Chapter X

Astronomical Applications

In the astronomical world an accurate new theoretical system of the kind developed in this work has a particularly broad field of usefulness. Astronomy has always been under a handicap, as compared with other physical sciences, in that it is almost entirely observational rather than experimental, and to further complicate matters, the observations give only what amounts to an instantaneous picture, the changes, if any, being too small in most instances to be measurable within the period of time available. Where observations extend over a wide range of distance it is true that they also extend over a wide range of time, because of the finite speed of electromagnetic radiation, but this gives us no time dimension for the individual objects and, in general, evolutionary processes cannot be observed; they must be inferred. Even where the evidence of an evolutionary sequence is fairly plain, the direction of the evolution is rarely indicated in any unequivocal manner, and the astronomer is usually forced to rely upon collateral information of one kind or another in making his interpretation of the observations.

The availability of an accurate new physical theory, developed and verified in other physical fields where the facts are more readily accessible, now gives astronomy a new source of information which is not subject to the limitations that are inherent in the procedure that the astronomer normally employs. All of the features of the RS universe are purely theoretical products obtained entirely from a development of the necessary consequences of the postulates of the Reciprocal System without introducing anything from the observed physical universe or from any other outside source. The previous pages have shown how the mere existence of space and time with properties as postulated necessarily leads to the existence of theoretical entities that are identical with photons of radiation, atoms of matter, sub-atomic particles, and so on. Further development of the consequences of the postulates similarly requires the existence of theoretical entities that we can easily correlate with stars, star clusters, galaxies, and other features of the astronomical universe, and it provides us with a complete definition of the theoretical properties of these entities. In view of the general proof that the theoretical RS universe is identical with the actual physical universe, it then follows that these theoretical entities and phenomena deduced from the postulates are true representations of the corresponding features of the physical universe. Since the theoretical development is not dependent in any way on existing observational or experimental knowledge, this conclusion is valid not only with respect to those features that can be verified by comparison with data from observation but also with respect to the features that cannot be so verified.

This new development therefore provides a unique opportunity of examining the subject matter of astronomy from an outside viewpoint completely independent of any conclusions that have been reached from consideration of the results of astronomical observation. In a sense, this is equivalent to getting a picture of the astronomical universe by means of a new kind of instrument of exceptional power and versatility. Like the invention of the telescope, the development of this new and powerful instrument now gives the astronomer an opportunity to widen his horizons greatly: to get a clear view of phenomena that have hitherto been hazy and indistinct, and to extend his investigations into areas that were totally inaccessible to the instruments previously available.

The picture obtained from this new instrument differs in many respects from present-day ideas—very radically in some instances—but the existence of such differences is clearly inevitable in view of the limited amount of information available to the astronomers and the consequent highly tentative nature of much of the astronomical theory currently in vogue. As has been demonstrated in the preceding pages, the correct explanation of a physical situation often differs from current ideas to a surprising degree even where the current theories have been successful enough to win general acceptance. In astronomy, where comparatively few issues have actually been settled, and differences of opinion are rampant, it can hardly be expected that the correct explanation will leave much of the previous theoretical structure intact.

In accordance with the general plan of this volume, the discussion of the astronomical situation will be limited to showing the effect that the new concepts of space and time have an astronomical thought in general, without going into any more detail than is actually necessary. It appears that this can best be done by considering two specific examples: (1) the globular clusters, which we will take as representative of the class of phenomena for which the previously available data are reasonably adequate but are erroneously interpreted because of incomplete and misleading collateral information, and (2) the white dwarf stars, which we will take as representative of the class of phenomena whose true status cannot be understood at all without making significant changes in basic concepts.

The globular clusters are by far the most numerous of the reasonably permanent stellar aggregates. Many galaxies, including our own, are accompanied by hundreds of these distinctive and conspicuous objects, and one galaxy, M 87, is reported to have in the neighborhood of a thousand associated clusters. But fitting these clusters into the structure of accepted astronomical theory has been a very difficult undertaking, and as late as 1946 an author was able to say that “no one has given an account of how these clusters must have originated or why they are found distributed as they are.”⁹⁶ Even today writers not infrequently repeat Jeans, characterization of these structures as “mysterious objects.” Present opinion favors something on the order of an explanation advanced by Von Weizsäcker in which he postulates that a vast cloud of dust and gas originally collapsed to form the central regions and disk of the galaxy and that portions of the material remaining behind in the outer regions consolidated to form the globular clusters. This view looks upon the clusters as essentially permanent features of the galaxy.

