The Reciprocal System of theory consists of the fundamental postulates, together with everything that is implicit in the postulates; that is, everything that can legitimately be derived from those postulates by logical and mathematical processes without introducing anything from any other source. It is the theory as thus defined that can claim to be a true and accurate representation of the observed physical universe, on the grounds specified in the earlier pages. The conclusions stated in this and related publications by the present author and others are the results of the efforts that have thus far been made to develop the consequences of the postulates in detail. However the findings that have emerged from the early phases of this theoretical development call for some drastic modifications of the prevailing conceptions of the nature of some of the basic physical entities and phenomena. Such conceptual changes are not easily made, and the persistence of previous habits of thought makes it difficult, not only for the readers of these works, but also for the investigators themselves, to grasp the full implications of the new ideas when they first make their appearance.
The existence of scalar motion in more than one dimension, which plays an important part in the subject matter of the two preceding chapters, is a good example. It is now clear that such motion is a necessary and unavoidable consequence of the basic postulates, and there is no inherent obstacle that would stand in the way of a complete and detailed understanding of its nature and effects if it could be considered in isolation, without interference from previously existing ideas and beliefs. But this is not humanly possible. The minds into which this idea enters are accustomed to thinking along very different lines, and inertia of thought is similar to inertia of matter, in that it can be fully overcome only over a period of time.
Even the simple concept of motion that is inherently scalar, and not merely a vectorial motion whose directional aspects are being disregarded, involves a conceptual change of no small magnitude, and the first edition of this work did not go beyond this point, except in specifying that the increase in the speed of recession of the galaxies is linear beyond the gravitational limit a tacit assertion that the increment is scalar.
Subsequent studies of high energy astronomical phenomena carried the development of thought on the subject a step farther, as they led to the conclusion that the quasars are moving in two dimensions. However, it took additional time to achieve a recognition of the fact that unit scalar speed in three dimensions constitutes the line of demarcation between the region of motion in space and the region of motion in time, and the first publication in which this point was brought out specifically was Quasars and Pulsars (1971). Now we further find that the same considerations also apply to the incoming cosmic particles. At the moment, it appears that the full scope of the subject has been covered, but past experience does not encourage a positive statement to that effect.
This experience demonstrates how difficult it is to attain a comprehensive understanding of the various aspects of any new item of information that is derived from the basic postulates, and it explains why identification of the source from which the correct answers can be obtained does not automatically give us all of those answers; why the results obtained by application of the Reciprocal System of theory, like the products of all other research into previously unknown physical areas, necessarily differ in the degree of certainty that can be ascribed to them, particularly in the relatively early stages of an investigation. Many are established beyond a reasonable doubt; others can best be characterized as work in progress ; still others are little, if any, more than speculations. However, because of the extremely critical scrutiny to which a theory based on a new and radically different fundamental concept is customarily (and properly) subjected, publication of the results of the theoretical development described in this work has, in general, been limited to those items which have been given long and careful examination, and can be considered as having a very high degree of probability of being correct. Almost thirty years of study and investigation went into the project before the first edition of this work was published. The additions and modifications in this new edition are the result of another twenty years of review and extension of the original findings by the author and others.
Inasmuch as the results of this development are conclusions about one universe derived in their entirety from one set of basic premises, every advance that is made in the understanding of phenomena in one physical field throws some light on outstanding questions in other fields. A review such as that required for the preparation of this new edition has the benefit of all of the advances that have been made subsequent to the last previous systematic study of each area, and a considerable amount of clarification of the subject matter previously examined, and extension of the development into new subject areas, was accomplished almost automatically during the revision of the text. Where it is evident that the new theoretical conclusions thus derived are firm enough to meet the criteria that were applied to the original publication they have been included in this new edition. But in general, any new ideas of major consequence that have emerged from this rather rapid review have been held over for further study in order to be sure that they receive adequate consideration before publication.
In one particular case, however, there seems to be sufficient justification for making an exception to this general policy. In the preceding pages, the discussion of the decay of the cosmic elements after entry into the material environment was carried to the point where the decay was complete, and it was noted that the ultimate result would necessarily be conversion of the cosmic elements into forms that would be compatible with the new environment. Since hydrogen is the predominant constituent of the material sector of the universe, this element must ultimately be produced from the decay products, but just how the transition is accomplished has not been clear theoretically, and empirical information bearing on the subject is practically non-existent. It would be a significant advance toward completion of the basic theoretical structure if this gap could be closed. Consideration of the question during preparation of the text of the new edition has uncovered some interesting possibilities in this connection, and a discussion of these ideas in the present work seems to be warranted, even though it must be admitted that they are still speculative, or at least no more than work in progress.
