At the 1984 ISUS conference in Salt Lake City a discussion of the “inter-regional ratio” concluded with an understanding that each of those concerned should write a statement of his ideas on the subject for publication in Reciprocity. What follows is Dewey B. Larson’s contribution.
The first point that should be noted in connection with this ratio is that it is a basic physical constant, like the gas constant, the gravitational constant, etc. Conventional physical theory has no explanation for any of these constants. It simply uses the, measured values, without attempting to explain where they come from, or what they mean, or even if they have any meaning.
If anyone has difficulty in following the theoretical derivation of the inter-regional ratio, I would suggest following this prevailing scientific practice for the present, and accepting this ratio as a measured value, leaving its theoretical status to be considered later, after more familiarity with the theory has been gained.
This ratio can, of course, be measured in the same way that the other fundamental constants are measured; that is, by applying one of the relations in which it participates. This is how I obtained it originally. I measured it and used it in my studies long before I formulated the Reciprocal System of theory and found a theoretical explanation for the measured value. In order to appreciate the significance of the ratio, it is necessary to have a reasonably good understanding of the basic features of scalar motion. The existence of this type of motion is not recognized by conventional science, but this is an obvious oversight, as scalar motion can be observed.
For instance, we find that the distant galaxies are all moving radially outward away from our own galaxy. Since we cannot justify assuming that our galaxy is the only stationary object in the universe, we have to conclude that we are likewise moving away from all of the other galaxies; that is, we are moving outward in all directions. A motion in all directions is a motion with no specific direction. Thus the motion
of the galaxies is scalar.
From the postulates of the Reciprocal System of theory we find that the basic motions of the universe are scalar; simply relations between space magnitudes and time magnitudes. Once we have recognized that motion of this nature does actually exist, even though conventional science does not recognize it, the postulate that this kind of motion, the simplest form of motion, is the fundamental entity is entirely logical. Of course, fundamental postulates have to be justified by their consequences, but it helps to know that they are soundly based. In a three-dimensional universe of motion there are necessarily three dimensions of motion. That is what the adjective “three-dimensional” means. But only one dimension of motion can be represented in the three dimensions of space portrayed by the conventional reference system. Any motion in this reference system can be represented by a vector, and a combination of any number of such motions is a one-dimensional motion represented by the vector sum. In order to grasp the significance of the expression “three dimensions of motion,” the term “dimensions” has to be interpreted in the mathematical sense; that is, the foregoing expression refers to a motion that requires three independent quantities for a complete definition. To distinguish these dimensions of motion from the dimensions of space, or of time, that can be represented in the conventional three-dimensional reference system, I am calling them scalar dimensions.
Any two scalar magnitudes of the same kind can be added algebraically. Thus two gallons of water plus three gallons of water amounts to five gallons of water. Scalar speeds are additive in a similar manner. A speed of x units added to a speed of y units arrives at a total speed of x+y units. But if the second of these motions is taking place in two scalar dimensions with speeds of y and z respectively, the quantities y and z are independent, by definition. Since z is independent of y, it is also independent of x+y. It follows that when a motion is taking place in two or more scalar dimensions, only the speed in one of these dimensions can be added to another speed.
The same principle applies where there are other differences between scalar quantities; for example, that between motion in space and motion in time. Motion in the time region is an extension of ordinary vectorial motion into a second speed unit, a unit of motion in time, which, for reasons explained in my books, acts as a modifier of the spatial speed—that is, as motion in equivalent space, rather than a motion in actual time—as long as the net total motion is below the neutral level, There are no fractional units in the universe of motion, but the equivalent of a fractional unit of space (or time) can be produced by adding units of the inverse entity. A speed in the range between one unit of motion in space and one unit of motion in time (which is two units when measured from the spatial zero) can be obtained either by adding a fractional increment to a unit of motion in space or by adding a negative fractional increment to a unit of motion in time. Like scalar motion in different dimensions, scalar motion in time is independent of scalar motion in space, and these two different procedures therefore produce results that are independent.
The full range of the time region motion is two scalar units, from zero spatial speed to zero temporal speed. Inasmuch as the motion beyond the unit speed level is independent of that in the range below unity, it is not limited to the one dimension of motion represented in the reference system, but extends over all three dimensions. In each dimension, the speed may be either a modified spatial unit or a modified temporal unit, as indicated in the preceding paragraph. Consequently there are 2³, or 8, different permutations of the spatial and temporal motions. Of these, only one, the all-spatial combination SSS is commensurable with quantities in the reference system, and appears as a magnitude in that system. If one of the spatial motions is replaced by a temporal motion, as in SST, the resulting combination of scalar quantities is different from SSS, and independent of it, just as the dimensional combination x+z is independent of the combination x+y. The same is true of the other possible permutations. The complete list is:
Here, then, is the size of the “container,” the capacity of the single space unit to contain compound units of motion in which the introduction of time components produces the equivalent of less than a unit of space. What we want to do next is to determine how many units of motion in the form of matter can exist in this 8-unit “container” . We have seen that the rotational motion of the atom around one of its three axes is one-dimensional. Each such rotation constitutes one unit of motion, and since the “container” has room for eight units it can accommodate eight of these rotations. So far we have been dealing with dimensions of space or time (equivalent space). Now we need to take into account the fact that the atomic rotation is taking place in three dimensions of motion, each of which can be resolved into three dimensions of space or time. In the two additional dimensions of motion the rotation of the atom is two-dimensional.
Each unit of this rotation occupies two of the scalar units of the “container”. Thus only four such rotations can be accommodated in each dimension of motion, the total number of different combinations of rotations for the motion as a whole is then 8 x 4 x 4 = 128. What this means is that the space unit can contain 128 independent scalar motions, only one of which, the SSS combination, in the one dimension of motion represented in the reference system, appears as an observable quantity in that reference system. For the rotational motion alone, the ratio of total to observable motion is 128 to 1.
The fact that the rotational motion is rotation of a vibration introduces an additional factor, as the units of motion involved in the vibration add to the total motion content of the atom. As explained in my books, this addition amounts to 2/9 of the rotational motion, making the complete inter-regional ratio 1 + 2/9 of the rotational motion, making the complete inter-regional ratio (1 + 2/9) 128 to 1.