Kinetons in the Reciprocal System
by Jan Sammer
The Reciprocal System defines the physical universe as a finite set of units of three-dimensional motion. For the sake of accuracy and brevity, I will call these fundamental units kinetons in the subsequent discussion. The kinetons are unobservable, but they come within the range of our instruments as soon as they are modified by some physical process. In the terminology of the Reciprocal System, they undergo displacement. Relative to the conventional fixed reference system, each kineton is travelling outward in three dimensions.
From Kinetons to Photons
The simplest modification that a kineton may undergo is the addition of a unit of one-dimensional energy (inverse speed, t/s) in one of the three dimensions of kineton progression, becoming a photon. Photons are produced in many different natural processes, perhaps the most common one being emission by atoms that have been excited by the addition of energy (inverse speed). Such atoms revert to their ground state by the emission a unit of this inverse speed in the form of a photon. But energy is not speed; it is inverse speed. In the material sector inverse speeds can only exist as modifications of existing speeds; they cannot exist independently. The atom’s excess energy must be attached to a preexisting speed. All material entities are subjected to a flux of kinetons, uncharged electrons and, to a lesser extent, of photons. Of these three, the kinetons are by far the most abundant. For this reason alone it could be expected that the unit of energy would most commonly attach itself to a kineton. Another consideration, besides sheer abundance, is that the kinetons are moving outward in three-dimensions, all of which are available to the excited atom for the disposal of its excess energy. The uncharged electrons are units of rotational space displacement, confined to the time region of the material aggregate. The electron will only accept energy in the form of a charge, that is, a rotational vibration, as a modification of its basic space displacement. For this transfer to take place, the atom not only has to pass through the space of the uncharged electron, but the encounter of atom and electron must take place along the correct rotational axis. Kinetons, on the other hand, will accept energy whatever their orientation, are extremely abundant, and can move through both space and time (matter). Hence we would expect the most frequent energy transfers to involve kinetons rather than uncharged electrons.
The addition of energy to a kineton results in a photon. Energy being one-dimensional, its effect on the kineton is confined to one dimension only. In the other two dimensions, the progression takes place as before.
From Energy to Speed and Back
Let us label the three scalar dimensions of the kineton a, b and c, and let us consider an event in which the unit of energy (inverse speed) is attached to dimension c. What happens when speed and inverse speed are superimposed on one another in one dimension?. Speed and inverse speed differ in the location of their point of origin. At the limit, zero speed is the same as unit energy; conversely, zero energy is the same as unit speed. In our example, the kineton is progressing at unit speed in dimension c, which means that it has zero energy in that dimension. But once a unit of energy is absorbed, the kineton immediately starts moving toward unit energy in dimenson c. As soon as it reaches unit energy, it finds itself at zero speed. It cannot exceed one unit of energy, but, being at zero speed, it can proceed to unit speed. We must recall that the energy was superimposed on the speed; this process did not eliminate the speed. As soon as unit speed (zero energy) is reached, the kineton can again begin moving toward unit energy in dimension c. This process will continue indefinitely, and constitutes the photon’s characteristic frequency, which is unity when only a single unit of energy is involved. As additional units of energy are added to dimension c, increasingly higher frequencies are produced.
Our characterization of the photon as oscillating between unit speed and unit energy is based on the different zero points of speed and energy; no outside mechanism is needed to produce the reversals at each zero point.
While the photon is oscillating in dimension c between unit speed and unit energy, its motion in the other two scalar dimensions, a and b, continues at unit speed. Our reference system coincides with only one of the dimensions of the scalar system. Let us consider a particular photon whose scalar dimension a is congruent with our reference system. We see the photon progressing outward along dimension a, and we observe it oscillating along dimension c. Although we could not ordinarily observe motion in a second scalar dimension, the oscillation in dimension c can be observed in a reference system congruent with dimension a because of the very nature of the oscillation. In the course of every cycle a point of zero motion (unit energy) is reached. While motion in a second dimension cannot be represented, zero motion can. However, there is no way of representing the photon’s motion in scalar dimension b.