In the theoretical universe developed from the postulates of the Reciprocal System, stellar aggregates identical with the globular clusters also make their appearance, but these clusters originate uniformly throughout space. Once formed, they are pulled into the galaxies by gravitational forces. On this basis each of the larger galaxies is necessarily surrounded by a large number of globular clusters which are simply in the process of falling into the galaxy. When they reach the galactic disk they will be broken up by the rotational forces, first into smaller aggregates—galactic clusters—and finally into individual stars that will be absorbed into the general structure of the galaxy.

Here we have two very different views as to the origin and ultimate destiny of the globular clusters, one derived from astronomical observations interpreted in the light of current cosmological theory; the other derived from a theoretical system developed in an entirely different physical field, but presumably applicable to the entire universe. For convenient reference we will designate these as the CA (current astronomical) and RS (Reciprocal System) theories respectively. Now let us look at the evidence, specifically those facts on which the two viewpoints differ, and which are therefore relevant for the purpose of supporting a decision as to which viewpoint is more in harmony with existing knowledge.

1. In spite of the observational difficulties involved, a substantial number of globular clusters have been located in inter-galactic space in recent years.⁹⁷ The existence of so many clusters not associated with galaxies is very awkward for a theory such as CA which regards these objects as having originated jointly with the galaxies, and the observed situation is therefore highly favorable to the RS theory, with which it is entirely in agreement.
2. The cluster system surrounding our galaxy does not participate in the galactic rotation.⁹⁸ This is difficult to reconcile with the CA theory. If the clusters were formed as a part of the galactic aggregate, then they should act as part of the galaxy and should participate, at least to some degree, in its motion. On the other hand, the RS theory says that the clusters are not part of the galaxy but are external objects that are being drawn in by gravitation. On this basis the reason why they do not participate in the galactic rotation is obvious.
3. The observed motions of the clusters are, in themselves, practically conclusive evidence of the validity of the RS theory. As Struve expresses it, the clusters move “much as freely falling bodies attracted by the galactic center.”⁹⁹ The RS theory says that this is exactly what they are, and that the observed motions are therefore just what we should expect. The CA theory views the observed paths as portions of extremely elongated orbits, but has no explanation as to why the cluster motion should have this highly abnormal characteristic.
4. Clusters closer to the galactic center are somewhat smaller than those farther out. Studies indicate a difference of 30 percent between 10,000 parsecs and 25,000 parsecs.¹⁰⁰ This is not necessarily inconsistent with the CA theory, but it is something for which that theory has no explanation, whereas it is definitely required by the RS theory, as the clusters are subject to more loss of stars by differential gravitational forces as they move in closer where those forces are stronger. On the basis of the CA theory the present distance of a cluster from the galactic center has no special significance, since the observed position is merely a point on an orbit, and hence there should be no correlation of distance with size or any other cluster characteristic.
5. Some clusters (M67, for example) resemble galactic clusters in size, shape and location, but resemble globular clusters in the types of stars which they contain, and therefore have H-R diagrams similar to those of the globular clusters.¹⁰¹ The existence of hybrid clusters of this kind is very difficult to account for in terms of the totally different cluster origins pictured by the CA theory. The RS theory gives a simple and straightforward explanation. It identifies M67 and others with the same general characteristics as former globular clusters, or parts thereof, which have only recently reached the galactic disk. The modification of the cluster structure under the influence of the strong rotational forces of the galaxy is already under way, but the evolution of the individual stars has not yet gone much beyond the globular cluster stage. The status of M67 as a recent arrival in the disk is corroborated by the fact that, if it is classified as a galactic cluster, it is one of the most populous of these units and one of the highest above the galactic plane.
6. The observed motions of the stars in the galactic clusters show that these groups are not stable and are breaking up at a relatively rapid rate. The large number of such clusters now in existence in spite of the short indicated life means that some process of replenishment of the supply must be operative. The RS theory says that the supply of galactic clusters is continually being replenished by globular clusters, which fall into the galaxy and are broken up by the rotational forces. This is the only adequate explanation that has ever been advanced, and since the current thinking of the astronomers does not permit them to accept it (although Bok and Bok, who discuss the question at some length, concede that it would be “tempting” to do so) they are forced to admit that “We do not pretend to know from where the (galactic) clusters came.”¹⁰²

