According to the theory developed from the postulates of the Reciprocal System, the destinies of the physical universe as a whole are controlled by two powerful and antagonistic forces: the force of the space-time progression, which carries all of the objects of our environment outward away from each other and tends to disperse these objects throughout space, and the force of gravitation, which moves every unit of mass inward toward all other masses, and tends to consolidate these masses into a single aggregate. Because of the dependence of the gravitational force on distance, the actual result is a compromise. Beyond the gravitational limits of the largest material aggregates the space-time progression holds sway, and the distant galaxies are receding from us and from each other with tremendous speeds. Inside the gravitational limits the gravitational forces are slowly but inexorably pulling all matter into larger and larger aggregates.
We have visible evidence of both processes. The “red shift” of the spectra of the distant galaxies enables measurement of their outward velocities. Similar observations on the globular clusters surrounding our Milky Way galaxy show that these clusters are in the process of falling into the galaxy, and we can deduce that the clusters that are observed in similar positions and similar numbers around other spiral galaxies are doing the same. As would be expected, the larger galaxies are not only capturing star clusters but also small galaxies, and we find such “satellites,” in the immediate vicinity of many of the larger units. Furthermore, astronomical observations reveal that there are many galaxies which are actually in contact, which means that they are in the act of combining, and the internal structures of many other large galaxies indicate that similar combinations have taken place at some time in the past.
The course of events indicated by the RS theory, and strongly supported by observational data, is that clusters of stars—globular clusters—are formed by condensation of dust and gas somewhat uniformly throughout space and are pulled in toward each other by gravitational forces. The rate of aggregation speeds up as the size of the aggregates increases, since a combination of two clusters has twice the pulling power of a single cluster and the volume of space within the gravitational limits increases even more rapidly. Pairs of globular clusters become small galaxies, small galaxies become large galaxies, and large galaxies become giants.
In the meantime a similar process of aggregation has been under way in the vicinity of the stars of which the clusters and the galaxies are constructed. A very substantial part of the total mass of the universe, perhaps as much as half, exists in the form of dust and gas. All diffuse material of this kind that is within the gravitational limits of the individual stars is continually being drawn in toward those stars, and that which is outside these limits will sooner or later come within the gravitational reach of some star because it is being pulled in toward the stars by the gravitational attraction of the galaxy as a whole. Current astronomical opinion tends to minimize the importance of dust and gas accretion in the life cycle of the stars, although some prominent astronomers, Fred Hoyle,119 for example, have contended that it plays a very significant role, and G. J. Whitrow reports that “Many students of the subject believe that this (accretion) is essentially the mechanism by which all large aggregates of matter, such as galaxies, have been generated.”120
The theoretical situation is very clear, and is in full agreement with Whitrow’s statement. The average star in the RS universe is continually growing by reason of this accretion of dust and gas. Some of the stars in the relatively dust-free independent globular clusters and small galaxies may be merely holding their own, or even losing a little mass by reason of an excess of radiation over accretion, but the big spiral galaxies are pulling in clouds of dust and gas as well as stars and star clusters, and with so much “food” available, the stars in these galaxies are growing at a relatively rapid rate.
All this would seem to point toward an eventual condition in which all matter would be gathered into giant galaxies composed of giant stars and separated by almost infinitely great distances. The theoretical development reveals, however, that such a state can never be reached, as there are factors, which limit the size of both stars and galaxies. A full discussion of this situation is beyond the scope of this present volume, but in brief, the existence of these limits is a consequence of increases in the magnitude of certain forces, which are directly related to the basic structure of the atom. These forces increase as the stars and galaxies grow older and larger, and they ultimately become strong enough to destroy the structures of the atoms that make up these physical aggregates. Size itself is not the crucial factor, but the limits for both stars and galaxies are related to the size.
In the star it is the build-up of thermal energy in the form of ionization and translational atomic motion that ultimately neutralizes a unit of the one-dimensional rotation of the atom and causes the catastrophic event known as a supernova, in which the star undergoes a gigantic explosion. Here the limit is reached at a particular size because the aggregate becomes hotter as it grows larger, a natural result of generating energy by processes which are roughly proportional to the cube of the diameter (the mass) and dissipating it by processes which are proportional to the square of the diameter (the surface area).
