It is apparent, both from the discussion of the cosmic sector of the universe in Chapter XIV and from the nature of the material branch of the compound motion system, that the cosmic branch of this system is an exact duplicate of the material branch, except that all directions are reversed. It might therefore seem quite logical to complete Chart D by adding a lower branch identical with the upper branch that we have traced out step by step in the preceding chapters. It should be recognized, however, that Chart D is a picture of the material system as it appears from within that system, and if a lower branch were to be added, utilizing the same terminology, this would be a picture of the cosmic system as it would appear from within the cosmic system.
No exception could be taken to such a picture from the standpoint of accuracy. Indeed, this may ultimately be the best mode of presentation. But for the moment it is quite meaningless here in the material system as any cosmic entities which may exist in the material environment have properties in this environment that are quite unlike those of their material counterparts. Cosmic matter, for instance, as we encounter it, does not even remotely resemble the matter with which we are familiar, and it is currently treated (not very successfully) as a totally different kind of an entity and under a different name. In expanding Chart D to include the cosmic system of motions it therefore seems advisable, at least in this initial presentation, to adapt the terminology to the existing situation in the material sector. Of course, the general outline of the chart is not subject to modification, and the symbols for the various types of motion will appear just as if the chart were being prepared on the cosmic basis, but the entities that have previously been identified and named will be shown on the enlarged chart under the names that have been given to them on the basis of the prevailing impression that they are indigenous to the local environment rather than fleeting visitors from a foreign sector of the universe.
The general situation is quite clear. On the one hand we have a theoretical system which asserts the existence, somewhere in the universe, of a vast number of physical entities related to but quite different from the familiar phenomena of our local environment, and further asserts the existence of processes whereby substantial quantities of these strange physical entities are injected into our environment. On the other hand, we have recently become aware of the presence of some extraordinary physical entities in our midst, the varieties of which are already so numerous that they are extremely embarrassing for the theorists who are trying to account for them, and the behavior of which is so unusual that “strangeness” has actually been treated as a definite physical property, subject to conservation laws, etc. Obviously we can equate the theoretical and observed phenomena, and our problem then becomes one of placing each of these foreign entities in its proper place in the theoretical picture.
As brought out in Chapter XIV, relatively large quantities of cosmic matter are injected into the material sector of the universe by the velocities generated in the explosions of the mature cosmic galaxies. It was also pointed out in that chapter, however, that the ordinary matter which is propelled into the cosmic sector of the universe by similar explosions of the giant old material galaxies exists as such only very briefly after its arrival in the new sector, because the system of motions that constitutes the atoms of matter must come to equilibrium with its new environment, and this requires a conversion of the material type of motion into motion of the cosmic type. The same is true in reverse and the life of cosmic matter as such is therefore extremely short after it enters the material environment. Nevertheless, it persists long enough to be recognized by various effects, which it produces.
From the nature of the process through which it enters the material environment, and with the benefit of the discussion of the inverse process, the entry of matter into the cosmic sector, we can easily deduce what the general characteristics of cosmic matter in the local environment will be. Let us ask, then, Is there any evidence of the presence of such entities: widely dispersed individual particles, originating from some source which cannot be clearly identified, appearing approximately uniformly throughout space and throughout time, and without preferential direction, traveling with extremely high velocities, in the neighborhood of the velocity of light, and decaying into some other type of particle within an almost incredibly short time? The answer is, Yes; we do observe entities of this kind. All of these characteristics, those which the cosmic matter ejected from the exploding cosmic galaxy should theoretically possess when it enters time material sector, are exactly the characteristics of the cosmic rays.
Identification of the primary cosmic rays as atoms of cosmic matter is, of course, in conflict with current scientific opinion, which regards these primaries as material atoms. It should be recognized, however, that reliable information concerning the primary rays is extremely difficult to obtain, and their identification as material elements rests mainly on a process of elimination which seemingly leaves these material elements as the only known type of particle that could meet the requirements. Electrons, positrons and photons are ruled out by experimental results that require an entity of a different type. Neutrinos are not capable of producing the observed results of cosmic ray interactions. Mesons and neutrons are eliminated from consideration because observations show that their life span is very short, and hence it is presumed that they must have been produced in the immediate vicinity of the locations in which they are detected. This apparently leaves the material elements as the only remaining possibilities, and the presence of multiple charged particles in the cosmic rays in proportions which conform roughly to the proportions in which the heavier material elements occur in observed structures seemingly makes the case conclusive.