Let us now reorient our reference system with respect to the natural system so as to make dimension b congruent with it, rather than dimension a. We will again be able to observe the oscillation in dimension c, as well as the progression in dimension b. But we will not be able to observe the progression along a. Since the orientation of our reference system in relation to the scalar system to which the photons conform is determined by chance in every individual case, we should expect to find two varieties of photons in nature, equally abundant, and distinguished by their orientation. Variety a will consist of those photons whose scalar dimension a is congruent with our reference system, and variety b of those whose scalar dimension b is so congruent. In both varieties, dimension c will be perpendicular to the direction of motion. But dimension c can be perpendicular in two ways, either horizontally or vertically. What is vertical for an observer along dimension a is horizontal for an observer along dimension b, and vice versa. The two varieties of photons are a function of their orientation with respect to the reference system; from the natural standpoint, no such distinction can be made.
A photon is polarized when its oscillation, which is perpendicular to the line of travel, is rotated by 90°. From the natural standpoint the polarization merely signifies that the photon’s orientation with respect to the reference system from which we view it is switched from a to b or from b to a. Polarization is normally achieved by passing a beam of photons through a special kind of crystal lattice. The polarizing medium is effective because it allows only one of the two varieties of photons to pass through it. Normally there is an even chance that the reference system from which we view the photon is congruent with scalar dimensions a or b. The polarizing medium screens out one of these orientations.
The Photon’s Two-Dimensional Path
The fact that the photon is moving linearly outward in two dimensions, while vibrating in the third is crucial in explaining the peculiar behavior of photons. Quantum mechanics has been successful in describing this behavior mathematically, but has failed utterly to account for it in any fashion that does not violate elementary principles of logic. Although the fundamental postulates require that photons move linearly outward along a two-dimensional path, while oscillating in a third dimension, Larson, followed by Satz, have confined the translational motion of the photon to a single dimension, allowing it to oscillate in a second. They have understood the combination of the photon’s oscillation and translational motion as accounting for its behavior as a wave in transmission, and as a particle in emission and absorption. They have declared the problem solved, without asking if their solution really accounts for the experimental evidence that has forced physicists to accept, at least provisionally, Bohr’s principle of complementarity. As for Kirk’s views on the photon, I confess that I do not fully understand them, though I have spent a considerable amount of time in the effort. But I gather that the second scalar dimension discussed by him refers to the oscillation, and not to a second dimension of translational motion.He has not even attempted to explain the double-slit experiment, or the EPR paradox, or the experimental evidence of the reality of that paradox in terms of his photon theory. These hard realities of late twentieth century physics must be clearly explicable by any photon theory worthy of the name.
The Double-slit Experiment
In the double-slit experiment, a beam of light is shone through two narrow slits at a screen. The screen displays an interference pattern such as would result if light travelled as consecutive waves, each passing through both slits at once, creating smaller waves issuing from each slit on the other side. These smaller waves then appear to interfere with one another, forming a characteristic pattern of maximum brightness in the area between the two slits, with dark bands on either side, and a less bright area directly behind each slit. If photons were simple bullet-like particles, like the corpuscles postulated by Newton, or even some sort of oscillating corpuscles, as posited by Larson and Satz, we would expect to find a bright area directly behind each of the slits, and only darkness in between. In modern physics the photon is a wave-like quantum phenomenon that appears to go through both slits simultaneously—although its path is indeterminate. But in the Reciprocal System, the photon travelling in two dimensions can pass through both slits simultaneously. We can represent both of these dimensions by constructing two independent Cartesian coordinate systems, each with its own set of double slits. The photon can be thought of as travelling along two one-dimensional paths in each of these systems—though in reality it is travelling along a single two-dimensional path. Hence each photon truly does enter through each of the two slits. This apparently counterintuitive conclusion follows from our earlier finding that the photon is moving in coordinate time as well as in space. No object can be in two different space locations at the same time; but in this instance we are dealing with two different locations in coordinate time, each associated with a different location in coordinate space. That is what two-dimensional motion necessarily means. A similar situation arises in relation to a massive body, such as the earth, which is moving inward in three dimensions toward all other locations. For each location in space toward which it is moving there corresponds a unique location in coordinate time. Any multidimensional motion must take place in this manner.
