The Larson Research Center

They say that the standard model of particle interactions (SM) is the greatest intellectual achievement of the 20th Century. It stands as something the LST community can point to that explains the structure of the physical universe. Of course, they confess at the same time that it’s far from perfect or even complete, but many books are written every year extolling its virtues. Certainly, no one in the LST community believes that future physical theory won’t contain the SM in some form or another.

However, when we view the SM from the perspective of the chart of motions, we see a great simplification. In the chart of motions, there are simply four degrees of magnitude in four bases of motion, but in the SM four types of forces, based on only one type of motion, are used to classify four elementary types of entities in each of three categories (disregarding anti-matter particles). The four entity types classified by the four forces are divided into two sets: the quark type form one set, constituting the heavy particles of the atom, the protons and neutrons (nucleons), and the lepton type form a second set, constituting the light particles of the atom, the electrons and neutrinos. The interactions of these four types of atomic entities are characterized as governed by the four forces of the SM, three of which are understood fairly well by the LST community, while the fourth is not.

The three forces that are understood are the so-called electromagnetic, the weak, and the strong force. The force that is not understood is the gravitational force. However, when the SM is expounded by LST teachers and authors, the concept of force itself, or of a force field, upon which the SM’s classification scheme depends, is seldom explained in detail. Yet it is important to recognize that the force field concept is treated as an autonomous concept in LST physics, as if it were something that has an independent existence like acorns or automobiles.

For instance, the theoretical strong force arises from the concept of a field quantum that is thought to bind three quarks as one, called a gluon. The theoretical weak force is thought to be a property of another field quantum, called an intermediate vector boson (IVB), that transforms one lepton, or quark, into another lepton, or quark, while the theoretical electromagnetic force is thought to be a property of a third field quantum, the photon, that transforms the charges of quarks and leptons. The theoretical field quantum of the gravitational force is thought to be the Higgs boson, but the interaction it is supposed to catalyze hasn’t been observed yet.

Of course, energy conservation is the governing principle of all these interactions, but it’s energy in the form of charge conservation that is the key to understanding the SM. The idea is that anything that happens in the physical universe is caused by these four force interactions, and they are regarded as properties of charges, not electrical, magnetic, and gravitational charges, but electrical and color charges. The color charges are the charge of the strong force, the electrical force is the charge of the electromagnetic and weak force, called the electroweak force.

Quarks have fractional electrical charges and one fractional charge is twice as great as the other, so two of one, when combined with one of the other, either totals one whole electrical charge, or eliminates it, depending upon the configuration (2(2/3) - 1/3 = 4/3 - 1/3 = 3/3, or 2(-1/3) + 2/3 = -2/3 + 2/3 = 0). The gluon quanta of the strong force carries the color charge of quark interaction.  They are called red, green, and blue, and any three bound quarks are associated with one of the three color charges, so that their combined color charge is always white, or neutral (zero).

Both energy and net electric charge must be conserved in all force interactions. No matter what, when physical entities interact, energy must be conserved and the net charge must be the same after as before the interaction. However, if we regard force as a quantity of charge, whether color charge, or electric charge, the question that really needs to be answered is, what is charge?

In the case of the EM charge, the force quanta, the photon, is not a charge carrier, but in the case of the weak charge, the force quanta, the IVB, is the charge carrier. In the case of the strong charge, the force quanta, the gluon, is the color charge carrier.  Whether the force quanta, called bosons, are charge carriers, or not, depends on the particulars of the gauge principle that applies in each case.  So, what are gauge principles, and how do they relate to these four “fundamental” forces?  The short answer is that they are principles of symmetry that relate to energy/charge conservation, or invariance, but that doesn’t tell us much.

Gauge theory is the underlying principle of the SM.  It was used to modify the initial quantum electrodynamics (QED) theory of the SM, and it is the basis of the SM’s quantum chromodynamics (QCD), often referred to as a “pure gauge theory.” In order to understand the underlying symmetries of the SM, it’s necessary to understand Lie groups and Lie algebras and how they contain elements of rotations expressed as products of multi-dimensional complex numbers.  These abstract concepts express magnitudes of “spin” and “isospin” that enable LST physicists to “renormalize” their calculations of wave equation solutions, predicting the outcome of particle interactions.  Without this capability to renormalize the calculations, the interaction theories give nonsensical results, but with it, the theories are quite successful, and it is the identification of the appropriate Lie group, in which the pattern of the charge properties is revealed as a specific mathematical structure, that makes renormalization possible.  In other words, given the mathematical structure of this pattern, and the observed strength of the relevant charge (coupling constant), the calculations give the accurate predictions of the LST’s SM.