The assertion of the Reciprocal System that these are cosmic elements rather than material elements now introduces a new factor into the situation. Elimination of all of the particles heretofore known, other than the atoms of matter, does not eliminate the possibility that the cosmic rays may consist of some new kind of particles, as the present work contends. The available observational methods cannot settle this issue, as they are not capable of distinguishing between cosmic atoms and material atoms at these extremely high velocities. The presence of a multiply charged particle, for instance could equally well indicate the presence of one of the higher cosmic elements as that of a heavy material element. Furthermore, there is some definite evidence indicating that the primaries are not material atoms. If we compare the reactions initiated by the cosmic rays with the results produced by fast-moving material particles in the accelerators, we find some striking differences, such as the great disparity in the production of K-mesons. The natural inference from this is that the cosmic rays are not fast-moving material particles. There is also evidence that some of the primary rays decay in flight. For example, it is often found that one of the particles leaving the site of the first physical event initiated by the primary is a pi meson which continues in the same direction as the primary and contains the bulk of the original energy. Since there is no reason to expect material atoms of low atomic weight to decay spontaneously or to decay to pi mesons, this is a further indication that the primaries are not material atoms.
The cosmic atoms, on the other hand, have just the properties that are necessary to explain the experimental findings. They are not material atoms, hence they do not have to behave in the manner of material atoms. They are stable in their own sector of the universe and they enter the local scene directly from that sector, not from some distant part of the material sector, so that stability in the material environment is not necessary in order to explain their presence. They become unstable when they arrive, and consequently it is quite in order for one of them to decay in flight if it avoids a collision long enough.
Strong support is also given to the cosmic atom explanation by analyses of the composition of the incoming rays. Current thought regards these rays as having originated somewhere within the observable universe. Just how they are produced and how they have acquired their fantastically high energies are still open questions and, as Sandage recently observed, constitute one of the ”major unsolved problems in astrophysics.”109 But in any event, if the rays are ordinary matter that has been accelerated to these high velocities by some unknown physical agency, as is now believed, their composition ought to be approximately that of average matter; that is, the proportions of the different elements in the primary rays ought to agree with the proportions found in the observation of material structures. The range of observed values is indicated by a recent study which found the percentage of elements above helium varying from 0.3 in the globular clusters to 4.0 in the extreme Population I stars and interstellar dust in the solar neighborhood.124 In order to agree with current theory the percentage of elements above helium should be somewhere in the middle of this range, and certainly not above 4.0 in any case.
The Reciprocal System tells us that the composition of the primary rays should not be that of average matter, but that of very old matter much older than the oldest matter within observational range. The proportion of heavy elements in matter increases with age (This is true with reference to the matter itself, regardless of whether the presence of old matter in a star is taken as a sign of stellar age as the Reciprocal System pictures it, or as a sign of stellar youth, in accordance with current astronomical thought) and in the oldest matter in the material universe, such as that in the stars of the central region of M87, for example, it should be well above 4.0 percent. The percentage of heavy cosmic elements in the cosmic rays should be essentially the same as the percentage of heavy elements in this very old matter of the material sector, since here again it is the galaxies that have reached the end of the current phase of the cycle that explode. This gives us a crucial test. If present-day theory s correct, the heavy element percentage should be below 4.0. If the Reciprocal System is correct, it should be substantially above 4.0. The verdict is clear and unmistakable. The percentage is well above 4.0. A review by C. J. Waddington reports that the elements above helium contribute 15.8 percent of the mass of the primary rays.125 Even after making allowances for whatever differences may exist in the manner of compiling and expressing these results, it is evident that the heavy element content of the cosmic rays is much above that of ordinary matter.
Thus, although the amount of information that is available concerning the primary cosmic rays is very limited, it nevertheless yields strong evidence in support of the theoretical conclusion that these rays are atoms of cosmic matter. It is also highly significant that the most extraordinary characteristics of the rays, those that present-day science has found so difficult to account for, are simple and obvious consequences of the status of these rays as cosmic atoms. Recent observational results have emphasized more than ever the extreme isotropy of the cosmic radiation and the almost incredible energy of the most energetic particles. Explanation of these properties in terms of known processes is a formidable task, and the attempts that have thus far been made in this direction are highly strained and inherently implausible. But these are the normal and most obvious properties of the incoming cosmic matter. Cosmic atoms entering the local environment must have initial velocities in the neighborhood of the velocity of light, since they originate in a region where all velocities are greater than unity (the velocity of light), and inasmuch as they enter from a region which is not localized in space, their distribution on arrival is determined by probability, and hence it must be isotropic.