The theoretical development tells us that the larger part of the mass of a star, which becomes a supernova, is dispersed into the surrounding space by the explosion. This conclusion is quite orthodox and it is confirmed by the existence of expanding clouds of diffuse matter, which have apparently been produced by explosions of this kind. The Crab Nebula is a familiar example. But the new theory also leads to the very unorthodox conclusion that the remainder of the mass of the star is accelerated to speeds exceeding that of light and is dispersed into time rather than into space. As brought out in Chapter X, there is also ample observational evidence available to confirm this aspect of the theoretical deductions, when the observational data is taken at its face value and is freed from the illegitimate interpretations that have been placed upon it in order to force the observed facts into conformity with currently accepted ideas.
After the expansive forces have been spent, the ever-present force of gravitation reasserts itself and the material that was dispersed into space gradually pulls together to form a new star. Meanwhile, exactly the same thing is happening to the material that was dispersed into time, except that in pulling this material together, the gravitational force is reducing the amount of empty time between these particles, instead of reducing the amount of empty space between the particles as it does in the case of the matter that was dispersed outward. In each instance the contracting mass of material attains a stellar temperature before the work of gravitation is complete, and the initial product of the process is therefore a double star in which one component is a red giant, a star in which the constituent particles are separated by a large amount of empty space, and the other is a white dwarf, a star in which the constituent particles are separated by an equally large amount of empty time. Further contraction of these stars, in space and in time respectively, ultimately eliminates the empty space and empty time and brings both stars to positions on the main sequence, which they approach from opposite directions.
While the contraction process is going on, and during residence on the main sequence after contraction is complete, each star continues accretion of material from its surroundings, and this process of growth culminates in another supernova explosion. Thus, even though the maximum size of the individual stars is limited, increasing age results in the formation of more and larger multiple star systems. In older galaxies and in the older regions of our own galaxy we can expect that there will be many systems similar, for example, to Castor, which has at least six components.
Although the foregoing description of the stellar evolutionary cycle is a purely theoretical series of conclusions derived, like all of the other conclusions of the work, entirely from a development of the consequences of the Fundamental Postulates of the Reciprocal System, there is ample opportunity to check the various features of the theoretical cycle against the results of observation. There are many gaps in the observational data, and it is not possible to check all of the theoretical deductions, but a great deal of information is available from observation and all of this information is in agreement with the theory as outlined or, at least, is not inconsistent with the theory. The new picture conflicts with other theories, of course. The evolutionary path of the stars in the theoretical RS universe is altogether different from that envisioned by present-day astronomers—in fact, the direction of evolution in the new system is directly opposite to that assumed in current theory—but current ideas on this score are definitely unreliable. As was pointed out in Chapter X, they rest entirely on a wholly unsupported assumption as to the source of stellar energy, and they are specifically contradicted by many items of evidence from astronomical sources. Thus, while the concept of a stellar thermal limit, the particular item with which we are concerned at the moment, is new to science, it is soundly based and well substantiated.
At this point it is again appropriate to call attention to the logical position which the new theoretical system occupies in such observationally uncertain fields as astronomy. A great deal of progress has been made in astronomy and astrophysics, particularly in the last few decades, but there are still immense vacant spaces in the accumulated body of astronomical knowledge and comparatively few of the conclusions that have been reached in this field can be regarded as anything more than tentative. Leading figures in the profession are continually warning their colleagues against placing too much trust in current theories. Harlow Shapley, for instance, emphasizes “the tentative nature of our astronomical theories” and tells us that “observation are still too scanty for confidence that our interpretations are durable.”121 W. J. Luyten similarly warns that “We must also be rather careful not to place too much confidence in our many current, but often shaky, theories.”122 The gist of these warnings is that present-day astronomical theory should not be mistaken for knowledge.
On the other hand, the conclusions of the Reciprocal System in the astronomical field are not subject to any more than that minor degree of uncertainty that applies to all human knowledge. They are direct deductions from general principles whose validity has been established in many physical fields where the facts are readily accessible and incontestable, and they do not depend in any way on the scope or accuracy of astronomical observations. Unless some error has been made in the deductive reasoning by which the detailed conclusions were reached from the pertinent general principles, the astronomical picture obtained from the Reciprocal System is therefore necessarily correct. The possibility of an error in the deductive process cannot be completely ruled out, of course, but where the chain of reasoning is short, as in this case, a serious error is not likely, and in the absence of any specific and definite conflict with observational information there is an overwhelming probability that the conclusions reached by the new system correctly represent the true physical facts. Any conflicts with currently accepted theories are wholly irrelevant in this connection in view of the admittedly uncertain and tentative nature of these theories.