Given the nuclear model of the atom then, each force of the SM exhibits an underlying mathematical structure that forms a unique Lie group that pertains to the domain of the relevant charges, revealed through the pattern of their properties.  Thus, the EM force pertains to the electrically charged Coulomb forces of interaction between atomic constituents, binding electrons and protons together for instance, and it always involves the bosons of radiation, or photons.  This pattern of charge properties exhibits the mathematical structure of the Lie group known as U(1), described by the single dimensional value of a complex number in the unit circle. The pattern of charge properties exhibited by the weak force, binding nucleons into nuclei, always involving IVB bosons, is described by the two-dimensional Lie group known as SU(2).  Finally, the pattern of (color) charge properties exhibited by the strong force, binding quarks into nucleons, always involving gluon bosons, is described by the three-dimensional Lie group known as SU(3).

 Hence, mapping these Lie groups to the chart of motions suggest a correlation, as shown below:

           Mag    U(1)   SU(2)  SU(3)

1. (1/1)⁰, (2/2)⁰, (3/3)⁰, (4/4)⁰
2. (1/1)¹, (2/2)¹, (3/3)¹, (4/4)¹
3. (1/1)², (2/2)², (3/3)², (4/4)²
4. (1/1)³, (2/2)³, (3/3)³, (4/4)³

However, the fact that, in the SM, the charge of gluons comes in the form of the three primary colors, to convey the concept of color charge, with the net charge of the three combined charges equaling zero, analogous to the white result of combining red, blue, and green colors, and the use of the same analogy, in the base 4 motion of scalar motion, is purely coincidental.  Nevertheless, it shows a close connection between the central concept of n-dimensional force, used in the SM, and the central concept of n-dimensional motion, used in the motion chart.

Hence, while the difference between the two approaches of classification is conceptually divergent, the intimation is that there is an underlying commonality.  One that we clearly expect and need to clearly understand, but which must be understood in terms of motion, not force, since in the RST, force is a property of motion, a quantity of acceleration, which is energy per unit time.

 

Probably the most fundamental interaction in the standard model of particle interactions, is the so-called pair production/annihilation interaction, explained in terms of field theory, the quantum electrodynamics field theory (QED), where the electromagnetic force and electrons are treated as fields of quanta, the photon and electron quanta. QED explains how these quanta interact as fields, predicting the positron quanta and the electron/positron to photon, and the photon to electron/positron transformation interactions.

At the LRC, we’ve yet to identify the theoretical entities corresponding to the electron, positron, or photon, but we know that, when we do, they will have to have the same properties and interactions as described in QED, but not in terms of force fields, but in terms of M motion. This means that we will need an RSt description of pair production/annihilation in terms of the UPR, SUDRs, and TUDRs. Last time we saw how, by taking a closer look at the SUDR, TUDR, and SUDR|TUDR (S|T) combo in a world line chart, we can see that the S|T combo has two M4 motions, designated the P and NP motions.

The P motion is so called because it progresses uniformly outward, a continual increase of space and time, while the NP motion does not progress outward uniformly, but oscillates inward/outward, as the increase/decrease of a unit volume of space/time. I provided a graph in the previous post to show how this works, but I have added to it somewhat in order to clarify the details of the P and NP components, as shown in figure 1 below:

Figure 1. The P and NP Components of M4 Motion

As figure 1 shows, the green arrows are “resultant” vectors, representing the two space and time components of the SUDR and TUDR constituents of the S|T. However, since the coordinates of the chart are q values, consisting of x, y, and z coordinates as one, 3D, coordinate, the green arrows represent a uniform expansion (progression) of time (SUDR) and space (TUDR), associated with the decrease/increase, or non-progressing, reciprocal aspect, in each case. I’ve added blue (space) and red (time) arrows to the previous chart to indicate more explicitly what’s happening.