A still more impressive confirmation of the validity of the identification of the cosmic rays as cosmic matter is furnished by the manner in which the cosmic ray decay processes and their products agree with the theoretical events in the RS universe Our next undertaking will be to examine the theoretical and experimental aspects of these processes.
Where the only difference between a new arrival and the local environment is in the magnitude of certain properties, as in the case of the high temperature gas cited in Chapter XIV, the process of adjustment to the environment is simply a matter of giving up some of the excess motion. The problem for the cosmic atom is more complicated, as some of the components of its motion differ from those of the material atoms not only in magnitude but also in direction, but those components that are compatible with the material system can come to an equilibrium with the local environment by the simple and rapid method of direct transfer. The first effect to which the cosmic element should theoretically be subject is therefore a sort of stripping action, whereby the excess amounts of these compatible components, the translational velocity, the electric charge, and the one-dimensional rotational displacement are ejected or transferred by contact. The product of this stripping process is a member of the series of cosmic elements, which has no effective one-dimensional rotation, the cosmic equivalent of the inert gas series, with a greatly reduced velocity and only a minimum charge.
In some of the recent cosmic ray work a distinction has been drawn between the original rays and the primary rays, the latter getting defined as the first which come under observation.126 The theoretical development confirms the validity of this differentiation. The original rays clearly must consist principally of c-hydrogen, and the product of the first stripping action will therefore be c-helium. The primary rays should thus consist mainly of c-helium. It should be noted in this connection that the cosmic atoms may lose part of their initial charge, but they are not likely to gain additional units of charge in the local environment, and a c-helium atom produced from c-hydrogen will have only one unit of charge, not two. The single charge of most of the primary particles is therefore consistent with the foregoing conclusions.
In order to complete the conversion from cosmic to material status the cosmic atom must undergo a more complex process that will ultimately reverse the direction of each of those components of the compound motion that give the atom its cosmic character. In the cosmic elements, including c-helium, the atomic rotation has a displacement in space, whereas the basic vibration has a time displacement. To convert c-helium into some unit or units of the material system it is necessary to exchange these displacements, so that we come out with a rotational time displacement and a vibrational space displacement. The linear vibration presents no particular problem, but it is difficult, if not impossible, for a multiple rotational displacement to convert directly from one status to the other. Before the actual interchange can occur, it is necessary that the atomic rotation be reduced to the equivalent of a single unit; that is, to the equivalent of a neutron, the sub-atomic member of the inert gas series.
It is not feasible to cover the subject of atomic rotation in detail in a general survey of this kind, and for present purposes it will merely be stated that the theoretical investigations show that any atomic rotation with displacement n is equivalent to a rotation in the opposite space-time direction with displacement k-n, where k is a limiting value that depends on the dimensions of the rotation. By reason of this relation, the ascending series of inert gas elements beginning with the sub-atomic neutron is equivalent to a descending series of cosmic inert gas elements, in which the equivalent of the neutron is c-krypton. In order to make the transition to the material system the c-helium of the primary cosmic rays must be built up into c-krypton.
At first glance it may seem contradictory to initiate a process of breaking down an atom into simpler units by building it up to a more complex structure, but it should be recognized that in order to build up to a higher cosmic level a cosmic element must either add space displacement or eject time displacement, which is exactly what a material structure does when it breaks down or disintegrates. The cosmic building-up process is thus a breaking-down process when we look at it from the material standpoint.
The transformation from c-helium to c-krypton is accomplished by the successive ejection of units of two-dimensional rotational displacement; that is, the equivalent of neutrons. In the local environment, at least, the one-dimensional and two-dimensional particles of near zero mass, the positron and the neutrino, which are jointly equivalent to the neutron, are more easily produced than the neutron itself, and the successive decay events therefore consist of ejections of pairs of neutrinos and positrons. Two such ejections are required to take the c-element from one inert gas position to the next and hence the decay products include not only the cosmic inert gases between c-helium and c-krypton but also the c-elements midway between these inert gas elements.