The EPR Paradox
In a paper published in 1935 Einstein, Podolsky and Rosen attempted to show that quantum mechanics led to the prediction that two photons, produced in a single event, and isolated from one another thereafter, nevertheless affect one another instantaneously; from this they concluded that quantum mechanics is an incomplete description of reality. The reality of this apparently paradoxical behavior of photons was recently confirmed by Alain Aspect. From the point of view of the Reciprocal System, the Aspect experiment has never been properly explained. Satz’s attempt to explain it by claiming that the two photons, while separated in space, are still contiguous in time, is self contradictory, since photons do travel in coordinate time as well as in space according to the Reciprocal System. One of the most elegant achievements of the Reciprocal System is its explanation of the apparent time-dilation at high velocities in terms of motion in time. The EPR paradox and the experiments that have confirmed its reality can only be explained if the photon is really moving outward in a two-dimensional path. If two separate and independent Cartesian coordinate systems are set up, both paths can be observed, though not simultaneously. In his experiment Aspect found interference between his two sets of isolated photons, and concluded that they were somehow communicating instantaneously, in violation of Special Relativity. But in the Reciprocal System, instead of two separate photons, we are dealing with a single photon travelling along a two-dimensional path. Since only one particle is involved, anything done to it in one coordinate system will be reflected in the other system. It is not a question of contiguity in time, but of identity.
The reader is invited to apply the photon as described in this paper to other experiments purporting to support quantum mechanics, including the so-called ”Delayed-Choice” experiment, in which causality appears to be violated. The apparent ”ghost-like” behavior of this particle, as well as of the charged electron, which too is moving in two scalar dimensions simultaneously, will be recognized as completely logical and understandable.
Doubly-oscillating Photons and the Laser
Since the postulates allow for the existence of a photon oscillating in one dimension while moving outward in the other two dimensions, do they also allow for the existence of another type of photon moving outward in one dimension and oscillating in two? In our terminology, could the kineton acquire two units of energy in two separate scalar dimensions, in b, as well as in c? This combination of motions appears to be somewhat improbable, but it is not impossible. We will call such photons doubly-oscillating photons. The oscillation in scalar dimension b would in almost every case be acquired only after the kineton had been transformed into a photon by the acquisition of a unit of energy in dimension c. Normally the chances that a photon will acquire energy in a dimension b are small because of the relative scarcity of photons, relative to kinetons, and because only two out of three possible orientations result in conditions favorable to the transfer. Moreover, as we shall see, the energy increment in dimension b has to be identical to the energy in dimension c. Though the formation of the combination appears to be somewhat improbable, it is stable once formed, and there is nothing in the postulates to rule out its existence. We should therefore expect a small proportion of photons to have a double oscillation. What properties would allow us to distinguish them from other photons? Since such photons would be travelling along a simple one-dimensional path, capable of being fully represented in a conventional reference system, they would not display any of the interference phenomena and wave-like features of regular photons. They would be polarized, since the one dimension of translational motion open to such photons would always be congruent with the reference system. A beam of such photons would not appear conical, like an ordinary beam, but would remain confined to a narrow cylinder. As the reader may by now have guessed, we are describing the properties of a laser beam. A laser beam is created by forcing the emission of photons from excited atoms by hitting them with other photons. The resulting photons have the same frequency and polarization as the incoming photons. The reason for the identical polarization has been explained. The frequency is the same because the number of units of energy acquired along scalar dimension b must equal the number along dimension c. Unlike an atom, the doubly-oscillating photon does not rotate, and therefore cannot distribute any imbalance between the two dimensions into a spheroid. In the laser the atoms that store the energy that is to be transferred to dimension b of the incident photons must be ”pumped up” to an energy level such that the energy difference between the excited state and the ground state of the atom is exactly equal to the energy of the incident photons. Viewing this process on the basis of our new understanding of what constitutes a photon, we conclude that under such circumstances the first photon is forced to acquire a unit of energy in a second scalar dimension. This eliminates its translational motion in dimension b, and its remaining translational motion in dimension a follows a classical one-dimensional path. Laser photons behave like Newtonian corpuscles should. The correctness of the above description of photon behavior could easily be tested by repeating the double-slit and Aspect experiments using laser beams. If this is done, the photon should behave as a classical particle. In the double-slit experiment, two bright areas will appear on the other side of each slit, and there will be no wavelike interference. In the Aspect experiment, likewise, there will be no ghost-like communication or interference.