Notice that the blue arrows of the TUDR’s uniform space progression are opposed to half of the blue arrows of the SUDRs non-uniform space progression, while the red arrows of the SUDRs uniform time progression are opposed to half of the red arrows of the TUDR’s non-uniform time progression.  In other words, the SUDR is uniform time progression, but “stationary” space progression, while the TUDR is uniform space progression, but “stationary” time progression.  The two uniformly progressing aspects therefore constitute uniform, outward motion, or P motion, while the two non-uniformly progressing aspects constitute the “in place” motion of the combo, or NP motion.

However, it’s possible that the oscillations of one S|T combo might be 180 degrees out of phase with another S|T combo, located nearby, so that the SUDR component of one is expanding, while the SUDR component of the other is contracting, with the same condition holding for their respective TUDRs; that is, a condition can exist where the respective displacements of S|T₁ are 180 degrees out of phase with those of S|T₂. Figure 2 below shows this situation as two S|Ts in the world line chart:

 

Figure 2. World Line Chart of Two Opposed S|Ts 

Since the two NP motions in the opposed S|Ts are 180 degrees out of phase (NP and -NP), their motions offset one another, but the P and -P motions are not offset, but orthogonal, as can clearly be seen in the close-up of the NP motion in the chart of figure 3, below:

 

Figure 3.  Close-up View of the M4 P and NP Motion of Two, Opposed, S|Ts

Clearly, the NP motion of the two S|Ts are opposed and thus they offset one another, but the space aspect of S|T₁’s P motion, and the time aspect of S|T₂’s P motion are orthogonal, thus they produce an outward ds/dt (or dt/ds), uniform progression, represented by the resultant, or the diagonal, between them (not shown).  The fact that the P motion of S|T₂ constitutes, in effect, a negative time progression, leads us to designate it as -P.

Of course, the similarity here with the standard model is striking.  Designating the P component of S|T₂ as negative is arbitrary.  The point is that we have two entities, with identical properties, except that the P component of one is the reflective inverse of the other, and when they combine, the Ps become an outward motion.

The Feynman diagram of QED represents a pair annihilation interaction as shown in figure 4, below:

 

Figure 4.  Feynman Diagram of Electron/Positron Annihilation

As in our world line charts, time increases going up in a Feynman diagram.  The arrow pointing down for the positron does not indicate that its change of position is from future to past, but that the mathematics works only if its time component is negative.  Of course, the temptation is to identify the M4 motions in figure 3 with the electron and positron of figure 4, but there’s a long way to go before we can do that.

One of the first things we want to understand is the difference between this interaction of fields in QED, and the well-known electromagnetic radiation that emanates from an accelerating charge.  The first difference is that in the QED interaction, the electron and positron cease to exist as entities of matter, replaced with an equivalent amount of radiation energy, converted according to the E = mc² formula. Thus, (E = mc2) —> (E = hv) in the transformation, which is to say that the M4 motion is transformed to M3 motion, disregarding any M2 motion, or E = 1/2mv² energy, of the particles.

In the case where the accelerating charge of the electron radiates energy, the electron does not cease to exist, but slows down, or speeds up, as measured by a change in the change of position rate, or velocity.  Hence, in this transformation, a portion of the energy of the electron’s M2 motion, E = 1/2 mv², is  converted to the energy of M3 motion, E = hv.  While the M4 to M3 transformation is described by QED equations, the M2 to M3 transformation is described in terms of Maxwell’s equations.  In either case, though, the appropriate equations of mathematics ensure us that energy is conserved in the respective transformations.

Nevertheless, the interesting part to us is not just that energy is conserved in the transformations, but that one form of motion is changed into another form.  It’s also very interesting to note that the M2 to M3 conversion is an “up-conversion,” from base 2 motion to base 3 motion, while the M4 to M3 conversion is a “down-conversion,” from base 4 motion to base 3 motion.  We would expect that motion is conserved in this conversion process, as well as energy, or that we could show the law of conservation in terms of motion, as well as in terms of energy.

However, in the energy equations, total energy is divided into potential and kinetic energy, which is proportional to the sine and cosine of a rotation angle, like that in a swinging pendulum, making it possible to formulate the change of energy in association with a change in the rate of change of position.  In this concept, velocity is defined in terms of “the limit” of delta t, and space is defined in terms of velocity times the limit, the vanishingly small limit of the continuum (see “The Need for Differential Calculus” post in the “The New Math” forum).

