The Larson Research Center

The nineth post in the BAUT forum follows.  These posts are a continuation of the RST thread in the “Against the Mainstream” forum of BAUT.

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What we are doing at the LRC is investigating how these multi-dimensional RNs correspond to material particles such as electrons, neutrinos, positrons, protons, neutrons, anti-protons, etc, and photons. Larson did the same thing, only he didn’t have the mathematical development that we have with the RNs.

He reasoned that the oscillations, 1/2 and 2/1, were periodic displacements; that is, that they were not “stuck” at 1/2 and 2/1, but could take on other space/time progression ratios, beginning with 1/3, or 3/1, and going to 1/4, 1/5, 1/6, … 1/n, or going from 3/1 to 4/1, 5/1, 6/1, …, n/1. The increasing values of the displacements in these time and space displacements represent lower and lower frequencies of photons (1/n), relative to the speed of light, and higher and higher frequencies of photons (n/1), relative to the speed of light.

These n speed-displacements, as he called them, on either side of unity, represented a continuous spectrum of radiation from infinitely below infrared to infinitely above ultraviolet. They are actually a discrete series of frequencies, but because they can mix and match on their way out of matter aggregates, which is their source, they appear as a continuous spectrum, unless filtered appropriately through a prism to separate them out.

Now Larson also reasoned that, since these oscillations were confined to one unit of space (ds/dt = 1/n), or one unit of time (ds/dt = n/1), which he assumed was a one-dimensional unit of space or time, these units could be rotated, like an oscillating vector can be rotated. This concept of the speed-displacements, as 1D vectorial oscillations, also enabled him to account for the propagation of the photons, because, if the oscillation were only effective in one of three dimensions, that left two dimensions in which no displacement was present (where ds/dt = 1/1 in each, undisplaced, dimension). Thus, such a photon was “free” in these two remaining dimensions; that is, it proceeded outward at unit speed, relative to a fixed refererence system, in one of these two free dimensions, which accounts for the observed outward propagation of different frequency photons, in every direction from a source, at the constant speed of light.

This was Larson’s scalar theory of radiation, if you will. If you consider that it was developed in the same time frame roughly that the quantum theory of light was being developed, during the 1930s and 1940s, when so little was known about radiation, especially among amatuer investigators, it is really an impressive model of radiation.

However, unlike traditional physicists, who were entirely focused on accounting for the energy levels of atomic spectra, using the Bohr model of the atom and traditional vector motion concepts, Larson deduced his model from first principles, by simply assuming that space is the reciprocal aspect of time in the equation of motion and nothing more.

It’s hard to imagine a more radical break from traditional physics than that which this concept represents, because it goes right to the heart of the system of physics used by centuries of physicists to account for nature, and, while they were able to calculate the energy of the atomic spectra, thanks to Heisenberg’s non-commutative product in the Taylor series, they had no idea how to explain the constant speed of light, or how to explain its spectrum of frequencies.

Indeed, they still can’t do this. In this respect, light is still a complete mystery, because while the difference in energy of the separate states of electrons in the atomic structure can be shown to correspond to the energy of the atomic spectra, using quantum mechanics, there is no understanding at all as to how this energy happens to be manifest as an oscillation, or how this oscillation, once it exists, propagates outward in every direction away from the atom, at the constant speed of light.

In contrast, Larson’s concept was consistent in this regard, but he couldn’t calculate the atomic spectra, try as he might. He finally gave up trying to solve the problem in the late 1950s, deciding to move on with his theory and to return to the problem at a later date. Of course, he never did return to it, and this has become a rather embarassing gap, or lacuna, in his theoretical development.

At the LRC, we are convinced that the reason Larson couldn’t calculate the atomic spectra values from his theory is symptomatic of a fundamental error in his development, and it is our objective to correct this error. However, while it’s easy enough to explain the error that we have found, it is a little more difficult to clarify its implications in the consequent development of the theory.

Therefore, I think that the best way to approach it is to employ Hestenes’ GA and the concepts of Clifford algebra in an effort to explain it, even though Larson knew nothing about them. Recall that GA is based on the fourth Clifford algebra, Cl₃, the fourth dimension, 2³ (starting with the zeroth dimension of the scalars), of the binomial expansion, or octonions, which is known as the 3D Euclidean algebra, but which mathematicians regard as eight dimensional, because 2³ = 8 (whew!)

If you start from the left side of the 2³ expansion, 1 3 3 1, you have four, independent, linear “vector” spaces (the space of traditional mathematics): the 2⁰ = 1 scalar space, the 2¹ = 2 vector space, the 2² = 4 bivector space, and the 2³ = 8 trivector space. Recall that, in GA, these four Clifford algebra spaces correspond to Euclidean geometry’s concepts of points, lines, areas, and volumes, so that the 2⁰ space is the space of real numbers (in GA), the 2¹ space is the space of 1D vectors in three dimensions (therefore three, orthogonal, vectors), the 2² space is the space of 2D bivectors in three dimensions (therefore three, orthogonal, areas), and the 2³ space is the space of 3D trivectors in three dimensions, which is a pseudoscalar, or an expanded point (volume). Mathematicians formulate these four, independent, linear spaces, in terms of basis vectors, written as

1) = e₀;
2) = e₁,e₂,e₃;
2) = e₁₂, e₁₃; e₂₃;
4) = e₁₂₃

Now, we can view Larson’s development as beginning at the left with the first linear space, the space of scalars, and proceeding to the right toward the space of trivectors; that is, we start with the unit progression, or universal expansion of space and time, where ds/dt = 1/1, a scalar, and we generate a vector through the “direction” reversals of one aspect of the scalar (ds/dt = 1/n or n/1.)