The cosmic atoms, which enter the material sector, are thereafter subject to all of the various influences that affect the material atoms in the local environment, and the details of the decay process are modified accordingly. The first decay products, for instance, are outside the zone of stability in a region of unit ionization level, because the material elements to which they are equivalent are outside the stability zone in their normal states, and these decay products are therefore radioactive. When the radioactive instability is compounded with the inherent environmental instability of cosmic elements in general, the lifetime of the normal c-atoms is reduced to the vicinity of zero and the decay of these radioactive c-particles is essentially instantaneous. Where conditions are favorable for the production of the +1 isotopes these first products appear briefly; otherwise, the initial decay product is the first c-element in the normal decay path that is within the zone of stability, c-silicon.
The principal identifying characteristic of a cosmic ray decay particle is its mass. From the reciprocal relation it is evident that the normal mass of a c-element with cosmic atomic number n is 1/n on the natural scale or 2/n on the atomic weight scale. For convenience the masses of the decay particles are usually expressed in terms of electron masses, and using the theoretical value of the latter, the normal mass of a cosmic element of atomic number n is 3646/n electron masses. The theoretical mass of the first slightly stable decay product, c-silicon, is therefore 1/14 natural units or 260 electron masses. This we can identify as the particle known as the pi meson, which has a mass usually reported somewhere in the range from 260 to 270 and is the first detected product in most cosmic ray events.
Cosmic silicon, the pi meson, theoretically decays to c-argon, which has a mass of 1/18, natural units or 203 electron masses. This we can; identify as the mu meson, the most common and longest lived of the decay products, which has a reported mass of about 206 and is produced by decay of the pi meson, as the theory requires. The next element in the regular order would be c-cobalt, with a mass of 135, but for some reason, probably because it is within one-half of a magnetic unit of the final conversion level, this particle has an abnormally short life, and the observed decay of the mu meson (c-argon) is a double process in which two positrons are emitted and c-krypton is produced. This c-element, on reversing the directions of its motions, becomes a neutron, or combination of neutrino and positron, and at this point the original cosmic atom has been completely converted to material particles.
If the +1 isotopes of the early decay products are formed, the added mass due to the gravitational charge is the same as if the c-atom were a material atom; that is, a one-unit charge adds one atomic weight unit (½ mass unit or 1823 electron masses). Also we find that, for some reason, which is not yet, clear, the transformation of c-helium to c-carbon does not occur readily, and instead of following this path, the decay proceeds by way of one of the adjoining c-elements, c-boron or c-nitrogen. In either case a decay to c-neon follows. Under conditions favorable for the production of the +1 isotopes, therefore, the complete decay scheme in the terrestrial environment is as follows:
|Total Mass |
|c-helium||½||0||1823||primary||c-B or c-N|
|c-krypton||converts to neutron or equivalent|
As indicated in the tabulation, the +1 isotopes of the lower cosmic elements in the decay path can be identified as the “hyperons” or heavy mesons that are reported by the experimenters.
In addition to the mesons produced by cosmic ray decay or by various processes in the particle accelerators, a number of so-called “antiparticles” also make their appearance in the same events. Core relation of the experimental findings concerning these particles with the corresponding theory is complicated by the fact that the reported results are in most cases inferences rather than direct observations and the nature of these inferences depends to a considerable degree on the theoretical viewpoint adopted by the experimenters. In many cases the new basic concepts developed in this work lead to altogether different interpretations of the observed facts. The following discussion of these particles will therefore be confined to the theoretical picture as it exists in the RS universe without regard to current interpretations of the experimental findings other than to say that there are no actual experimental results, as distinguished from interpretations of these results, that are in conflict with the theoretical conclusions based on the postulates of the Reciprocal System.
Recognition of these particles is based primarily on the annihilation process in which the rotations of two oppositely oriented particles cancel each other and an equivalent amount of energy in the form of radiation is released. Two of the sub-atomic particles of the material system, the electron and the positron, are antiparticles on this basis, since the effective rotational displacements of these two particles are equal in magnitude and opposite in direction. As might be expected, the combination of the electron and the positron was the first annihilation process that was detected. No other pair of antiparticles exists in the material system, but there is a similar pair in the cosmic system, and each material atom or sub-atomic particle is the antiparticle of the corresponding structure of the cosmic system. Direct combination of complex structures such as the atoms is not feasible from a practical standpoint, and the annihilation reactions are there fore limited to the sub-atomic particles, with the possible exception of hydrogen. Anti-mesons in the usual sense (that is, particles with properties in the local environment similar to those of the mesons, but oppositely directed) are, of course, impossible, as the antiparticles of the mesons are material elements. The inferential identification of anti-mesons in some of the current reports from the experimenters cannot be taken seriously.