Doubly-oscillating Photons and Atom Building
In Nothing but Motion Larson finds that atoms are built on two intersecting photons, but he has not shown that such an entity can exist. In truth such an entity would be highly improbable, if not impossible. If two photons were ever to meet in such a way that they would intersect, there is nothing that could hold them in that position. Like all other outward-moving entities, they would separate again after the passage of one unit of time. In his account of atom building in Basic Properties of Matter, Larson concludes that in the most common process two singly-rotating systems (the neutron and the neutrino) combine into a single doubly-rotating system (an atom). But in order to create a stable doubly-rotating structure the two separate photons that constitute the neutron and neutrino must be made to intersect. Such an intersection will only be stable if it is actually a single doubly-oscillating photon, created out of two singly-oscillating ones. Doubly-oscillating photons are required by the theory and are observed in nature. They are the building blocks of the atoms. The discovery of doubly-oscillating photons should make possible a probabilistic calculation of atom-building, which remains one of the more obscure aspects of the Reciprocal System. While the probability of two photons remaining intersected is vanishingly small, if not actually zero, there obviously are many natural processes in which a photon is able to acquire a unit of energy in a second scalar dimension.
 Copyright © 1992 by Jan Sammer. All rights reserved
 Nothing But Motion (Portland, 1979), p. 54; Ronald W. Satz, The Unmysterious Universe (Troy, NY, 1971), pp. 24-25.
 Tom Kirk, ”The Photon: Displacement in a Second Scalar Dimension,” Reciprocity XIX, No. 2, p. 5–12, and idem, ”Dissection the Birotational Photon,” Reciprocity XX, No. 3, pp. 14–19. I concur with Kirk that K.V.K. Nehru’s bi-rotational photon is completely unwarranted by the postulates, and hence part of a different theory of physics, if not of a different physical universe altogether!
 The Feynman Lectures on Physics by Richard P. Feynman, Robert B. Leighton, and Matthew Sands (Palo Alto, 1963), Chapter 37.
 Albert Einstein, Boris Podolsky, and Nathan Rosen, ”Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” Physical Review, 47, 777-80 (1935).
 Alain Aspect, ”Proposed Experiment to Test the Nonseparability of Quantum Mechanics,” Physical Review, D14, 1944–51 (1976).
 Ronald W. Satz, ”A Note on Scalar Motion,” Reciprocity XIX, No. 3, p. 12; cf. idem, The Unmysterious Universe, p. 26.
 William C. Wickes, Carroll O. Alley, and Oleg Jakubowitz, ”A ‘Delayed-Choice’ Quantum Mechanics Experiment,” in Quantum Theory and Measurement, edited by John A. Wheeler and Wojciech H Zurek, (Princeton, 1983), pp. 458–461.
 Nothing But Motion, p. 127.
 Basic Properties of Matter (Salt Lake City, 1988), p. 279.