The striking fact is that wherever the data obtained from observation favor one explanation over the other, they invariably indicate that the RS theory is correct. Why then do the astronomers persist in their support of an explanation, which conflicts, with so much of the available knowledge in their own field? It is true that the astronomical profession has been inclined to favor theories that envision formation of galaxies as complete units rather than theories which build them up by some kind of an aggregation process, but it does not deny the possibility that the latter may be correct, and it recognizes cosmological theories incorporating the aggregation hypothesis—the Steady State theory advocated by the Cambridge group of astronomers, for example—as legitimate speculations, hence this preference is not sufficient to explain the blind allegiance which is given to the CA theory. What has actually happened is that the astronomers have rejected the evidence from their own observations and have turned their backs on simple and logical explanations which they admit they are “tempted” to accept, solely in order to conform to an unsupported assumption that has been made by another group of scientists in another field of science. This is one of the most astounding situations in all scientific history.

The crucial issue in this case is the direction of stellar evolution. There is ample evidence to indicate the existence of some kind of an evolutionary process in which certain characteristics of the stars change with time, but this evidence, by and large, merely shows that such an evolutionary pattern exists; it does not identify the direction of the evolution. There are, however, some purely astronomical methods by which this direction can be indirectly determined. One of the most unequivocal and positive answers can be obtained from a study of the galactic clusters. The evolutionary status of the individual clusters covers practically the entire known range of stellar types, extending all the way from groups composed of stars similar to those in the globular clusters (example: M67) to clusters composed largely of hot blue and white stars (example: the double cluster in Perseus). The question, then, is, Which is the young cluster and which the old?

We can answer this question by examining the density of the clusters. There is no doubt but that these galactic clusters are expanding; the motions are rapid enough to be measured. Their density is thus decreasing with age. Furthermore, the short lifetimes of the existing clusters preclude the possibility that either the average size or the average density of such a cluster as originally formed has changed materially during the time interval involved. It therefore follows that the clusters with the higher average density are the younger and those with the lower average density are the older. Studies show conclusively that the clusters of the M67 type have the higher average density,¹⁰³ hence these are the young clusters and the clusters of the Perseus type are relatively old. The same studies also show that the average young M67 type cluster is located higher above the galactic plane than the average Perseus type cluster, which is just what would be expected if these clusters are formed by the disintegration of globular clusters that fall into the galaxy, in accordance with the RS theory.

But these simple, straightforward and consistent conclusions from astronomical evidence are summarily rejected by the astronomers purely on the ground that they conflict with the physicists’ conclusion that the source of energy in the stars is the conversion of hydrogen to helium. If the physicists’ theory of stellar energy generation is correct, the hot blue and white stars must necessarily be relatively young, since their supply of hydrogen “fuel” could not last long at the rate they are emitting energy. On this basis the Perseus type clusters, which are made up largely of such stars, must be very young. Many astronomers are not too happy about this conclusion. As expressed by Bok, “It is no small matter to accept as proven the conclusion that some of our most conspicuous supergiants, like Rigel, were formed so very recently on the cosmic scale of time measurement.”¹⁰⁴ But rather than challenge the conclusions of the physicists, the astronomers have stifled such thoughts, ignored the evidence from their own field, and meekly acquiesced in the line of thought dictated by the physicists.

Even if the physicists were able to produce some very strong evidence in support of their conclusions, such submissiveness on the part of the astronomers would be surprising enough, but the fact is that the physicists have no such evidence to offer. The hydrogen conversion process is pure assumption. There is no actual evidence that such a process ever takes place in the stars or anywhere else. The unstable isotopes of hydrogen can be stimulated in such a manner as to cause them to do rapidly what they will do of their own accord sooner or later in any event, and the stable isotope can be forcibly altered—that is, by the expenditure of energy—but there is no observational or experimental justification for the belief that the stable isotope can be caused to become unstable. The mere fact that the conversion process would be exothermic, or exoergic, if it occurred, does not necessarily mean that it will take place spontaneously. Endothermic processes are familiar features of our physical world. The controlling factor is the relative probability, not the energy balance, and, so far as we know, the hydrogen atom is just as probable a structure as the helium atom under any physical conditions.

