The Larson Research Center

It’s been so long since I’ve posted anything on research, I’m afraid people will think I’ve abandoned the work. However, the truth is, I’ve had to turn my attention to practical matters, leading to a neglect of the theoretical.

But I have some unpublished articles that have lain around for sometime, because I haven’t been able to get up enough momentum to finish them, or think them out completely. I think I will go ahead and post them anyway, though, just to get something out there to think about. Maybe that will help me get going again, even if it might be embarassing. Here’s the first one:

In our virtual lab in Second Life, we’ve been playing with SUDRs and TUDRs and their combinations, S|T units. Here is a short video of three S|T units combined as a neutrino triplet from our toy model of standard model entities:

The animation of the SUDR (red pseudoscalar) is driven by the changing diameter generated by the difference between the sine and -sine function, while the TUDR (blue pseudoscalar) is driven by the changing diameter generated by the difference between the cosine and -cosine functions.

In essence, this means that the expansion/contraction of the pseudoscalars is a function of two, counter-rotating, rotations, as shown in figure 1 below:

Figure 1. Two Counter Sine Functions (left), and Two Counter Cosine Functions (right), Define Inverse Diameters of Oscillating Pseudoscalars (not synchronized)

Consequently, with these two functions, we can analyze the pseudoscalar oscillations, and their combinations as S|T units. The first thought was to plot the changing 1D, 2D and 3D pseudoscalars in terms of π, which produced some interesting wave forms, but then the idea ocurred to us to take a point on the surface of the pseudoscalars as a zero reference. This means that the origin “moves” with respect to the reference point and gives us a way to compare the n-dimensional magnitudes as a function of time (space); that is, the 20 point increases from 0 to 1 * 10 , and back to 0, while the 21 function changes from 0 to 6 * 11, during the same time, while the 22 function changes from 0 to 12 * 12, and the 23 function changes from 0 to 8 * 13 and back, during one cycle.

In this way, everything is positive, and never negative, just as the magnitude of the diameter is always positive and never negative.  While this is interesting, the big challenge is to capture the inverse relationship. In what way is the TUDR oscillation the inverse of the SUDR? From the standpoint of the expanding/contracting diameter, there is no difference between the two oscillations of figure 1. The oscillation on the left is the +/- cosine projected on the horizontal diameter, while the oscillation on the right is the +/- sine projected on the vertical diameter, but the geometric inverse of the unit diameter is twice its size.

If this were not bad enough, how do we represent the temporal diameter with a spatial diameter? The answer, I believe, is to follow the math. As far as the math is concerned, the inverse of 1/2, is 2/1, and this is simply a doubling of the numerator, from 1 to 2, and a halving of the denominator, from 2 to 1, the mediato/duplacio math of the ancients.

Another way to express the same result is to keep the size of the diameter the same, but to quadruple the frequency of the TUDR, with respect to the SUDR. Figure 2 incorporates this idea.

       Figure 2. Normalized SUDR and TUDR Oscillations

Of course, this is tantamount to assuming that the relative frequencies of the oscillating pseudoscalars is a valid comparison, but I don’t see any other way of comparing them. If this works, we can leverage the knowledge of hetrodyning and harmonics. Something we’ve already explored to some extent.

Philip Gibbs, in his FQXI essay, “This Time – What a Strange Turn of Events!” writes: 

Minkowski used the symmetry in the Lorentz transformation to bring together space and time making them merely different dimensions of spacetime. Yet time is somehow different in our mind. This difference is characterised by an arrow of time that defies the symmetry. In our conscious experience our past is clear and fixed but our future is uncertain. From the laws of thermodynamics we learn that this difference is due to entropy which always increases as time passes. Entropy is a measure of information and by the rules of quantum mechanics information of (sic) conserved. There is a paradox, but information can be as clear to us as the letters on this page, or as hidden and disordered as the states of the molecules in the air around it. As time passes, the disorder increases and entropy measures this change.

