The Larson Research Center

After posting the previous post below, I could almost hear the guffaws, and the last words I wrote, asking if there is any other way to make the space|time dimensions of the force equations work out, were ringing in my ears. Then, with a sudden flash of insight, I realized that, in fact, there is another way.

In the meantime, walking the dog, I kept thinking about the idea in the post below.  Certainly, the dimensions are correct, but how could a time interval substitute for an area.  Intuitively, we know that the affect of the electrical charge (inverse speed) is omni-directional, or scalar.  The force, due to the charge, is a manifestation of this scalar motion in a given direction, or multiple directions, in the case of multiple charges, just as I pointed out with the expanding galaxies analogy. Since spatial distance, is a measure of the space aspect of a given vectorial motion, disregarding its time aspect, then it follows that temporal distance is a measure of the time aspect of a given vectorial motion, disregarding its space aspect. 

Nevertheless,  since time does not have direction in space, vectorial time motion is not possible and thus, the new force equation, with its scalar time interval, even if it is valid, would be hard to conceptualize, let alone use.  So, I’ll probably just have to take my lumps on that one, even though there’s much more that I can say about it that I think is useful.

As I mentioned, however, I realized soon after posting the previous article that there is another way to make the space|time dimensions of the force equations consistent, and, to boot, it sheds a great deal of light on the whole idea of what force and acceleration are.  In this approach, we have to challenge Larson’s dimensional assignments to units of inverse speed, which is something that I’ve seen coming for a while now, because they are inconsistent with the new understanding of numbers in the chart of motion (CM).

Recall that the CM contains the four numbers 1-4 and the dimensions of these from 0 to 3, forming a four by four matrix of magnitudes (it probably should be called the chart of magnitudes, instead of the chart of motion.)  We’ve mostly referred to M₂ and M₄ motion, and sometimes M₃ motion in the CM, but not M₁ motion, probably because it isn’t motion; that is (1|1)ⁿ cannot be displaced, regardless of its dimensional exponent, n. 

However, be this as it may, there is a difference between a unit point, (1|1)⁰, a unit line, (1|1)¹, a unit area, (1|1)², and a unit cube, (1|1)³.  The difference is the degree of duality in each dimension, or maybe what we could call potential duality.  The point is (no pun intended), in the mathematics of dimensions, there is the scalar magnitude, and then there is the pseudoscalar magnitude; that is, (1|1)⁰, is a point, or magnitude with no direction, and (1|1)³ is a sphere, or magnitude with all directions, one being the inverse of the other, in a sense.  Therefore, the dimensions of a point charge must be one or the other, but as we saw below, LST physicists can’t make the zero-dimensional point charge work, because of infinities (currently driving string theorists), and they can’t make the three-dimensional spherical charge work either, because of the need for “Poincare stresses.”

However, the situation with Larson’s RST-based theory is not much better, even though it doesn’t face the same challenges as the LST theories.  Nevertheless, the reason is, again, due to dimensions, but this time the problem is not reflected in unwanted infinities or the need for compensating forces, but rather because the dimensional analysis of the force equations shows a problem with the assignment of the space|time dimensions in both the charge and gravitational equations.  In the charge equation,

F = (Q1Q2)/d², 

the space|time dimensions of the charges are the same as energy (t/s).  However, both energy and charge are scalar quantities, not vector quantities.  Hence, they should have the dimensions of scalars, which is dimension zero, the dimensions of a point, not dimension one, the dimensions of a line.  The problem is that the dimensions of scalars, n⁰, hasn’t been carefully thought out by physicists, probably because they have been taught that n⁰ is always equal to 1, while n¹ is equal to n, which is true enough, but that’s not the whole story.

In the quantitative interpretation (QI) of number, setting the dimension of a number to zero is tantamount to setting it to one, but in the operational interpretation (OI) of number, the interpretation used in the reciprocal system of mathematics (RSM), one has a different meaning, because there are an infinite number of ones, from 1|1 to ∞|∞, and one is always greater, or lesser, than another one. This has huge ramifications, but one effect (LOL) on our theory development is that the dimensions of charge and energy must change from t/s, to t⁰/s⁰.  Because these two concepts are scalar concepts, they must have the dimensions of scalars, but without a knowledge of the OI numbers, the LST physicists had to find a way around this dimensional inconsistency to avoid problems, and they did it through the definition of work, an ingenious workaround, to say the least (but, again, no pun intended, really).

However, in the new system, we have no need for the expediency used by the LST community to define energy in terms of work.  Therefore, when we correct the dimensions of the scalar charges, the force equation between charges becomes dimensionally consistent:

F = (Q1Q2)/d² =  ((t/s)⁰(t/s)⁰)/s² = (t/s)⁰(1/s²) = t⁰/s²,

and energy has the dimensions of a scalar, while space has the dimensions of area, which properly describes force, as energy per unit area, (t⁰/s⁰)/s².

When we turn to the gravitational force equation, things get even more interesting, because we not only change the number of the exponents of the space|time dimensions, but we actually invert the dimensions themselves.  The reason is subtle, but so are the concepts involved, which is why they have been so troublesome for so long. Recall that, according to all observation in the LST community, inertial mass and gravitational mass are exactly equivalent.  No difference has ever been detected, mystifying the physicists.  In the RST community, however, there is no mystery to this at all, because they are the same; that is, mass is simply a measure of the inherent inward scalar motion that constitutes matter.  Matter consists of discrete units of three-dimensional, inward, speed, while mass is the three-dimensional opposition, or 3D outward speed that it takes to cancel, or overcome, the inward speed.

Thus, if we substitute the dimensions of the inward motion of matter, for the dimensions of the outward resistance of matter, we also switch from a concept of force (a quantity of resistance to motion), to a concept of acceleration (a quantity of motion), without affecting, in the least, the quantitative variables of the equation.  Thus, the gravitational equation of acceleration, A, becomes:

A = G(M1M2)/d² = K((s/t)³(s/t)³)/s² = K(s/t)⁶/s² =  K(s⁴/t⁶),

and, applying our Bott periodicity theorem correction, this becomes

A = K(s^4-4/t^6-4) = K(s⁰/t²),

where the dimensions of the universal gravitational constant, Big G, drop out, and only a dimensionless constant, Big K, remains, representing the magnitude difference between the first and second tetraktys of the RSM.  This also correctly shows the scalar view of acceleration, where it is a speed “density,” so-to-speak, or scalar speed per square unit of time, (s⁰/t⁰)/t².

Of course, all this is so new, it’s totally subject to revision, but for now, at least, it seems to make an awful lot of sense.