In contrast, the energy of M3 and M4 motion is defined in terms of fixed units of space and time and the velocity is constant, not changing.  Hence, the central idea of LST physics, the laws of conservation of energy and momentum, expressed in terms of the equations of varying motion, cannot be applied to motion that does not vary in the same way.  In other words, the classical ideas of energy and momentum conservation, as invariant quantities through transformations of space and time have to be treated differently, when the definitions of space and time change, as they do in base 3 and base 4 motion.

 

Larson wrote a book entitled Beyond Newton, and people now days talk about physics “beyond the standard model,” but the standard model is really the crowning achievement of Newton’s program, and to go beyond Newton is to go beyond the standard model. 

However, Larson never really compared his work with the standard model in any direct way.  He wrote his Case Against the Nuclear Atom, but this was early on.  By the time the standard model was in place in the late seventies and became  somewhat accessible to non-professionals in the eighties, it was too late.  The members of ISUS not only were never able to address the standard model viz-a-viz the RST, but they generally took an attitude of animosity towards it and the quantum mechanics it rode in on.

Nevertheless, it is embarrassing that, while the standard model is capable of very accurately predicting the fundamental interactions among the debris of high energy particle collisions in the accelerators, Larson’s physical theory, the RSt, which he developed from the new system of physical theory, the RST, can not even play in that game. It’s as if the standard model could predict where every ball ends up, from the opening break on a pool table, but while the RSt has nothing to say about the positions of the balls, it can tell us what the standard model cannot tell us - what the balls on the pool table are made of. 

Hence, both the standard model and the RSt are incomplete.  Newton’s program assumes the existence of matter, radiation, and energy, with the properties of propagation, gravitation, mass, charge, spin, etc. as inputs (19 - 24 such parameters altogether) to the standard model, but has worked out the “fundamental” interactions of matter in terms of M2 motion.  The RSt, on the other hand, assumes only the existence of M4 motion, with its properties of quantum units and two reciprocal aspects, but has worked out the fundamental composition of matter, radiation, and energy, with their respective properties, in terms of M4.

The reason why I place quotes around “fundamental” in the phrase “fundamental” interactions is that this indicates the source of the aforementioned animosity among ISUS members towards the standard model.  Force, Larson argued, is a property of motion, by definition, and cannot exist as an autonomous, or “fundamental,” entity. The fact that the LST community has ignored this implication of the definition of force is one of the major Neglected Facts of Science, Larson wrote about so compellingly.

However, this temptation to smugness is something that members of the Society cannot afford to indulge, as honest investigators of the truth.  The standard model is not regarded as the greatest intellectual achievement of the 20th Century for nothing.  The modern world of high-energy physics, and physics in general, depends upon the understanding inherent in it.  How foolish do we look, if we deny its worth, just because we think we know that forces can’t be fundamental?

What we really need to do is to roll up our sleeves and go to work to find the common ground between the standard model and the RSt.  To do this, we need, first of all, to understand what the standard model of “fundamental” forces is and how it works, so that we can relate its concepts and principles to those of the RSt.  Of course, here at the LRC, since we are developing the RSt along somewhat different lines than Larson did, the challenge is to relate the standard model to our particular development, which we are documenting in the SPUD. 

In the SPUD, we show how the “direction” reversals in the unit progression, shown in the PAs, lead to the formation of reciprocal, unit, speed-displacements, called SUDRs and TUDRs.  We show how these discrete units of space/time progression, located on either side of the unit space/time progression line, in our  world line charts, and their combination, as S|T combos, located on the unit progression line of the charts, relate to the space/time progression in general.  However, we can further clarify what the S|T combination entails by incorporating the motion of the PAs on the charts, as shown in figure 1 below:

Figure 1.  M4 (scalar) Motion World Line Chart

Figure 1 shows that M4 motion consists of two motions simultaneously.  The propagation motion of continual s/t increase, and the non-propagation motion of continual s/t increase/decrease, are both components of the S|T combo.  What this means, in effect, is that the S|T combo is both a point and a pseudopoint, simultaneously.  Of course, the pseudopoint is a 3D expansion, while the point is a 3D oscillation, so the coordinates of the chart are points in the sense of the value q, specified by three coordinate points. Thus, a change in q indicates a change in volume, or size.  Red ques (red s) are space coordinates, while blue ques (blue t) are time coordinates. 