Time can distinguish itself from space in this way because the spacetime metric has a Lorentz signature that assign a different sign in the time dimension versus the three space directions. Thus in locally flat Minkowski spacetime distances are measured by the invariant quantity

ds2 = dx2 + dy2 + dz2 – c2dt2

Part of the mystery of time is to understand where this signature comes from. Why three plus signs for space and only one minus sign for time? Even with this separation of dimensions there should remain symmetry under time reversal t -> -t, but the arrow of time breaks this symmetry. What is the origin of this arrow? From what bow did it take flight?

When we understand that the progression of time is only one aspect of the space/time progression, and that the progression of space is its reciprocal, we can understand the broken symmetry. It’s broken when the uniform motion is quantized by the continuous reversals in the space, or the time, aspect of the progression, as shown in the graphic of the previous post below, which is shown again in figure 1.

Figure 1.Two Fixed Reference Systems Created by Pseudoscalar Oscillations.

In figure 1, we see the arrow of time is created when the s/t pseudoscalar oscillations nullify the space progression, and the arrow of space is created when the t/s pseudoscalar oscillations nullify the time progression. Of course the two systems are separated by the unit space/time progression, which is c-speed from the 0 point of both systems.

From the perspective of either system, the zero speed (or frequency) of the inverse system is four times its own zero speed (or frequency); that is, 1/2 * 4 = 2/1. Another way to say the same thing is that, if we take the frequency of one system as the fundamental, the frequency of the inverse system is two octaves above that frequency, regardless of which one we select as the fundamental (i.e. 1/2 + 1/2 = 1 and 1 + 1 = 2).

If fermions are triple combinations of s/t and t/s pseudoscalars, whose net frequency is at the fundamental, or whose net motion is at the spatial zero, then a natural question to ask is, “What effect does vectorial motion have on their time (space) flow?” Einstein’s theory shows that time slows down relative to inertial systems in motion. We can illustrate this effect as shown in figure 2.

Figure 2. Vector Motion Slows Down Time.

Of course, the difference between the space/time of figure 1 and the spacetime of figure 2 is that, in figure 1, both space and time are progressing, whereas, in figure 2, only time is progressing, and while the change in space of figure 2 is a vectorial motion of an object, a one-dimensional change of x, y, z, locations, tied to events that are separated by spacetime, the events in one inertial frame happen slower (height of green arrow), relative to the events in another inertial frame, depending upon their relative speed (length of the purple and blue arrows).

In figure 1, we see that it’s the oscillation in the space progression, effectively nullifying it, that creates the inertial frames of figure 2. So, a more accurate representation would show the oscillation of an inertial frame, in both the s/t and t/s cases, as shown below in figure 3.

 Figure 3. The S/T and T/S Pseudoscalar Oscillations in a World Line Chart

The space/time progression of the oscillating s/t pseudoscalar is illustrated in the vertical bar of figure 3, where the space aspect of the continuous expansion is oscillating, while the time aspect continues its uniform increase. In the horizontal bar, the oscillation of the t/s pseudoscalar is illustrated, as, in this instance, the time aspect oscillates, while the space aspect continues its uniform increase.

In either case, the orthogonal paths of the oscillations show that the indicated system is at the zero point of their respective fixed reference system, created by the oscillations. Now, let’s give the same vector motion to the pseudoscalars as that shown it figure 2. Notice, depending on the vectorial speed, that the vertical bar will slant toward the horizontal, just as the green arrow does in figure 2, and the horizontal bar will slant toward the vertical.

However, there is a difference in how the x, y, z, spatial dimensions are to be understood in the two figures. In figure 2, the change in locations is defined by 1D motion, whereas, in figure 1, every point in the graph is a 3D change in the size of the locations; that is, vectorial motion causes the bar to slant to the horizontal, but it’s a physical impossibility to represent vectorial motion in three directions at once.

Therefore, we have to understand the oscillations of figure 3, not as 3D psuedoscalar oscillations of figure 1, but as 1D pseudoscalar oscillations. On this basis, it would take a composite of three charts like that in figure 3 to illustrate all the vectorial motion possibilities (this has important implications later.) But, to illustrate the relation of vector and scalar motion, we can imagine a 1D pseudoscalar oscillation, affected by high-speed 1D vectorial motion, as shown in figure 4 below.