The physicists’ conclusions in this instance have been based on (1) the difference in mass between four hydrogen atoms and the one helium atom that would be formed by their combination, a difference which indicates that the hydrogen conversion process, if it could and did take place, would furnish at least approximately the kind of a source of energy that the observed output of radiation from a normal type star requires, and (2) the lack of any known alternative. If the explanation thus produced were completely in harmony with the known facts, it might be quite acceptable in spite of its dubious foundations, at least on a tentative basis, but even without the direct contradictions that were discussed earlier, the hydrogen process, as Bok says, does not satisfactorily explain the enormous energy output of a star like Rigel. E. J. Opik not only agrees that “a more powerful source of energy must be assumed” for the giants, but also questions the applicability of the hydrogen process to the white dwarfs.¹⁰⁵ The strong astronomical evidence indicating that the direction of stellar evolution is opposite to that which would necessarily exist if hydrogen is the stellar “fuel” merely adds further emphasis to a conclusion that is already implicit in such shortcomings as those cited by Bok and Opik: the conclusion that the hydrogen conversion process is not the source of stellar energy. If we must have a “more powerful energy source” for the giants, this can take care of the normal stars as well; we do not need two different processes.

An explanation of the much different energy generation process derived from the postulates of the Reciprocal System is beyond the scope of this volume. The objective of this present discussion is to show how the theoretical picture of the universe obtained from the new system exposes the weaknesses of existing theory, clarifies doubtful points, and enables fitting current astronomical knowledge into a consistent and logical pattern. The alternative process for generation of stellar energy, a full description of which has been published elsewhere, is, of course, entirely in harmony with this new astronomical pattern. It provides abundant energy not only for the supergiant stars but also for the novae and supernovae as well, and it results in an evolutionary sequence that conforms to the astronomical evidence in all respects.

Application of the powerful new RS instrument to such a study of the globular clusters thus gives us a quite different picture of these structures and their relation to the astronomical universe in general. This study also furnishes a demonstration of the second type of contribution, which the Reciprocal System makes to astronomical knowledge: the formulation of the new physical concepts that are necessary for the understanding of certain astronomical phenomena that are otherwise inexplicable. The answer thus supplied to the hitherto puzzling question as to why these globular clusters hold together but do not collapse into a single mass was, however, explained in detail in Beyond Newton, and a different illustration will therefore be discussed in this work. As a background for this presentation, let us look at the matter of physical separation between objects.

If a number of objects that were originally in contact move outward in space away from each other, they are then separated by intervals of space. Because of the symmetry of space and time, it is also possible for objects to move outward away from each other in time, and as a result of such movement the objects are then separated by intervals of time. When expressed in this manner, the foregoing statement seems commonplace enough, but in the first example we say that the objects are now separated by empty space, and it follows that the second group of objects are now separated by empty time: a concept which is likely to seem little short of outrageous to those who are accustomed to staying within the bounds of conventional thought.

Our initial emotional reactions are, however, definitely untrustworthy when we are undertaking to examine new ideas. Good scientific practice requires that we should test these new ideas, if possible, rather than jump to conclusions without adequate factual grounds. Inasmuch as the presence of empty time in any material aggregate will have a striking effect on the properties of such an aggregate, one possible way of testing the validity of the conclusion as to the existence of empty time is to look for objects that possess these extraordinary properties. If such objects can be located, their existence then constitutes strong evidence in support of the deductions that have been made from the underlying theory.

Since empty time is the antithesis of the empty space that plays such a prominent role in our local environment, the most likely place to find empty time is in some distant object existing in relative isolation; that is, an isolated astronomical object. And in order to be visible for our examination, such an object will have to be self-luminous. In other words, we are looking for a special and very peculiar kind of star. Let us see just what properties this star should have.

By way of contrast, we will look first at the properties of a star containing a maximum amount of empty space. Such a star has a very large diameter, a very low density, and because it is radiating from a surface area that is very large compared to the stellar mass, its surface temperature is relatively low, giving the star a dull red color. From these characteristics the star derives its name; it is a red giant, a member of a stellar class well known to astronomers. If we now substitute for this maximum amount of empty space an equivalent amount of empty time, the stellar characteristics are radically changed. Inasmuch as more time, according to the reciprocal postulate, is the equivalent of less space, this star has a very small volume and an extremely high density. Since it is radiating from a relatively small surface area, the surface temperature is high and the color is blue or white.