The 3D expansion, or pseudopoint (P), continues expanding, as long as space and time are progressing, but the 3D point associated with it, and inseparably connected to it (NP), remains stationary in the space/time location of its origination, unless acted upon by an outside agency.  However, since the frequency of the TUDR (2) is four times higher than the frequency of the SUDR (.5), from the perspective of the SUDR space/time location, the natural harmonics are present as well; that is, a frequency twice that of the SUDR (the first octave from the fundamental SUDR frequency and the second harmonic), three times it (third harmonic), and four times it (fourth harmonic and second octave, the TUDR). These harmonics play a significant role in the structure of the S|T combo, but I won’t comment on this aspect for now.

What I want to point out now is that since the S|T entity consists of two types of M4 motion, the continual expansion and the continual oscillation, as clearly show in figure 1, there are two ways that it can interact with other, similar, entities: one way is as a stationary entity of unit size, and the other is as an expanding entity of unit speed.  As the chart in figure 1 shows, the first is a 1/1 ratio, while the other is a 2/2 ratio, but this is deceiving, because the oscillation of the NP motion, as indicated by the double-headed arrow in the lower left box, hides the fact that it is also two units of motion, one each in two “directions.”  Thus, the total motion is actually P + NP = 2/2 + 2/2 = 4/4 units of M4 motion, which is what the RN equation expresses (ds/dt = 1/2 + 1/1 + 2/1 = 4/4).

In the SPUD, we show how adding M4 units of SUDR or TUDR motion to the S|T combo, balances it, or unbalances it, but in all cases the total number of units is always a unit value, n/n.  This aggregation-of-units process increases the quantity of the units in the combo, or its density of space/time we might say.  However, it also shows how this system of motion must relate to the standard model on a fundamental level.  We reach this conclusion based on the following considerations:

The fundamental classification of the standard model classifies physical entities in terms of three interactions:

1. The “strong force” that forms heavy units of matter called hadrons (e.g. protons and neutrons).
2. The “weak force” that binds these units of matter together into nucleons of hadrons.
3. The “electromagnetic force” that binds lighter units of matter called leptons to the nucleons made up of hadrons, to form atomic units.

In the tetraktys of motion, containing the four bases of motion, we have the same classification, but in terms of motion, not forces:

1. M4 motion, which is motion, based on change of scale (numbers) in the bound units (SUDRs & TUDRs bound as S|T units).
2. M2 motion, which is motion, based on change of position between bound, or S|T, units of M4 motion.
3. M3 motion, which is motion, based on an internal, change of interval, motion in the oscillation component of the M4 bound units.

Of course, this is just a start, but already the parallels are striking.  The S|T units may be balanced or unbalanced.  If unbalanced, the unbalance is in two, opposite “directions,” giving us three possibilities that are parallel to the three possibilities of the standard model: neutral, positive, or negative.  The neutral, positive, and negative values come in discrete values.  The lighter values of neutral, positive and negative are much lighter than the heavier values of neutral, positive and negative, but the scalar difference is not in the “density” of the “directions,” neutral, positive, or negative, but in the magnitude of the total density; that is, a much heavier neutral entity, can be unbalanced, or “charged,” by just one unit of “direction,”  in the same manner, and to the same magnitude, as the lighter neutral entities.

We’ve been aware of the “direction” parallel for some time now, but the concept of the two simultaneous components of M4 entities is new, and the parallel with the standard model that we see right off is in the de Broglie relation, where each quantum physical entity has an associated wavelength, given by:

λ = h/ρ

where h is Planck’s constant and p is the momentum of the entity.  If Planck’s constant is proportional to P in M4 and its “momentum” is proportional to the NP component, then what we have is the same ratio; that is, the wavelength, s, is just an expression of the unit ratio of P/NP = (2/2)/(2/2) = 1, or the ratio of the two components of the natural unit of motion, 4/4 = 1/1.  To see this, we have to recall Larson’s insistence that the dimensions of h are t²/s², the same as momentum, not the dimensions of action, t²/s.  Thus, if Larson is correct, we get

(t²/s²)/(t²/s²)  = 1, not s.

Hence, we conclude that the de Broglie relation is part of the RST model, as well as the standard model.  There are many other parallels, which we will be pointing out as we approach the answer to the question, “What is conserved in the transformation of M4 motion?” but that’s enough for now. 