Figure 4. 1D Pseudoscalar Vector Motion

In figure 4, the red space/time arrow increases diagonally, to the upper right, as the s/t pseudoscalar expands, in space and time equally. Subsequently, it increases diagonally to the upper left, as the s/t pseudoscalar decreases in space, as time continues to increase.

Inversely, the blue time/space arrow increases diagonally, to the lower right, as the t/s pseudoscalar contracts, in time, but continues to increase in space, while it subsquently increases diagonally to the upper right, as the t/s pseudoscalar expands in time, while space continues to increase.

Hence, we can see the perfect symmetry of the space/time | time/space relationship. But now, when we add vectorial motion to these pseudoscalars, the vertical, s/t, pseudoscalar rotates right, to the unit speed diagonal, while the horizontal, t/s, pseudoscalar rotates left, to the unit speed diagonal, represented by the green boxes with green arrows.

The most interesting thing to note at the unit boundary is the directional changes of the red and blue arrows. As the s/t pseudoscalar’s speed increases to c-speed, the time component of its expansion arrow disappears. It increases in space only, while on the contraction part of the cycle, the space component of the contraction arrow disappears, indicating that only the time component is increasing in this half of the cycle.

The full implications of this development are not well understood as yet, but it seems clear at this point that any increase in vectorial speed of the s/t pseudoscalar, beyond the unit level, crossing the c-speed boundary so-to-speak, is tantamount to a decrease in the vectorial speed of a t/s pseudoscalar. Moreover, we can see that, what would appear to be an increase of s/t vectorial speed, is actually a decrease in t/s vectorial speed, which completely transforms the red diagonal arrows of the s/t pseudoscalar into blue diagonal arrows of the t/s pseudoscalar and vice-versa!

Thus, the arrow of time, the arrow that defines the entropy on the s/t pseudoscalar side of unit speed, reverses direction, as the arrow of space, on the t/s side of unity, defining a reverse entropy! (note to John: is this not tantamount to the direction of matter’s time arrow (s/t) being opposed to the direction of energy’s time arrow (t/s), described by you?)!

To underscore that the directions of the two scalar arrows (i.e. the two “time” arrows) progress in opposite “directions,” a final graphic serves to more clearly illustrate it geometrically, in figure 5 below.     

Figure 5. The “Directions” of the Two Arrows of “Time” in Our RST-based Physical Theory are Opposed.

While our RST-based theory differs from Larson’s, in that his theory doesn’t incorporate the principles of the tetraktys in its development of the consequences of the RST, yet it continues to amaze me how the trail he blazed continues to be our guiding light.

Not only was he the first to solve the problem of the asymmetry of the “arrow of time,” and in the process uncover the t/s side of the universe, but he went on to show how high-speed vector motion, with the dimensions of scalar motion, and the unit c-speed datum, produces a cosmology of such beauty and grandeur that the contemplation of it is in itself almost a religious experience.

Of course, there is much, much more to learn about it. We have scarcely begun.

In this forum, and in the essay submitted to FQXI Essay Contest, we have concentrated on discussing the small scale phenomena of the universe of motion. While it’s certainly crucial to show the way space/time emerges from the fundamental motion of the universe, through vibration, to form the basic constituents of motion that make up the standard model (SM) and periodic elements, people are also interested, probably even more so, in the development of the new system’s concepts of large scale phenomena.

As a result, I’ve decided to enlarge the scope of the discussion of the essay in the FQXI forum, by changing the focus of the discussion on the nature of time, from the small scale to the large scale phenomena of the universe of motion. However, the editor in the FQXI forum is so limited that it makes it very difficult to carry on the discussion there. Therefore, I will post the entries here and provide a link to them there.

In the last FQXI forum entry, I explained the unit datum of the universe of motion, where the displacement of time, or space, in the unit motion, through pseudoscalar vibration, forms two, fixed, reference systems, relative to the unit motion datum. One of these is based on the 1:2 ratio, created by the oscillating spatial pseudoscalar, while the other is based on the 2:1 ratio, created by the oscillating temporal pseudoscalar. This concept is illustrated in figure 1 below:

Figure 1. Two Fixed Reference Systems Created by Pseudoscalar Oscillations.

