In the last century, Ronald W. Satz wrote an article for Reciprocity, the journal for the International Society for Unified Science (ISUS), entitled, “Permittivity, Permeability and the Speed of Light in the Reciprocal System.”
In that article, he theoretically derived the force equations for electrostatic and magnetic charges, by showing that the space/time dimensions for these equations are correct, when the space/time dimensions for permittivity and permeability are correctly understood.
He shows that the correct space/time dimensions for the electric charge force equation are,
t/s2 = (s2/t)(((t/s)(t/s))/s2),
thanks to the dimensions of the permittivity term, (s2/t), which are those required on the right hand side of the equation to equal the space/time dimensions of force on the left hand side.
Satz gives us his rationale for using the space/time permittivity dimensions of the RSt, which differ from those of the LST, in that they are the inverse of the RSt’s space/time dimensions. Of course, such a clarification of space/time dimensions of permittivity, enabling this impressive derivation of the equation, which is missing in the LST community, went unnoticed then and is still obscure, even to this day.
Nevertheless, Satz went on in the article to derive the equation for the magnetic force law, as well, using the space/time dimensions of permeability, in the same manner. He shows that the correct space/time dimensions for the Coulomb law of magnetostatics are,
t/s2 = (s4/t3)(((t2/s2)(t2/s2))/s2),
but, as Satz explains in the article, the concept of permeability is more correctly understood as a magnetic analog to electric resistance, which we might as well consider “impermeability.” If we do this, we must invert the term, putting it in the denominator of the equation, so that the “impermeability” term of the equation becomes (1/t3/s4).
While this brilliant derivation of the force equations in terms of space/time dimensions still cannot make the headlines it deserves in the LST community, it is now confirmed, by the work of Xavier Borg of Blaze Labs, where he has, independently of Larson’s work, shown that the SI units of the LST are easily reduced to space/time dimensions, and that those for permittivity and permeability agree completely with those of the RSt, as can be seen from the table and explanation here.
Indeed, we can now extend Satz’s work to the gravitational force law and derive its equation as well, using the space/time dimensions of the gravitational constant, G, given in Borg’s table. These space time dimensions of G are (s6/t5) and inserting them into the force equation for gravitational mass, we get:
t/s2 = (s6/t5)(((t3/s3)(t3/s3))/s2),
Something that physicists might have really been interested in, especially given the energy equations, E= mc2 and E = hv, which are also expressable in terms of space/time dimensions,
t/s = (t3/s3)(s2/t2) = (t2/s)(1/t).
Though the implications of these insights might be lost on theoretical physicists busy “battling for the heart and soul of physics,” as we have blogged about on our “The Trouble with Physics” blog today, they should not be lost on followers of Dewey Larson.
However, I caused a real dust-up in conversations with online ISUS discussion groups, when I suggested using space/time dimensions with the force law, F = ma, years ago. I still don’t know exactly what the problem was, but I remember it caused Ronald Satz a great deal of heart burn.
Since then, of course, we’ve gone our separate ways, and I no longer have to worry about what anyone thinks of my ideas, even though I think I’ve made a fool of myself on more than one occasion. Yet, nothing ventured, nothing gained, as they say. If I happen to write what I think and what I think is not thought through enough, no one but me suffers for it, and I learn and grow in the process.
So, with that in mind, let me share what I have been thinking lately. As the readers of the three blogs on this site know, the recent entries of the New Math blog have dealt with a new multi-dimensional, scalar number system. By the usual definition and understanding of the term “scalar” in mathematics and physics, this may seem to be an oxymoron, but this is only the case, if rational numbers and motion are connected to the concept of direction.
Normally, scalars are used in the sense of denoting magnitude only. This is why Hestenes caused such a stir, with his geometric product at the heart of his geometric algebra. It mixes scalars and vectors in a way never contemplated in vector algebra.
But the idea of multi-dimensional scalar math is much simpler. It posits that numbers themselves have multiple dimensions. Not just in an operational sense, where a quantity of factors in an operation denotes dimensionality, but in the sense of the unit scalar itself.
Just as 11, 12 and 13 denote 1, 1x1 and 1x1x1 operationally, and mathematically are equivalent, but a unit line, a unit square and a unit cube are definitely not equivalent, so too are the unit scalars in the new math. They are equivalent is some sense, but not in another.
The difference is in the orthogonality of the factors. When each term in the algebraic operation of more than one term is orthogonal to the others, the result is quite different than when they are not. Geometric algebra has a way of dealing with this, but it mixes vectors and scalars in such a way that it becomes a much more powerful language than vector algebra.
However, in the world of scalar motion, we are dealing with something quite different. One-dimensional scalar motion produces a one-dimensional length, with magnitude in two “directions” (a line). Two-dimensional scalar motion produces a two-dimensional area, with magnitude in four “directions” (a circle), while three-dimensional scalar motion produces a volume, with magnitude in eight “directions” (a ball).
As the LRC’s investigation of these multi-dimensional scalar motions has proceeded over the years, it has been discovered that the units of the corresponding numbers used to denote these 2, 4 and 8 “directions” of scalar magnitude differ.
For the two, one-dimensional magnitudes of the length, the units are the familiar units we designate with the symbol 1, but for the four, two-dimensional magnitudes of the area, and the eight, three-dimensional magnitudes of the volume, the unit is not 1, but the square root of 2 and the square root of 3, respectively.
For the details, please see the entries on the New Math blog. The challenge before us on this blog is how to use the New Math to advance the LRC’s RSt. Recall that the bottom line of Larson’s RST is that the universe is composed of nothing but motion, combinations of motion and relations between them.
Given that, in our RSt, the scalar motions begin as three-dimensional vibrations, or pulsations, called Space Unit Displacement Ratios (SUDRs) and Time Unit Displacement Ratios (TUDRs), and, because of their unique properties, they may combine into SUDR|TUDR combinations (or S|T units), and then further combine into one, two and three dimensional combos, identified with the LST community’s fermions and bosons, we require a multi-dimensional system of mathematics to investigate their properties and interactions properly.
The standard, or legacy system of mathematics is based on concepts analogous to vector motion, i.e. motion with direction, while we need a system of mathematics based on concepts analogous to scalar motion, i.e. motion of magnitude only, but magnitudes with “direction,” the 2. 4 and 8 “directions” referred to above.
Whether or not we will succeed in this endeavor, remains to be seen, but it couldn’t be any worse than the awful situation the LST community now finds itself in.