Are there any such stars? There are. Millions of them in our galaxy alone, astronomers estimate, on the basis of the relatively large number found within the distance at which such objects are visible. The strange stars known as the white dwarfs have exactly the characteristics described: small diameter, comparable to that of a large planet, fantastically high densities, far out of the range of anything known elsewhere in the universe, and a high surface temperature, giving these stars a white color. A significant point in this connection is that the order of magnitude of the maximum deviation of the density of these white dwarf stars from the normal density of solid matter is just about the same as that of the maximum deviation of the density of the red giants in the other direction; that is, the extreme white dwarf contains just about as much empty time as there is empty space in the extreme red giant, as would be expected from the space-time symmetry principle.

Of course, present-day physical theory also has an explanation of sorts for the peculiar characteristics of the white dwarfs. This theory postulates that the high density of the dwarfs results from a collapse of the atomic structure that allows the atomic nuclei to pack together in a solid mass. As brought out in The Case against the Nuclear Atom, the so-called atomic “nucleus” is purely fictional, but even if atoms did have a nuclear structure, current theory has no plausible explanation of why the “collapse” occurs. The proponents of the theory talk vaguely about the lack of support at the center of the stellar mass after the star’s “fuel” has been exhausted and the atoms no longer have sufficient kinetic energy to maintain the normal gaseous relations. But there is no adequate explanation as to why this situation, even if it did exist, should affect the internal relations within the atoms. The atoms at the center of the star are subject to the full pressure due to the weight of the overlying material in any event, and the exhaustion of the hydrogen “fuel“, would not change this situation. Actually the compressive force acting against the central atoms should be somewhat less at the time of exhaustion of the hydrogen than it was previously, if the evolution of the star takes place as assumed, since the superimposed weight would be reduced by the amount of mass radiated away.

Furthermore, there are other astronomical facts that even the proponents of the “collapse” theory admit are irreconcilable with the theory, on the basis of present knowledge. One of the most obvious of these is the common occurrence of binary stars, which consist of giant-white dwarf pairs. If the white dwarf status is the result of advanced age, as the theory contends, then it is entirely out of order for such a star to be paired with a theoretically much younger type of star in a combination whose components, in all probability, must have originated contemporaneously. An isolated case of this kind might be explained as a freak, but these giant-dwarf pairs are familiar features of the stellar universe. In view of its inability to account for such phenomena, together with the complete lack of any logical explanation as to why there should be any internal collapse of the atom, the current theory can hardly be considered a satisfactory product.

The “empty time” explanation, on the other hand, is simple and logical, and it agrees with the astronomical observations easily and naturally. On the basis of this theory, it is not necessary to postulate any unusual or extraordinary events such as an atomic “collapse” to account for the characteristics of the white dwarfs. The very high density of the dwarfs, this theory says, is exactly the same kind of a phenomenon as the very low density of the giants, the only, difference being that the separation between the atoms in one case is in time, while in the other case it is in space. The giant-dwarf combinations, which have been such a stumbling block for previous theories are then easily accounted for, as there is nothing to prevent the simultaneous production of stars, which differ only in the nature of the separation between the constituent atoms. Indeed, it will be shown in Chapter XIV that such pairs are not only possible, but normal developments.

It should also be noted that the currently accepted explanation is entirely ad hoc. There was no advance intimation in physical theory of the existence of any such structures as the white dwarfs; on the contrary, the first reports of the observations made on Sirius B were met with disbelief, and their validity was conceded only after so much confirmatory evidence became available that further resistance to recognition of the facts was virtually impossible. The explanation now in vogue is not something that developed naturally out of the preexisting structure of theory; it is simply the best the theorists could do in the way of meeting an awkward situation which was thrust upon them by the findings of the men in the observatories. There is no reason to believe that any such theory as that of “atomic collapse” would ever have appeared if the white dwarfs had not first been located by astronomical observations.

