The Larson Research Center

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.