However, regarding the oscillation thus produced, as a one-dimensional oscillation, as Larson did, affects only one of the three, orthogonal vectors, in the adjoining vector space, the remaining two vectors in this space are not confined by oscillation to one unit, which accounts for the propagation of the single oscillation, relative to a fixed reference system, as explained above.

The subtle contradiction that the two, undisplaced, vectors in the vector space are therefore, by definition, scalars, not vectors, is not readily apparent when GA is not available to illuminate what is happening, but we will return to this point later. In the meantime, Larson reasoned that once a vector exists in the vector space, by virtue of the 1D oscillation in the scalar, that this vector could then be rotated, transforming it from the vector space to the adjoining bivector space to the right of the vector space. Since rotation of the vector is about the mid-point of the vector, and two such rotations are possible, the motion in the bivector space consists of two bivectors, say a^b and a^c, constituting a 2D rotation.

Rotating this compound bivector in the b^c plane, completes the compound rotations, which now consist of [(a^b + a^c) + b^c], which is equivalent to a^b^c, a trivector, in Larson’s development. Notice, however, that the rotation of the one vector, in two dimensions about the mid-point, produces the second and third vector (b and c); that is, Larson reasoned that the rotation was a displacement of a different type, a rotational displacement we would say, so that, while we start with only one vector, rotating it in two dimensions about its mid point, this is tantamount to generating two more vectors, and the wedge products of these vectors can be used to represent two rotations, one a 2D rotation, and one a 1D rotation of the 2D rotation. The concept is illustrated using GA generated graphics in figure 1 below:

 

Figure 1. One 2D + 1D Combination of Rotations as 3 Vectors, 3 Bivectors, and 1 Trivector

However, the problem referred to earlier, wherein, the vectors in the vector space are really not vectors, but scalars, is now exacerbated by the fact that they are transformed into vectors through displacement by rotation in the bivector space, if you will, so that they don’t become vectors directly, but indirectly, by virtue of rotation. I say that this is subtle, because it is consistent, if one considers that the initial, 1D, vibration is an object that is free to rotate as an object would, or at least, it seems to be consistent.

For instance, an extended object, such as the single blade of an aircraft propeller, rotates in a plane orthogonal to the plane of the thrust it produces, but this plane of rotation rotates as the aircraft rotates around its latitudinal axis, thus, in a sense, the combined rotation of the propeller in a given plane of rotation, and the rotation of the plane of rotation itself, is a two-dimensional rotation. Meanwhile, the compound rotation of the rotating propeller (let’s detach it from the aircraft) can also be rotated around the third axis as well.

If units of rotation are equated with units of displacement from unity, in separate scalar magnitudes in this manner, the compound rotations of figure 1 can be equated to independent 2D and 1D scalar motions, which is exactly what Larson does. In this way, he can then add and subtract various units of 1D and 2D “scalar rotation” to form composites that constitute theoretical entites, corresponding to observed physical entities such as electrons, positrons, neutrinos, protons, antiprotons, neutrons, etc, and because the non-rotated oscillation propagates at unit speed, as radiation, he has all he needs to construct the world’s first general theory of the universe, a theory of everything, so-to-speak, where the entire physical structure of the universe consists of nothing but motion.

The concepts of force, such as electrical, magnetic, and gravitational force, as properties of the constituent motions of a given theoretical entity, emerge from the development in a natural and very compelling manner. At the same time, the concepts of space and time forming this system lead to an entirely different cosmology, where the big bang concept of infinite matter/energy, expanding outward in cosmic inflation, producing the elements of matter in the process through nucleosynthesis, and aggregates of matter through gravity, which just happens to be perfectly balanced at this particular time in the evolution of the universe, so that the density of matter/energy is neither curving the spacetime fabric outward, nor inward, is replaced by an entirely new cosmology.

In the RST cosmology, the universe is cyclic, but not in the sense of a singular evolutionary process of matter/energy, dominated by laws of enthropy, but in a parallel evolutionary process dictated by the laws of motion, where the unit space/time progression produces two, inverse, sectors of the universe, constantly engaged in an eternal feedback loop.

The details of this development, as far as Larson could develop them are contained in his works, and they are amazingly consistent and compelling, much more so than the standard hot big bang cosmology, especially as more and more observations such as galaxies older than they should be in a serial type evolutionary process, and observations of gravitational anomalies that are attributed to dark matter and dark energy, etc. are made. However, there is a fly in the ointment: Larson’s concept of “scalar rotation,” upon which the whole development rests, is an oxymoron!

I’ll explain this in the next post.