On the other hand, it is clear that the postulates of the Reciprocal System demand the existence of such structures as the white dwarf stars. As long as material aggregates exist in which the constituent atoms are separated by empty space, the symmetry principle makes it impossible to avoid asserting the existence of material aggregates in which the constituent atoms are separated by empty time. There will no doubt be a tendency to question the foregoing statement on the ground that it is a product of hindsight, which is notoriously much more clear than foresight, but the recognition of inverse relationships of this kind has been an important feature of the development of the Reciprocal System and initial presentation of this system in The Structure of the Physical Universe, published in 1959, contained many predictions based on this same symmetry principle which asserted the existence of phenomena then wholly unknown to science.

Some of these predictions have actually been verified in the meantime. Included among them was one, which required the existence, somewhere in the universe, of events millions of times more energetic than the most violent explosions then, known to science. In view of the radical nature of this prediction and the incredulity with which the astronomers received it, its subsequent verification is one of the highlights of the short history of the Reciprocal System, and we are justified in designating this as number nine in the list of Outstanding Achievements of the system.

In the 1959 publication the exact structure of the compound motions that constitute the atoms of the chemical elements was worked out in detail, and the nature of the process by which the more complex elements are built up from smaller units was determined. Further study of this process then disclosed that it must ultimately terminate in the destruction of matter, which reaches a certain limiting degree of complexity. Since the building-up process is one which continues through time, this means that there is a limiting age of matter and, in turn, the existence of such a limit leads to the conclusion that the oldest and largest galaxies will end their careers in gigantic explosions.

The original text admitted “It must be conceded that this seems rather incredible on first consideration. The explosion of a single star is a tremendous event; the concept of an explosion involving billions of stars seems fantastic, and certainly there is no evidence of any gigantic variety of super-nova with which the hypothetical explosion can be identified.” But the text insisted that these explosions must nevertheless occur, even though nothing of the kind had ever been identified, as their existence was “an inescapable deduction from the principles previously established.” It also went on to point out that there actually was one observed phenomenon which could very well be the result of the kind of an explosion predicted by theory, even though it was not currently viewed in that light:

In the galaxy M87, which we have already recognized as possessing some of the characteristics that would be expected in the last stage of galactic existence, we find just the kind of a phenomenon which the theory predicts, a jet issuing from the vicinity of the galactic center, and it would be in order to identify this galaxy, at least tentatively, as one which is now undergoing a cosmic explosion, or strictly speaking, was undergoing such an explosion at the time the light now reaching us left the galaxy.¹⁰⁶

When it was originally published this prediction was rejected by the astronomers as utterly fantastic; now they are frantically trying to find an explanation of their own for recently discovered phenomena of exactly the kind predicted. However incredible the existence of explosions millions of times more energetic than the super-nova explosions of single stars may have seemed in 1959, today’s observations leave little doubt but that such phenomena actually exist. Additional studies made on the jet issuing from M87, notably by I. S. Shklovsky, have confirmed the conclusion that this is an actual ejection of fast moving particles, and have determined that the energy of the jet is enormous. “What is the nature of this phenomenon?” Shklovsky asks, and answering his own question he goes on to say, “It would be natural to think of some explosion of grandiose proportions, exceeding by far even such exceptional phenomena as supernova outbursts (the energy of this explosion would exceed that of a supernova by a factor of about 10⁷…).¹⁰⁷ But the explosion explanation was still too radical and Shklovsky gave it scant consideration at the time. Not until about 1961 was this hypothesis actually taken seriously. In September of that year a note in the Scientific American reporting on recent suggestions that galactic explosions might be taking place begins with this comment:

What is the origin of the prodigious quantities of radio energy emitted by the radio “stars” outside the Milky Way? A few years ago it was generally agreed that the power came from collisions between galaxies. Since then this explanation has begun to seem more and more dubious, and radio astronomers are now casting about for another mechanism.¹⁰⁸

Since then the evidence confirming the existence of exploding galaxies has grown rapidly. A recent report by Allan R. Sandage lists a number of galaxies from which jets similar to that of M87 are issuing, and describes observations on the galaxy M 82 which are apparently conclusive evidence that “the galaxy was the scene of such an explosion some 1.5 million years ago.”¹⁰⁹

Observational verification of a prediction that ventured so far off the beaten track is, of course, a major triumph for the Reciprocal System, particularly since this conclusion was not the product of a fertile scientific imagination but was reached by means of logical reasoning from basic premises established in other fields of science. But this is not the whole story. The development of the theoretical RS universe did not stop with the explosion. It went on to determine what happens to the material scattered by the galactic explosions, and it concluded that, after some intervening steps, this material manifests itself in the form of the cosmic rays. All this was brought out in detail in the 1959 publication. Now, many years later, the astronomers are just getting around to taking suggestions of this kind seriously. “Evidence of a titanic explosion in the nucleus of a nearby radio galaxy suggests that such events may be responsible for a large part of the cosmic radiation striking the earth,” is the summary, which introduces Sandage’s article.