 

I’m still going to talk about the law of conservation of motion in all this, but I also want to try to clarify what it is that we are doing, to help us get our bearings, so-to-speak, before we get too far down the road. In the LST, the grand goal of the program has been to classify the basic structure of the physical universe in terms of a “few interactions” among a “few fundamental particles.” The standard model of particle physics is the result of this effort and it is very successful, in that sense, capable of predicting physical phenomena to very high accuracy.

However, the standard model is not very satisfying in terms of explaining what the physical structure of our universe is and why it takes the form that it does. We know that there are photons, electrons, positrons, neutrinos, and the various hadrons formed from what is believed to be quarks, and all of these are organized into three families, one of which is stable, but knowing that electrons, positrons, etc interact via photons, and that the quarks of heavy hadrons might be held together by gluons, is not very helpful when the descriptions of these entities are in terms of their measured properties, such as mass, charge, spin, etc. We know what an electron is because we can measure its mass, its charge and its spin and, given this information, we can now predict how it will interact with other electrons, or with other entities under different conditions.

Fine, but what do we tell the kids when they ask us, “What is mass, Daddy?” or “What is charge, or spin?” As long as there are no answers to these questions, explaining that the energy of an electron changes when it aborbs or emits a photon, isn’t enough. The new system of physical theory, and the new system of mathematics comprise a new program of research, or science, the goal of which is not the classification of particles of matter, in terms of a few, fundamental, interactions, but rather the uncovering of the process by which the infinity of one is manifest in the infinite diversity of everything. That is to say, we don’t focus on the forces, or interactions, of nature to understand what its underlying reality is, but rather we focus on identifying those patterns of motion, combinations of motion, and relations between motions, which we have assumed make up the structure of the physical universe.

This is our program, and it gives us a unique insight when we study the standard model, because we can see that base 2 motion is only a part of the picture. Base 3 and base 4 motion obviously play a crucial role in the drama, as well. Thus, we seek to understand how these different types of motion interrelate, not just in terms of interactions that affect the positions, momenta, and total energy of particles and fields, but also in terms of the origin of their magnitudes of mass, charge, and spin.

Hence, in our program, we are interested in what’s “inside” physical entities, and we don’t need to accelerate them to high velocity and smash them into one another to investigate these things. In fact, it’s probably a better approach for us to examine them in the regime of condensed matter physics, where the complication of base 2 motion is reduced to the lowest possible level, rather than raised to the highest possible level, as in particle physics.

However, the history of both the successes and the failures of particle physics is very useful in our program, because it characterizes the thinking of those who have faced the challenge of trying to make sense of the base 3 and base 4 motion, given only a knowledge of base 2 principles. Take, for instance, the concept of the Heisenberg uncertainty principle (HUP) and its use in justifying the concept of virtual photons, in the electromagnetic interactions.

The use of this principle has provided great results, but in spite of every effort to discover the foundation upon which it rests, it’s as mysterious as ever. We can understand how the exchange of virtual photons between electrons can be rationalized by the HUP, but it leaves us with a strong suspicion that this process is an analogy at best, and misguided at worst. While it’s true that a one-dimensional base 3, or interval, motion of sorts is created when, say one skater tosses a medicine ball to another, and Newton’s laws act to increase the interval between the skaters, but we are relunctant to believe that this is anything more than an M2¹ analogy of a true M3¹ motion ( from now on, I’ll use the letter M instead of the word base.)

As a matter of fact, when we look carefully at M2, M3, M4, we know that the familiar M2 motion takes three, independent, forms, or dimensions of magnitude, and we also know that M3, cannot take but one, 3D, form, under ordinary circumstances. Otherwise, it couldn’t be scalar motion. It’s a pretty good bet then, given the importance of symmetry, that M3 is more constrained that M2, and less constrained that M4, which leads us to conclude that it cannot take three independent forms, but only two: a two-dimensional, and a three-dimensional form, but not a one-dimensional form.