A recognition of the status of the Reciprocal System as a fully integrated unit whose validity has been established in other physical fields and which is therefore independent of the current state of knowledge in the particular field to which it is being applied is more essential than ever when we turn to a consideration of the magnetic analog of the thermal limit in the stars, the limit of magnetic ionization, not because the conflicts with existing theory are any more numerous or more serious here than elsewhere, but because in this field there are no existing theories. Neither physical nor astronomical theory even recognizes the existence of magnetic ionization, to say nothing of the relation of this ionization to atomic weight, the existence of an ionization limit, the effects of this limit, and the other related items that are discussed in this volume and its predecessors. The important point to recognize here is that regardless of the present state of observational knowledge, the section of the new theoretical structure which is applicable to these particular phenomena participates in the proof of the validity of the system as a whole. When we have established the accuracy of our aerial map by checking it against the known facts in the areas that are accessible, we then know that the map gives us a true picture in any sub-area that may happen to be inaccessible. The same is true of the Reciprocal System. Like the aerial map, this system can be tested as a complete unit, and when we have established its accuracy as a whole, we have also established its accuracy in each separate area, regardless of whether or not we are able to verify the conclusions in all areas individually.
We have already seen, in the preceding chapter, how the magnetic ionization level builds up as the age of matter increases. This build-up cannot continue indefinitely, however, as the ionization adds mass to the atom, and the total mass that an atom can have is limited. The reasons for this limitation are too involved for discussion in this general survey, but such a discussion is hardly necessary for present purposes since the existence of such a limit is an observed fact. Beyond uranium, the last of the elements which occur naturally on the earth’s surface, the artificial production of new elements is meeting increasingly greater difficulties as each additional step is taken and it is evident that a limit is being approached. When the oldest material in a galaxy, which will normally be concentrated near the galactic center, reaches this limit, this matter will disintegrate in a manner similar to that in which part of the matter of a star disintegrates when it reaches the thermal limit. Since a large amount of nearby matter is close to the limit when the first such disintegrations occur, the surrounding material is brought up to the limit by the ejections from the first explosion and once initiated, the explosion ultimately involves all or most of the galaxy.
In order to clarify the nature and results of the kind of an explosion that takes place here, it is advisable to consider the relations between the several major regions of the universe in more detail. These regions are shown graphically, in a linear sequence, in Figure 3. At one end we have the time region, in which n units of time are associated with one unit of space, and hence all motion is in time. Next is the time-space region, in which n units of time are associated with m (a smaller number) units of space. Then comes the space-time region, in which n units of space are associated with m units of time, and finally the space region, in which n units of space are associated with one unit of time.
The ratio of space to time in this diagram increases from left to right. At the extreme left time is infinite, space is unity, and velocity is zero. At the borderline between the time and time-space regions time has decreased to unity, space remaining constant, and velocity is therefore unity in one dimension. As we continue toward the right through the time-space region, the amount of space increases in the other dimensions, and at the center of the diagram the velocity is unity in all three dimensions. The right half of the diagram is a duplicate of the left half in inverse order, beginning with unit reciprocal velocity, passing through the space-time region, where time decreases until at the region boundary it is only sufficient to attain unit reciprocal velocity in one dimension, and then through the space region to the extreme right where time is unity, space is infinite, and reciprocal velocity is zero.
In the time-space region, the region of our everyday experience, the progression of space is outward (toward infinity) and since outward in space is equivalent to inward in time, the equivalent progression of time is inward. In the space-time region these directions are, of course, reversed. A similar reversal takes place at the boundary of the time region. Beyond this boundary space remains constant and only time increases. This is equivalent to a decrease in space. An increase in space in the space region, with time remaining constant, is likewise equivalent to a decrease in time.
The progression does not actually undergo a change in direction. It originates anew at every space-time unit, and the directions in which it originates are different in the individual regions. Gravitation must follow suit, as it is inherently a motion in opposition to the progression. But this fixed relation to the progression is not shared by independent motions. If an object enters the time region with an inward motion in space which it acquired in the time-space region, it still continues with the equivalent of an inward motion in space here where actual space motion is not possible; that is, it moves outward in time.
