The Larson Research Center

Last Spring, we started discussing an initial effort to develop the quantitative side of our RST-based theory (here), beginning with the fundamental magnitude conjecture (FMC).  The FMC simply states that there are three (four counting zero) fundamental numbers, or magnitudes (with quantity, dimension, and direction properties), from which all others are constructed. Raul Bott proved this true for the dimension property, and I’m simply conjecturing that, if it holds for one property of number, or magnitude, it probably holds for the other properties as well.

After discussing the FMC, we turned to the subject of force and acceleration (here and here), noting that Larson didn’t try to redefine these concepts in scalar terms, but only tried to clarify certain conceptual and dimensional aspects of them. For our purposes, however, we redefined them as scalar concepts, in terms of speed density (acceleration), and inverse speed density (force), varying by the inverse square law.

Then we really went out on a limb (here), by using these new definitions to treat the dimensional problems of force equations as misunderstandings of scalar quantities, which, if viewed in the context of the tetraktys and Bott periodicity, lead to a reconciliation of the infinities that plague the LST theories, reconciling the conflict between a point and a sphere.

But trying to stay on track with the quantitative development, we turned our attention to quantifying the SUDR and TUDR and the SUDR|TUDR combo, oscillations (here). We found that describing these oscillations in terms of the transition from local (point) to non-local (sphere), the changing “localness” property of space and time in the S|T combo acts like the conservation of energy between the reciprocal properties of kinetic and potential energy in a pendulum system of motion. But instead of using the sine and cosine functions, to mathematically describe the harmonic oscillations, we discovered (here) that the function that was needed could be represented by the reciprocal rotations of two, meshed gears, which led (here) to the discovery of the binary functions of compressed/stretched springs via the “gear group” of rotations, where the concept that “half as much” is the reciprocal of “twice as much” took us into the two, reciprocal groups, one under addition, and the other under multiplication, with all sorts of implications.

Of course, things were actually a little muddled for a while, as it wasn’t clear right away how the sine/cosine functions related to the binary functions of the gear group, so the discussion turned to the math aspects for a bit (here, here and here), which, in turn, led to discussing how the gear group relates to the LST’s gauge principles, using complex numbers of “size one” (here, here and here).

In the meantime, trying to explain some of these things, the crucial difference between the sine/cosine functions and the binary functions was finally recognized, which then led to the explanation of quantum spin (here). Needless to say, dealing with such fundamental concepts at this dizzying pace was difficult to handle, so I’ve had to take a break to regroup and try to see where all this leads and what should be done next. After all, the objective of the quantitative development is to get to the point where we can calculate the atomic spectra.

All of these concepts are no doubt going to play an important part in the quantitative analysis, but the question still is, where do we start? The answer is clear: We have something the LST community hasn’t had in a long time, a model of the photon, electron and other observed entities, as well as a foundation for understanding the principles of quantum behavior, such as uncertainty, spin, duality, etc.  Therefore, what we do now is test this model to see if the observed interactions of these entities can be predicted from the models and the quantum principles inherent in the 3D, space|time, oscillation.

The first step in this process is to relate the basic S|T unit to Planck’s constant h. Recall that in the early days, Millikan established the value of the charge of the electron and the validity of Einstein’s equation relating the kinetic energy of an ejected electron (photoelectron) and the scalar energy of the photon that ejects it, in the photoelectric phenomenon. In our RST-based model, this is an interaction between S|T boson triplets and S|T fermion triplets. Hence, it appears that a quantitative analysis of this interaction would be a good starting point for testing our conceptual model.

Einstein’s photoelectric equation is

1/2mv² = hv - P,

where h is Planck’s constant, v is the frequency of the incident radiation, and P is the work necessary to accelerate the electron to escape velocity, so-to-speak. Since Planck’s constant is the unit of energy, dt/ds in our model, the total energy is some multiple of h determined by the number of cycles per second of oscillation inherent in the incident radiation v. The dimensions of the kinetic energy, mass, m, times the square of the velocity, v, are

(dt/ds)³ * (ds/dt)² = dt/ds

However, as noted above, we have redefined the concepts of force and acceleration in terms of speed, and inverse speed, density, from the scalar point of view, eliminating the need for the LST community’s ploy, wherein long ago it resorted to the concept of work (force time distance) to reconcile the dimensions of energy. That is to say, as long as the force vector is perpendicular to the distance (thus, there is no direction of displacement) vector, the inner product of the two (a scalar) is zero and no energy (work) is expended, but if a displacement takes place, then the scalar value of work (energy) is non-zero.

This ingenious workaround is necessary when dealing with mechanical concepts of energy, which depend on moving mass (momentum), but when dealing with the concept of rest mass, then Einstein’s other energy equation,

E = mc²

is applicable. Of course, in this case, we are not talking about a moving mass, and, therefore, there is no applicable force vector involved, as there is in electric, or gravitational, potential and kinetic energy. However, acceleration is involved, because inertial mass is equivalent to gravitational mass. Hence, in our new scalar view of force and acceleration, when we deal with rest mass, we must switch from the force concept of energy per square unit of space, (t/s)⁰/s², to the acceleration concept of velocity per square unit of time, (s/t)⁰/t².

But now we have the same problem as the LST physicists had with the definition of scalar energy, only in terms of scalar velocity; that is, we need to express a scalar quantity of velocity in terms of a vector quantity of acceleration and time, when it does work, like ejecting (accelerating) an electron from a metal surface, in the photoelectric interaction. 

Obviously, we have our work cut out for us (no pun intended! LOL)