If this is so, then the chart of the bases of motion that we’ve been discussing, would have entries like the following, disregarding the unit base of motion (M1) and the zero dimension of magnitude:

M2 M3 M4

1D —— ——

2D 2D ——

3D 3D 3D

We get our clue for this conclusion, from the intuition that, since we know that M2 motion defines the change of its space aspect, in terms of the positions of objects, then, probably, M3 motion defines the change of its space aspect, in terms of something else, not in terms of the changing position of objects. If this is correct, then the most likely candidate for what defines the changing space aspect of M3 motion is the wavelength of radiation. However, a wavelenth cannot be changed independently, without also changing the wave amplitude, by a proportionate amount. Nevertheless, two such magnitudes may be summed together, with their wavelengths coincident, but their amplitudes orthogonal. Consequently, if M3 motion is radiation motion, then it could not take a 1D form, just as M4 cannot take the 1D, or 2D, form, at least under normal, unconstrained, conditions.

This leads us to yield to the temptation to classify M2 motion as the motion of matter, M3 motion as the motion of radiation, and M4 motion as the motion of energy.  Of course, the motion of energy is scalar, which fits nicely enough in our taxonomy, but we are so used to thinking of it in terms of radiation, even though we know that radiation differs from energy per se, that the use of the word in this context appears problematic.  It would be better if we could find another word, especially since, once we invert the space/time dimensions of M2, M3, and M4, and we are on the energy side of unity, reference to the “energy” of “energy motion,” M4, would be really confusing.

One approach is to stop referring to the other side of unity as the energy side, and consistently refer to it as the inverse side of unity, and its magnitudes as inverse motion magnitudes, or IM1, IM2, IM3, and IM4, or use Mbar, but it’s hard to write the bar symbol in web page text.  Whatever the decision on that score, we have another new concept that we can now articulate better: the energy concepts that correspond to the motion bases become very clear:

1. M2_E = 1/2mv²
2. M3_E = hv
3. M4_E = mc²

UPDATE: Introducing the notation “M” for the four motion bases, M1, M2, M3, and M4, for the first time in this post, I inadvertantly got them mixed-up in the text above, which is really, really, confusing.  I fixed them now, so the post should be more coherent.  I applogize for any grief this might have caused.

Well, we finished up the LRC Seminar in American Fork last night.  I’d been working on the presentation all week. It was entitled, “LRC Science, What is it? Part II.”  In the first part, on the 15th of November, I tried to establish the rationale for asserting that the LRC science is scalar science, as opposed to vector science, but, in spite of my best effort, I didn’t think I carried the day with the “docs.”  They’re not an easy crowd to convince, but then that’s good.

This time I had more ammunition.  It’s a new chart I’ve designed to show that the four numbers of the tetraktys are actually four dimensions of motion.  We talked about how, from the ancient Greeks, to modern times, the focus of science has been on this mysterious and enchanting collection of numbers. I’ve already discussed the new chart in the New Math blog, but I’ll insert it here too, in figure 1 below. I’ve thought since last night, that, given that each dimension of motion is a number raised to a power, the word dimension in this connection might be confusing. So, I’ll refer to them as bases of motion, instead of dimensions.  Each base of motion is raised to a power of magnitude.

 

Figure 1. Four Bases of Motion 

Each base of motion is a fundamentally different way to represent a change of space over time (velocity), or a change of time over space (energy).  The second base defines the units of the first base, by a change of space (time) position, the third by a change of space (time) interval, and the fourth by a change of space (time) scale.  Our discussion of this chart last night focused on how the legacy scientists are trying to exploit the principle of rotation symmetry to explain all natural phenomena, but here we see that rotation is not necessarily the appropriate principle to use, since it applies to the second base of motion (base 2 motion), or the familiar vector motion of position change in space.

Of course, the base 2 motion and the base 3 motion are a familiar part of LST physics, and they have been thoroughly studied, but the base 4 motion, scalar motion, is not even recognized by LST scientists. Consequently, the most relevant question asked last night was, naturally enough, “What is it that is conserved in base 4 motion?”  However, even though this is the first question one would expect of a physicist, I had to stop and think about it.  My first thought was, well, in a universe of nothing but motion, the thing conserved has to be motion, and I said so, but I’ve never heard of a law of motion conservation.  We are all familiar with the conservation laws of momentum and energy, but a conservation law of velocity?  How is velocity conserved? It started me thinking.

But before I start explaining what those thoughts were, notice how the chart shows n-dimensional magnitude as space magnitude. This is because dsⁿ/dtⁿ is a measure of space magnitude in our experience, but what about the dtⁿ/dsⁿ magnitudes? Obviously, the same principles of three dimensions of magnitude for each base of dt/ds motion hold, but then the magnitudes become magnitudes of time, as if we were looking at linear, square, and cubic dimensions of time magnitude!