It should be noted that in the RS universe, the antiparticle is the inverse of the corresponding particle, not the negative. It is true that the units of space and time which enter into the construction of these particles are oppositely directed from the scalar stand point, and each is therefore the negative of the other, in a sense, as well as the inverse, but when these units are associated as a particular type of motion the “anti” form corresponding to velocity s/t is not -s/t but t/s. The properties of cosmic matter as defined by the Reciprocal System are thus considerably different from those of the ”anti-matter” which has been the subject of so much speculation in recent years. Negative mass, for instance, is not possible. If the mass of a material atom is m, the mass of the corresponding cosmic atom is not -m but 1/m, which is still a positive quantity.
The possibility that some of the observed galaxies may be composed of anti-matter or that the juxtaposition of matter and antimatter may be responsible for the strong radio emission and other peculiarities of certain galaxies is also ruled out. The new theoretical system confirms the existence of cosmic galaxies composed of cosmic matter or, as it is now rather inaccurately termed, anti-matter. These cosmic galaxies are exact counterparts of the material galaxies but they are not localized in space and we cannot see them. Cosmic gravitation operates to move units of cosmic matter toward each other in coordinate time, rather than in space, and the various cosmic masses therefore assume fixed relative positions in time, or move toward such fixed positions, but move away from each other in space, and the atoms of a cosmic galaxy are widely dispersed spatially.
It is probable that when the proper identifications of the particles already detected are made, the cosmic sub-atomic particles will all be accounted for experimentally, but little is yet known about any of the cosmic elements aside from those in the direct cosmic ray decay path, and beyond the normal c-elements there are a host of c-isotopes, c-ions, and other structures yet to be discovered. Furthermore, the cosmic elements are subject to combining forces of the same nature as those which are responsible for the great variety of chemical compounds in the material system, and in addition to individual units of the types shown in the compound motion diagram, cosmic chemical compounds exist in the same tremendous number and variety as the compounds of the material elements.
Whether or not the incoming stream of primary cosmic rays contains any appreciable number of such cosmic compounds is still uncertain, but there is an increasing amount of evidence indicating that compounds of cosmic and material elements are formed in the local environment. For example, the lambda meson (c-neon) is reported to participate in a number of combinations with various isotopes of hydrogen, which disintegrate after a brief existence. On the basis of current atomic theory these “hyper-fragments” are the result of replacement of an electron in the atomic structure by the lambda meson. According to the Reciprocal System, on the other hand, there are no individual “parts”, in an atom, and both the electron and the meson are independent units of the same general nature as the atom. In this system the hyperfragment is a combination of the material atom and the meson: a cosmic-material chemical compound.
This suggests the interesting possibility of a direct test of the two conflicting theories, as current theory would indicate that it should be possible to produce an H1 hyperfragment by substituting a meson for the lone electron which is supposed to exist in the H1 isotope, whereas the Reciprocal System says that the simplest combination of this kind is one between the meson and the H1 isotope, which would be called an H2 hyperfragment. On this basis an H1 hyperfragment would be nothing but a lambda meson. Actually no H1 hyperfragment has been detected, and the test therefore favors the Reciprocal System, as far as it goes. Unfortunately it is not conclusive, as it is always possible that the existence of the H1 hyperfragment is barred for some other reason. However, proof of the existence of an H1 hyperfragment would have been conclusive in the other direction, and it is highly significant that here again, as in so many other places throughout the numerous fields of physical science, whenever the new theory exposes itself to a fatal blow, that blow is never delivered; the opposition may be able to show the existence of a doubt because existing knowledge is incomplete, but it cannot demonstrate any direct conflict with known facts.
Addition of the structures discussed in this chapter to those shown on Chart D now completes the diagram of the compound motion system. All of the known primary units of the physical universe—particles, atoms, and modified forms of each—have now been placed in their proper positions in relation to the system as a whole. In view of the awkward position in which previous theories are now being placed by the many new particles that are currently being discovered by the experimenters, it is also interesting to note that the final diagram, Chart E, includes an immense number of different kinds of units that still remain undiscovered. This alters the balance between the theorist and the experimenter very decidedly. Instead of lagging far behind the experimental branch of science, as it has done for the past several decades, the theoretical branch, by virtue of the new developments reported herein, is now far ahead of the experimenters. It is clearly in order to designate this major improvement of the theoretical position as Outstanding Achievement Number Fourteen.