But even though the astronomers are finally arriving at some of the conclusions that were published in The Structure of the Physical Universe in 1959, the Reciprocal System is still one jump ahead of them, as they were unprepared for the discovery of the exploding galaxies and this discovery has confronted astronomy with a serious problem in accounting for the origin of the tremendous amounts of energy generated in these events. As Sandage says, “It is obvious that conventional energy sources are not adequate to explain the phenomena we are now observing, and some totally new energy principle may have to be devised.” The Reciprocal System is not embarrassed in this way because it is not, like the astronomers, groping around in the dark trying to find an explanation for an observed phenomenon. The existence of this phenomenon was deduced from the fundamental principles of the new system long before it was verified observationally, and in a deductive process of this kind the reasons precede the conclusions; they do not have to be the object of a search after the conclusions are reached. The theoretical discovery that matter, which reaches limiting values in the centers of the oldest galaxies would suddenly release an immense amount of energy, was the basis for the conclusion that these galaxies would explode.

Although neither the astronomers nor the physicists seem to have recognized the point as yet, this need for a “totally new energy principle” cuts the ground out from under the currently accepted hypothesis that the conversion of hydrogen to helium is the source of stellar energy. Inasmuch as this conversion process is purely hypothetical, without any experimental or observational evidence to back it up, the principal argument in its favor has always been the lack of any alternative process capable of producing the required amounts of energy. The conclusion voiced by Opik that we must find “a more powerful source of energy” for the giant stars has already seriously weakened this argument, and Sandage’s admission that a totally new energy process must be found to account for the energy output of the galaxies now administers the coup de grace.

The major problems of astronomy and cosmology, including the cosmic ray situation, will be discussed later in this volume after some necessary foundations have been laid, but this present chapter was placed here in order to introduce the concept of empty time as a typical and rather striking example of the kind of new concepts which will be encountered in the subsequent pages, and which must be clearly understood before the full significance of the theoretical arguments can be grasped. The concept of empty time is wholly foreign to present-day thought, and in the context of this structure of thought it seems absurd, but a careful examination discloses that this impression is created only because the idea conflicts with some of the usual assumptions as to the nature and properties of time.

Modern science has sacrificed so many basic principles for the sake of new physical theories of its own devising that it is now in a rather poor position to object to any new idea or concept as a matter of principle. A profession that can give up the concept of absolute magnitudes for the benefit of Relativity, that can give up the idea of causality for the benefit of quantum theory, that can give up the idea of the objective reality of atoms and particles for the benefit of modern atomic theory, and that can seriously consider giving up the principle of conservation of matter (or matter-energy) for the benefit of the Steady State theory of cosmology, can hardly be taken seriously if it attempts to stand firm on basic principles at this late date. But the truth is that no basic principles are involved in this case. The new development simply shows that the prevailing assumption that time is one-dimensional is erroneous, and that it is actually three-dimensional. Everything else then follows as a matter of course. The existence of empty time is then logically possible and a theory incorporating this concept has the same logical standing as one that conforms to previously existing patterns of thought.

The next five chapters will introduce a number of new concepts which are at least as foreign to current thinking as the idea of empty time, and may even seem more bizarre on first consideration. Here again, however, the basic situation is the same. On the initial contact with these ideas they appear strange—weird, perhaps—not because they are inherently illogical or absurd, but simply because they, like the idea of empty time, conflict with some of the assumptions concerning the nature of space and time which have remained unchallenged for so long that their true status has been forgotten. What is now necessary is to go back and correct the erroneous basic assumptions and then to adjust the prevailing directions of thinking accordingly. It should be remembered in this connection that when there are difficult problems to be solved some change in existing ideas is imperative, and if the problems are of long standing, the necessary change is likely to be a major one.