The first of these tentative new conclusions is that the muon neutrino is not a neutrino. As the theoretical development now stands, there is no place for any neutrinos other than the electron neutrino and its cosmic analog, the electron antineutrino, as it is currently known. Of course, the door is not completely closed. Earlier in this volume it was asserted that sufficient evidence is now available to demonstrate that the physical universe is, in fact, a universe of motion, and that a correct development of the consequences of the postulates that define such a universe will produce an accurate representation of the existing physical universe. It is not contended however, that the present author and his associates are infallible, and that the conclusions which they have reached by these means are always correct. It is conceivable that further theoretical clarification may change some aspects of our existing view of the neutrino situation but the theory as it now stands has no place for muon neutrinos.
As brought out in the previous pages however the theory does require the production of a different massless particle in the processes in which the muon neutrino now appears and the logical conclusion is that the particle now called the muon neutrino is the particle required by the theory: the massless neutron. From the observational standpoint this changes nothing but the name, as these two massless particles cannot be distinguished by any currently known means. On the theoretical side, the observed particle fits in very well with the theoretical deductions as to the behavior of the massless neutron. This particle should theoretically be produced in every decay event, whereas the neutrino should appear only in the last step, where separation of the residual cosmic atom into two massless particles takes place. This is in accord with observation, as the muon neutrino appears in both the pion decay and the muon decay, whereas the electron neutrino appears only in the decay of the muon. Empirical confirmation of the theoretical produce lion of massless neutrons in the earlier decay events has not yet been observed, but this is understandable.
The reported products of the decay of a positive muon are also in agreement with the massless neutron hypothesis. These products are currently considered to be a positron, which, according to our findings, is M 0-0-1, an electron neutrino, M 2-2-(1), and a muon antineutrino, which we now identify as a massless neutron, M 2-2-0. The positron and the electron neutrino are jointly equivalent to a second massless neutron. Their appearance as two particles rather than one is probably due to the fact that they are the products of the final conversion of the residual cosmic atom, in which the electric and magnetic rotations are oppositely directed, rather than merely discrete particles ejected from the cosmic atom.
It is claimed that muons also exist with negative charges, and that these decay into the antiparticles of the decay products of the positive muon: an electron, an electron antineutrino, and a muon neutrino. These asserted products are the equivalent of two cosmic massless neutrons. The production of such particles, or of cosmic particles of any kind, other than the members of the regular decay sequence, as the result of a decay process, is rather difficult to reconcile with the theoretical principles that have been developed. Theoretical considerations indicate that there is no such thing as an antimeson, and that the negatively charged muon is identical with the positively charged muon, except for the difference in the charge. On this basis, the decay products should differ only in that an electron replaces the positron. Inasmuch as two of the decay particles in each case are unobservable, there appears to be a rather strong probability that their identification in current physical thought comes from the ninety percent of interpretation rather than from the ten percent of observation that enters into the reported results. However, it is the existence of some unresolved questions of this kind that has made it necessary to characterize the contents of this chapter as somewhat speculative.
On the basis of the theoretical decay pattern, the incoming cosmic atoms are eventually converted into massless neutrons and their equivalents. The problem then becomes: What happens to these particles? There are no experimental or observational guideposts along this route; we will have to depend entirely on theoretical deductions.
The massless neutron already has a material type structure--that is, a negative vibration and a positive rotation--and no conversion process is required. Likewise, no decay or fragmentation process is possible because this particle has only one rotational displacement unit. Progress toward the hydrogen goal must therefore take place by means of addition processes. Addition of a massless neutron to a positron, a proton, a compound neutron, or a second massless neutron, would produce a particle in which there is a single rotating system of displacement 2 (on the particle scale). As indicated in Chapter 11, it appears that such a particle, if it exists at all, is unstable, and in the absence of any means of transferring one of the units of displacement to a second rotating system, the unstable particle will decay back to particles of the original types. Such additions will therefore accomplish nothing.