The completion of the compound motion chart also brings us to the end of our brief survey of the application of the Reciprocal System and its new concepts of space and time to the basic phenomena of the physical universe. Two additional chapters will follow, but they will be concerned with collateral aspects of the subject rather than continuing the descriptive process begun in Chapter VI. At this time, therefore, some general comments regarding the results, which have been attained by the new theoretical system, are appropriate.
In the concluding words of his physics textbook, John C. Slater expresses the ultimate goal of physical science as follows:
And finally, we hope, some general theory will appear, so broad that all our present branches of physics appear as special cases of it…. We may hope that the progress toward this greater generalization will not be too discouragingly slow.127
Up to now, the construction of such a theory has never even been attempted. The most far-reaching aim ever seriously pursued by science has been that of constructing a “unified field theory” and even if that goal had been reached, the product would still fall far short of being the kind of a comprehensive theory that Slater calls for. There would still have to be innumerable separate theories in individual physical fields, perhaps related to the unified field theory in the rather vague manner in which many of the individual theories now extant are related to Relativity or to some version of the quantum doctrines, but containing their own individual assumptions and ”constants” just as existing theories now do.
The theoretical system described in this work is the first that has ever been presented as a complete general theory in the sense in which Slater is using the term: a general system of postulates which defines the basic properties of the universe and from which all subsidiary theories that are required in the individual fields of physical science are derived directly and in full form without the necessity of any supplementary or auxiliary assumptions within the separate fields. Here, for the first time, the structure of the atom is deduced from the same set of postulates as the structure of the galaxy, the expansion of the universe is explained by the same forces that account for the cohesion of solid matter, and the theories applying to the most distant regions of the universe are derived from the same general principles as the theories applicable to the most common everyday phenomena. Here, also for the first time, the nature of the basic entities of the universe—radiation, matter, electricity, magnetism, ect.—is explained, and the relation of these previously “unanalyzable” phenomena to the space and time of which the universe is constructed is specified in detail.
A question may be raised as to why the first general physical theory should claim to be the correct theory, in view of past experience which indicates that the first product in any field usually has a great many imperfections, which are eliminated only through a long process of improvement and modification. The answer is that the minimum requirements that a theoretical system must meet in order to justify presentation as a possible explanation of the universe as a whole are so stringent that it is out of the question for any such system to meet these minimum requirements unless it is correct in all essential respects. It is difficult enough for a theory to achieve full success in one field; few previous theories have ever successfully applied the same theoretical premises to two major physical fields; the requirement that a system must be applicable to all major fields, a requirement that must be met at least reasonably well before any system can even be advanced for consideration as a general theory of the universe, is simply prohibitive for anything other than the correct theory. It has therefore been necessary for science to get along with separate and often conflicting theories in the various areas until the general state of knowledge advanced far enough to enable the correct basic theory to be formulated.
In order to accomplish the objective which Slater had in mind when he expressed the hope that a comprehensive general physical theory would shortly be forthcoming, it is not sufficient merely that such a theory be devised; it is also necessary that this theory should be understood and that it should be recognized for what it actually is. This is not as simple a matter as it might appear on first consideration, primarily because the general tendency, as Dyson pointed out in the observation previously quoted, is “to picture the new concept in terms of ideas which existed before”, and on this basis any genuinely new idea in an existing field of knowledge seems absurd. A new theoretical system can be understood and appreciated only if it is examined in its own context. For instance, the contents of this present chapter make no sense at all if they are viewed in terms of atoms composed of “elementary particles,” of motion taking place in space only, of space and time as components of a “four dimensional continuum,” and so on. But if this chapter is examined in the context of the fourteen others that have preceded it, every item in the development fits in logically and harmoniously as a part of a complete and consistent theoretical system.
The new theoretical system presented in this work, the Reciprocal System, is precisely the kind of a product that the scientific profession has been asking for. All that is needed now is an understanding of the theoretical structure and recognition of the fact that it meets all of the specifications. Amending Slater’s comments to bring them up to date, “We may hope that progress toward this understanding and recognition will not be too discouragingly slow.”