In the spatial reference system, time progresses as a scalar. In the temporal reference system, space progresses as a scalar. SM bosons are formed as biform combinations of oscillating spatial and temporal pseudoscalars, while fermions are formed from triform combinations, as shown in figure 1 of the essay.

What is not mentioned in the essay, however, but is clearly implicit in this space/time structure of discrete units of scalar motion, is its supersymmetry, wherein every combination of the SM toy model has a counterpart in an inverse SM toy model that applies to the fixed temporal reference system.

Hence, there are two sets of combinations of bosons and fermions, and two sets of periodic elements, possible, where the difference is that one is the inverse of the other. Of course, since unit speed (c-speed) is the common boundary between the two sets of motion combinations, the two reference systems are separated by high speed motion, just as 1/2 = .5 is separated from 2/1 = 2, by a factor of four, i.e. 4 * .5 = 2.

This change in the theoretical picture has a profound impact on the cosmology of the new system. Instead of thermodynamic entropy being the major process of the physical universe, it is actually relegated to a relatively minor role, while the space/time, time/space, progression takes over the major role, as the driving force of change in the theoretical universe of motion. 

Of course, the first question in any theoretical cosmology always concerns its concept of initial conditions. In the theoretical cosmology of legacy physics, the question of initial conditions is problematic, since it requires an infinitely dense, infinitely small, mathematically impossible, singularity, to start things off.

In the cosmology of the new system of theory, the initial conditions are not quite so problematic, but still require a hypothetical assumption of unit vibration in the space/time | time/space progression. Given this oscillation, however, the system provides some remarkable results, showing why the invariance of special relativity holds, and why the covariance of general relativity works so well. 

Moreover, without the need for an initial hot big bang, the cosmology of the new system is cyclic, where the gravitationally condensed matter of the low-speed sector is input for the energetic subatomic gas of the high-speed sector and vice-versa, through the transformation of the high-speed vector motion of one reference system into the low-speed vector motion of the other.

Understandably, the details of how this transformation works is the subject of much research, but in general terms, it is governed by the same fundamental properties of magnitude, dimension, and direction, that determine the characteristics of the small scale phenomena that we’ve been discussing.

One of its most dramatic impacts, however, is on our understanding of the arrow of time, which we will discuss next.

In the last entry, we announced the breakthrough, following Montgomery and Jeffrey (M&J), that allows us to form atoms from nothing but motion. In our case, time and space speed-displacements (SUDRs & TUDRs) join to form biforms called S|T units. These S|T units combine to form triforms, which act as preons to form two basic types of combinations called bosons and fermions. Bosons are photons, while fermions are quarks, electrons and neutrinos, each with their “antiparticles.”

The way M&J’s model works, three quarks constitute a triform, depending on the mix of quarks. With two up and one down quark, a proton can be fitted to a neutron, with two down and one up quark, in such a way that the up and down quarks constitute bonded pairs at the three apexes of two triangles in two planes. Combining a proton & electron, H, with a neutron, forms deuterium, ²H, and adding two deuterium atoms together forms a hexagonal lattice of helium, ⁴H, or the alpha particle, which then becomes the basic building block of their table of nuclides.

However, following nuclear reactions, tritium, ³H and ³He are formed first, as intermediate stages, by adding another neutron to ²H, which decays in about 12 years to ³He, but just how this works in the model is not so clear. Moreover, in the M&J model, the bonds between the constituent quarks are formed from electrical and magnetic forces, which are not used per se in an RST model, since force is defined as a property of motion.

These considerations have forced us to take another path in the development of the periodic table of elements that modifies the way the constituent quarks of the protons and neutrons are paired to form higher combinations, compared to the M&J model. Instead of forming a Dagwood sandwich from a deuterium atom, by adding a neutron on the other side of the proton, sandwiching it in between the two neutrons, in tritium, which decays into a proton|neutron|proton sandwich of helium three, we, again, form a triangle of triangles, following the quark pattern of triangles within a greater triangle.