The additions that are actually possible constitute a regular series. The decay product, the massless neutron, M ½-½-0, can combine with an electron, M 0-0-(l), to form a neutrino, M ½-½-(1). Another massless neutron added to the neutrino produces a proton, M 1-1-(1). As has been indicated, addition of a massless neutron to the proton is not feasible, but a neutrino can be added, and this produces the mass one hydrogen isotope, M ½-½-(2).
So far as the rotational displacement is concerned, we now have a clear and consistent picture. By addition of the supply of massless neutrons resulting from the decay of the cosmic rays to electrons and neutrinos, particles that are plentiful in the material environment, hydrogen, the basic element of the material system, is produced. But there is still one important factor to be accounted for. There is no problem in the addition of the massless neutron to the electron, but in adding to the neutrino to produce the proton a unit of mass must be provided. The question that must be answered before this hypothetical hydrogen building process can be considered a reality is: Where does the required mass come from?
It appears, on the basis of the recent extensions of the theory, that the answer to this question can be found in a hitherto unrecognized property of particles with two-dimensional rotation. As explained in Chapter 12, mass is t³/S³, the reciprocal of three-dimensional speed, whereas energy is t/s, the reciprocal of one-dimensional speed. Obviously, there is an intermediate quantity, the reciprocal of two-dimensional speed, t²/s². This has been recognized as momentum, or impulse, but it has been regarded as a derivative of mass. Indeed momentum is customarily defined as the product of mass and velocity. What has not been recognized is that the reciprocal of two-dimensional speed can exist in its own right, independent of mass, and that a two-dimensional massless particle can have what we may call internal momentum, t²/s² just as a three-dimensional atom has mass t³/s³.
The internal energy of an atom the energy equivalent of its mass is equal to the product of its mass and the square of unit speed t³/s³ x s²/t² = t/s. This is the relation discovered by Einstein and expressed as E = mc². In order to provide the unit mass required in the addition of a massless neutron to a neutrino to form a proton, a unit quantity of energy, t/s must be provided.
The kinetic energy of a particle with internal momentum M is the product of this momentum and the speed: Mv = t²/s² x s/t = t/s. Inasmuch as the massless neutron has unit magnetic displacement, and therefore unit momentum, and being massless it moves with unit speed (the speed of light), its kinetic energy is unity. Thus the kinetic energy of the massless neutron is equal to the energy requirement for the production of a unit of mass, and by coming to rest in the stationary frame of reference the massless neutron can provide the energy as well as the rotational displacement necessary to produce the proton by combination with a neutrino.
Here, then, is what appears, on initial consideration at least, to be a complete and consistent theoretical explanation of the transition from decay product to material atom. There is, of course, no observational confirmation of the hypothetical processes, and such confirmation may be hard to get. The conclusions that have been reached will therefore have to rest entirely on their theoretical foundations for the time being.
It is worth noting that, on the basis of these conclusions, the hydrogen produced from the decay products originates somewhat uniformly throughout the extension space of the material sector, inasmuch as the neutrino population must be fairly uniformly distributed. This is in agreement with other deductions that were discussed in the first edition, and will be given further consideration in Volume II of this work. The standing of the conclusions that have just been outlined is considerably strengthened by the fact that the two lines of theoretical development meet at this point.
As stated earlier, the inflow of cosmic matter into the material sector is counterbalanced by an ejection of matter from the material sector into the cosmic sector in the form of high-speed explosion products. These are the two crucial phases of the great cycle which constitutes the continuing activity of the universe. But the slow process of growth and development that the arriving matter undergoes before it is ready to participate in the events which will eject it back into the cosmic sector, and complete the cycle, is an equally important, even though less spectacular, aspect of the cycle. Consequently, one of the major tasks involved in developing a theoretical account of the physical universe from the basic postulates of the Reciprocal System is to trace the evolutionary path of the new matter, and of the aggregates into which that matter gathers. Our first concern, however, must be to identify the participants in physical activity, and to define their principal properties, as these are items of information that will be required before the events in which these entities participate can be accurately evaluated. Now that we have arrived, at least tentatively, at the hydrogen stage, we will defer further consideration of the evolution of matter to Volume II, and will return to our examination of the individual material units and their primary combinations.