is 0 in the Outside Region, an independent Linear motion can occur as a primary motion. Further, in the Inside Region, the minimum possible Linear motion being 0, the most elementary primary motion possible would be 1 unit of rotational motion.
(4) On the other hand, in the Inside Region, an independent Linear motion cannot exist. It can occur only as the Linear motion OF a Revolution, since 1 Revolution--and not zero--is the minimum possible rotational motion that already exists as the primary motion. (The reason for Larson to take the photon as a LV is that he thought that rotation can't exist without "something" to rotate, and therefore the LV logically precedes rotation. On hindsight we can see that this is true for the Outside Region only. For the Inside Region, where the atomic rotations actually exist, the OPPOSITE turns out to be true.)