Thus, in the LRC’s RSt model, quark triangles form proton and neutron triangles, and, now, these nuclei triangles form atomic triangles, as tritium and three helium. Of course, we have to remember that these triangles are only 2D diagrams, or schematics of the physical triangles of 3D merged spheres, but otherwise, it works out well.

Recall, that another difference in our model is that we include electrons with the quarks of protons, so we are dealing with atoms, not atomic nuclei, which don’t exist in our model. With only motion to work with, we have only two opposite, or dual, quantities to form the bonds between quarks, time motion and space motion ( time-displaced units = SUDRs and space-displaced units = TUDRs).

When deuterium forms, the total space and time units of motion balance out, which can be expressed as shown in figure 1 below:

Figure 1. Quarks, Nuclei and Deuterium

As shown in figure 1 above, the quarks bond perfectly as the proton|neutron mirror one another, with the electron sandwiched in between them, and the number of positive units equals the number of negative units. However, where do we go from here? As depicted in the bottom right panel of the figure, deuterium has no way to bond to deuterium. The polarity of the motion combinations match, so we seem to be stuck.

In the M&J model, the alpha particle, helium four, is formed from this latter combination of deuterium, by postulating that electrical and magnetic forces exist between the deuterium nuclei sufficient to bond them together (no mention is made of the electroweak force, only the electromagnetic force, as far as I can determine). Subsequently, once the deuterium atom is formed in this manner, another nucleon is added to the appropriate mirror nucleon to begin the formation of another alpha component (with tritium and helium three, as intermediaries, although tritium is not shown on the website)

Nevertheless, it’s clear from figure 1 that we cannot follow that procedure in our model, using motion combinations. Fortunately, though, if we re-arrange the nuclei triangles, so that, instead of mirroring them, as two layered planes, as shown in figure 1, we connect the nodes in a planar array of triangles, as shown in figure 2 below, we not only can form tritium and helium three, but helium four as well, and, indeed, every other isotope combination in the table of nuclides.

Figure 2. Planar Array of Nuclides Tritium and Helium Three

Since down quarks are composed of two green (balanced) S|T units and one red S|T unit (i.e. red = more SUDRs than TUDRs,) the unbalance is one red unit, or -1, while in the up quarks, there are two blue units with one green unit, for an unbalance of 2 blue units, or +2. With the three red units, -3, of the electron, the polarities balance out for each isotope, no matter how many protons and neutrons an atom is composed of. Therefore, we can simplify the diagrams by using colored triangles, blue for protons, and green for neutrons. Assuming that each node is an U-D quark bond, we can obviously diagram any atom in a planar array of triangles arranged on the sides of a polygon, with the requisite number of sides corresponding to the total number of protons and neutrons making up the isotope, as illustrated in Figure 3 below.

Figure 3. Schematic Diagram of LRC’s Model of Periodic Elements

Of course, there’s much more to the model than just a data schema, such as physical parameters that can account for physical properties, especially periodicity, mass and absoption/emission spectra, but then this is great progress.

As the regular readers of this blog know, the LRC’s RSt starts with nothing but motion, postulates “direction” reversals to obtain SUDRs and TUDRS, and combines these into SUDR|TUDR (S|T) units that constitute preons, forming the various entities of the standard model (SM). These entities take the form of two types of triforms, the bosons formed in a planar array of three S|T units, and the fermions, formed in a triangle of three S|T units, as illustrated with bar magnets, in figure 1 below:

Figure 1. The Two Triforms of S|T Combinations

However, unlike magnetic poles, S|T units are formed from discrete units of time-displaced, s³/t⁰ = 1/2, scalar motion and space-displaced, s⁰/t³ = 2/1, inverse scalar motion. Hence, a given S|T unit can have either an equal number of SUDRs and TUDRs, or an unequal number. To indicate the different possibilities, schematically, we employ a bar with three colors, red, blue and green. The SUDR component of the S|T units is indicated with the color red on one end of the bar, while the TUDR component is indicated with the color blue on the other end. When a given S|T unit has more of one component than the other, the color of the greater component is placed midway between the ends of the bar. If the unit has an equal number of the two components, the color green is placed between them. The result for up and down quarks is shown in figure 2 below:

Figure 2. The Up and Down Quarks Formed from S|T Preons

Of course, we were quite pleased with this much progress in our theory, but when we tried to take the next step, to form the atomic nuclei from the quarks, a proton with two up and one down quark, and a neutron with two down and one up quark, so we could move on to the periodic table, we always ended up with a complicated mess, which had little discernible order to it. Moreover, just how we were going to fit the electrons into the pattern was not apparent at all. As a result, our research focus shifted to other areas. Until this week, that is.

Last Wednesday, Jerry Montgomery and Rondo Jeffery, announced the dramatic results of their efforts to model atomic nuclei, based on arranging quarks as three particles, forming a triangle (see: their website). Immediately, it became clear that this was indeed the way to do it! Not only does this dramatically solve the problem they were working on, to successfully model the nucleus of legacy physics, solving the many difficulties with the historic approaches, but it also solves the problem in the LRC’s efforts to combine quarks and electrons in our RSt, taking us to the next level!

In pondering their nuclei model, they realized, as we did in pondering our preon model, that with three components, there is only one geometric possibility, three points must form a plane, a triangle. Of course, in our case the colored bars are only a schematic representation of the three psuedoscalar eigenstates merging together physically, as shown in figure 3 below:

Figure 3. The Physical Triform of Fermions

Nevertheless, the result is the same. The only geometric possibility of combining three points is a plane. From there it was easy, following their lead, we just combine our triangular quarks into a larger triangular proton or neutron, instead of trying to make them into some complex 3D configuration, as we had been attempting to do. Figure 4 below shows the arrangement:

Figure 4. The Proton and Neutron Arrangement of Quarks

As Jerry and Rondo point out, and as is clearly evident from figure 4 above, folding these two nuclei upon one another, like closing an open book, brings each quark into alignment with its inverse companion quark. But what may be news to them (hopefully welcome news!) is that, like a cutout in the middle of a book, a perfect slot for the electron is created!!!! Our preon model of the electron is shown in figure 5 below:

Figure 5. S|T Combinations Forming the Electron of the Standard Model

Clearly, there has not been enough time to examine all the ramifications of this yet, but the preliminaries sure look promising. Just a look at the colors shows why protons are positively charged (four blues and one red), but neutrons are not (two blues and two reds), but adding an electron to a proton neutralizes it (four reds, four blues), and the combination of one electron, one proton, and one neutron is neutral (six reds and six blues).

Following the Jerry and Rondo model, our model of a proton/electron/neutron “sandwich” would be joined at the base with another sandwich, just like it, but vertically inverted, to form the helium atom, which in their model forms a basis for building a lattice of atomic nuclei only. No mention of electrons is made, if I’m not mistaken. Presumably, though, the latticework of their nuclei is somehow surrounded by a cloud of electrons, required by the shell model of the legacy system’s atomic concept, based on quantum mechanics.

As has already been pointed out by Paul deLespinasse, however, in Larson’s RSt, the atomic model does not admit various, independent, entities to exist in the atom, such as rotating electrons, a la the Bohr model of electronic orbits, or the QM model of electron clouds. In Larson’s model, the atom consists of nothing but discrete units of scalar motion. Larson’s model consists of n-dimensional rotations of a linear vibration and combinations thereof. Meanwhile, our new RSt model consists of combinations of n-dimensional vibrations period. No rotation is involved, even thought the constituent entities, electrons, protons, and neutrons retain their identities, schematically. A roadmap of the requisite combinations is shown in figure 6 below:

Figure 6. From Quarks and Leptons to Helium

Though different than Larson’s RSt model, the LRC’s RSt model treats the atom in the same way his model does, as nothing but discrete units of scalar motion. It’s important to remember, that the pattern of quarks and leptons in an atom, such as helium, indicate discrete units of scalar motion. There are no moving particles in the atom, and no nucleus.