With the benefit of the foregoing explanation we are now able to analyze the effects of the two types of astronomical explosions. The explosion of the star is due to reaching the lower limit of matter: the destructive limit in one dimension. Here the increase of thermal motion and positive ionization, both of which are space displacements, forces the net time displacement down to zero. This is the boundary between the time region and the time-space region of our everyday experience. When the ensuing explosion occurs, part of the material of the star is ejected forward into the time-space region to form the familiar outward expanding cloud of dust and gas, and part is ejected backward into the time region. This later material expands outward into time, but since all of this time motion takes place in the same units of space in which it originates, the matter remains localized in space, and it ultimately regains stellar status as a white dwarf star.
The magnetic ionization, on the other hand, adds to the net time displacement rather than decreasing it. This ionization therefore pushes the net total displacement up to the upper limit of matter. When the explosion occurs and a substantial part of the mass of the galaxy is transformed into kinetic energy, the ejected material is at a space-time level near the boundary between the time-space region and the space-time region. If the amount of matter involved is relatively small, as in the case of terrestrial radioactivity, the products attain very high velocities but remain in the time-space region. In the galactic explosion, where a tremendous amount of matter is involved, the velocities are much greater and, as in the case of the supernova explosion, the ejected material is distributed to both sides of the boundary. That which is ejected backward into the time-space region moves outward in space and manifests itself as a visible cloud of particles, such as the jets issuing from the central regions of M87 and a number of other galaxies. That which is ejected forward into the space-time region similarly moves outward in time. But unlike the time region, into which the products of the super nova explosion are dispersed, the space-time region is not localized in space, and the high-velocity products of the galactic explosion therefore pass completely out of our material universe.
Now let us ask, What becomes of this material? It may seem a rather nebulous undertaking to attempt to follow the purely theoretical products of a theoretical process into an observationally inaccessible region, but the Reciprocal System recognizes no limits other than the limits of the physical universe itself. However inaccessible the space-time region may be to observation, it is just as accessible to theoretical development as the region in which the familiar phenomena of our experience are located.
The reciprocal principle tells us that for every entity and every phenomenon of our material universe there is another, which is identical in every respect except that space and time are interchanged. All of the features of our material universe belong on the left side of Figure 3 in the time region and the time-space region. The corresponding regions on the opposite side of the centerline contain exactly the same features in reverse. What we call the material universe is therefore only half of the total; it is one sector of the universe as a whole. There is another half, which we will call the cosmic sector, that is the mirror image of the material sector.
There may be some question as to why an adjective like “cosmic” was selected to designate the phenomena of the second half of the universe rather than “non-material,” which is a seemingly obvious choice since present usage practically forces us to call our familiar half the “material” sector. It appears likely that the use of the term non-material” would lead to confusion, as some of the entities normally considered non-material are definitely part of the material sector of the universe as herein defined. The neutrino is a good example. There is also an element of convenience in using a special adjective such as “cosmic” inasmuch as we will be able to identify the phenomena of the cosmic sector, very few of which have names of their own, by the names of the corresponding phenomena of the material sector with the addition of the word “cosmic.” Thus the analog of matter in the cosmic sector will be known as cosmic matter, abbreviated c-matter. Use of the expression “non-material matter“, on the other hand, would be rather awkward.
With this understanding of the general situation in the cosmic sector of the universe, let us now return to the material, which was hurled across the boundary into this sector by the galactic explosion. The structures of which this material is composed are entirely foreign to their new environment and hence they are very subject to change. To illustrate the kind of a situation that exists here we may consider the status of a small mass of high temperature gas released into a low temperature environment. A high temperature is not inherently any less probable than a low temperature, but it is less probable in a low temperature environment, and hence this gas immediately begins to lose heat and to move toward thermal conformity with its surroundings. The material atoms are compound motions and they do not respond to changes in environment as readily as the simple thermal motion, but the same principles apply, and when these atoms arrive in the cosmic environment they immediately begin losing or gaining motions of such a nature as to bring them into harmony with their surroundings. This means, in short, that they are quickly converted into structures of the cosmic type. Such conversion is always possible because all physical structures, both material and cosmic, are composed entirely of units of space and units of time, and as long as enough units are available there is always a process or combination of processes by which any structure can be converted into any other structure. As a result of the entry of the material explosion products, therefore, a quantity of new cosmic matter is formed in the cosmic sector.