Of course, we’ve been doing this all along in the equations, only we call the n-dimensional time magnitudes different names and think of them as scalars, not time vectors. Obviously, the names of these three time scalars are energy (dt/ds), momentum (dt²/ds²), and mass (dt³/ds³), but they correspond to the line (ds/dt), area (ds²/dt²), and volume (ds³/dt³) space magnitudes in the chart above. Moreover, there’s another disconnect too, because we aren’t accustomed to thinking of linear, square, and cubic units of motion either, even though these are clearly what the chart implies.

However, it becomes clear what is happening when we recognize that time has no direction in space, and space has no direction in time; that is, the dimension of time in our velocity equations is scalar (n⁰), regardless of the dimension of the motion.  Also, In base 2 motion, all change of space is linear change, otherwise the object changing position would grow in one, or in the other, or in both, of the remaining two dimensions. So, the two-dimensional base 2 motion, ds₂²/dt₂², is interpreted as two space vectors, or V₁ = ds/dt x V₂ = ds/dt, and we use the cross product in vector algebra to obtain the resultant vector, ds/dt, or the dot product to get the scalar, which, being complements of one another, vary depending on the orthogonality of the vectors. 

Nevertheless, in the case of GA, the inner product and the outer product are combined, into the geometric product, to calculate a 2D area defined by the angle of the vectors, like someone drawing a two-dimensional space, by rotating one vector into a second dimension relative to the other.  Thus, GA defines a 2D magnitude through a 1D rotation, which is related to the 1D magnitude of the resultant vector of vector algebra, only different:  One is a magnitude of motion, the result of forces in different directions, while the other is an unspecified magnitude of higher dimension, usually thought of as a magnitude of space.  Why is this?  Because, as Newton said, geometry has nothing to say about how the “right lines and circles” of geometry are drawn.  These are determined by “principles brought from without,” the principles of mechanics.

But now we see that there are several principles of mechanics at play here.  As a matter of fact there are three such principles, and any one of them can produce the magnitudes of geometry, but not all in the same manner.  Change of position motion is one way, but it is not the only way to do it.  Change of interval, and change of scale will also do it.  What confuses our understanding of what is going on is the incorrect notion that n-dimensional magnitudes are magnitudes of space, when in reality, they are only magnitudes of motion with two, reciprocal aspects, space and time.

The proof of this is in the recognition that neither space or time can be measured independently.  Only motion can be measured.  We can measure past, or future, motion that changed, or will change, the positions of objects, by repeating the original motion, but disregarding the magnitude of the time or space aspect of it, in order to get the reciprocal aspect of it that we want.  For example, we can repeat the original motion that separated two objects, by moving a measuring rod between the two positions of interest and reading how many space units are required to span the distance, regardless of the time it takes to move the rod into place.  Thus, the speed may not be the same as the original motion separating the two objects, but the motion of the rod has shown us what the magnitude of the space aspect of that motion must be, regardless of the time aspect.

We call this measured distance between the two objects “space,” but it doesn’t exist as something independent of the motion between the objects.  It certainly is not something that exists between these two locations that can be curved, warped, or vibrated, for instance.  Such an idea is absurd. Thus, the motion between the positions of objects, or the area underneath or above, to the right of, or to the left of, or in front of, or behind the position of a plane of objects, or the volume within a cube, or sphere, of objects in different positions, is a representation of the linear, quadratic, or cubic magnitude of past motion that separated the objects, and nothing else.

Furthermore, it doesn’t matter whether the past motion was base 2, 3, or 4 motion.  In fact, there’s no way to tell the difference in most cases, and this thought brings me to the point I wanted to explain, about the idea of conservation of velocity, but I’ll have to wait until next time to relate my thoughts on that.  The only point that I need to make now is that, by interpreting velocity equations as magnitudes of motion, we need to recognize that these magnitudes can be n-dimensional, as the chart shows, not just one-dimensional, as in the vectors of base 2 motion.  For instance, two or three dimensions of time in a velocity equation, can be interpreted as the time aspect of two or three-dimensional magnitudes of motion, as well as the second, or third derivative, of one-dimensional motion.