This cosmic matter is the inverse of the corresponding feature of the material sector of the universe. Corresponding to the atoms of ordinary matter, which are linear vibratory space displacements rotating with displacement in time, there are cosmic atoms, which are linear vibratory time displacements rotating with displacement in space. As there are material sub-atomic particles, similar to the material atoms except that they have effective rotational displacement in only one or two dimensions, so there are cosmic sub-atomic particles that bear the same relation to the cosmic atoms. And just as the addition of rotational vibration to the material atoms and particles generates material isotopes, ions, and other charged particles, so similar additions to the cosmic atoms and particles generate cosmic
The new c-matter is widely dispersed initially, but the cosmic atoms are subject to mutual gravitational forces and to the gravitational attraction of previously existing aggregates of c-matter. Both of these operate to draw the particles closer together in time, as gravitation in the space-time region is directed inward in time rather than inward in space. The particles of c-matter thus ultimately condense into cosmic stars, the stars gather in clusters, the clusters combine into cosmic galaxies, and the galaxies grow into larger galaxies. In the meantime the cosmic stars of which the galaxies are composed have been reaching the thermal limit and exploding, producing increasingly large multiple star systems, and the cosmic magnetic ionization in the central regions of the older galaxies has been steadily rising. Finally a giant old cosmic galaxy, a cosmic replica of M 87, reaches the magnetic limit, explodes, and hurls the greater part of its substance across the boundary line into the time-space region.
The theoretical discovery of this second half of the physical universe, a finding which, in one stroke, doubles the size of the already vast cosmos, is unquestionably one of the Outstanding Achievements of the present work, and it will be number thirteen on our list. Here again it should be remembered that this is not a wild speculation or an ad hoc postulate; it is a necessary and unavoidable consequence of the Fundamental Postulates of the Reciprocal System, and it participates in the proof of the validity of that system as a whole. Since the system is valid in general, it is valid in every part, because it is a single integral unit, not, like present-day physical science, a collection of individual theories.
One of the important consequences of the new findings is that they provide a definite answer to the hotly debated question as to whether the universe is evolving or whether it is in a “steady state.” The conclusion of the new system is clear and unequivocal. The expansion of the material galaxies carries all of the matter in the universe outward toward infinite space. But no galaxy can continue moving outward indefinitely. There is a limit to its age, and hence to its outward travel. When this limit is reached the galaxy is destroyed, and the matter of which it was composed has to begin anew in the opposite sector. Here it will ultimately become a part of a system of cosmic galaxies, equal in all respects to the material system, but expanding in time rather than in space and thus carrying all of its constituent units outward toward infinite time, which is equivalent to zero space. Here again there is a limit, and when a cosmic galaxy reaches this limit it, too, is destroyed, and the material of the galaxy is transferred back to the opposite sector to start the process all over again. The movement inward toward zero space in one sector cancels all that was accomplished by the movement toward infinite space in the other sector. Thus the universe is always changing, yet always remains the same. It is in a steady state.
Existing ideas as to the nature of this steady state must, however, be modified substantially. There are two major objections to the steady state hypothesis in the form in which it has been presented by its principal advocates, the Cambridge group of astronomers. First, it violates the conservation principles by postulating the continual creation of matter ex nihilo (out of nothing). Second, it is internally inconsistent, inasmuch as the oldest galaxies are continually growing older and larger, which contradicts the principle that the universe always looks the same from any point in time: an essential feature of the postulated steady state. Hoyle attempts to explain this contradiction on the basis that the older galaxies disappear “over the time horizon” because of the recession phenomenon, and consequently the age of the oldest galaxy within observational range will always remain essentially the same.123 But this explanation is satisfactory only up to the time that our own galaxy becomes the oldest one within observational range. Beyond that time the age of the oldest galaxy in this region of space continually increases, which is directly contrary to the basic hypothesis.
The Reciprocal System disposes of both of these objections simultaneously, as it sets a limit on the age and size of the galaxies, and in so doing it replaces continuous creation of matter with a cyclic process in which the matter from which new galaxies are formed is derived indirectly from the disintegration of the galaxies that reach the end of their life spans. As explained earlier, the matter propelled into the cosmic sector by the violent explosions of the oldest material galaxies is converted into cosmic matter and becomes the raw material from which new physical structures are formed in the cosmic environment. The explosions of the mature cosmic galaxies maintain the equilibrium between the two sectors by ejecting an equivalent quantity of cosmic matter back into the material sector. Here the same kind of a process takes place. The cosmic matter is quickly converted to ordinary matter and it then constitutes the raw material from which new physical structures are constantly being formed in the local environment to maintain the steady state. In the next chapter some of the details of the conversion process will be examined.