The record of advancement of astronomical knowledge has been largely a story of the invention and utilization of new and more powerful instruments. The optical telescope, the spectroscope, the photographic plate, the radio telescope, the photoelectric cell—these, and the major improvements that have been made in their power and accuracy, are the principal landmarks in astronomical progress. It is a matter of considerable significance, therefore, that in application to astronomical phenomena the Reciprocal System of theory has the characteristics of a new instrument of exceptional power and versatility, rather than those of an ordinary theory.
Astronomy has many theories, of course, but the products of these theories are quite different from the results obtained from an instrument, inasmuch as they are determined primarily by what is already known, or is believed to be known, about astronomical phenomena. This existing knowledge, or presumed knowledge, is the raw material from which the theory is constructed, and conformity with the data already accumulated and the prevailing pattern of scientific thought is the criterion by which the conclusions of the theory are tested. The results obtained from an instrument, on the other hand, are not influenced by the current state of knowledge in the area involved. (The interpretation of the results may be so influenced, but that is another matter.) If these results conflict with accepted ideas, it is the ideas that must be changed, not the data from observation. The point now being emphasized is that the Reciprocal System, like the instrument and unlike the ordinary theory, is wholly independent of what is known or believed.
Stars and galaxies are found in the existing astronomical theories because they are put into those theories. They are aggregates of matter, they exert gravitational forces, they emit radiation, and so on, in the theoretical picture, because this information was put into the theories. They theoretically generate the energy that is required to maintain the radiation by converting matter to energy, because this, too, was put into the theories. They conform to the basic laws of physics and chemistry; they follow the principles laid down by Faraday, by Maxwell, by Newton or by Einstein, because these laws and principles were put into the theories. To this vast amount of knowledge and pseudo-knowledge drawn from the common store, the theorist adds a few assumptions of his own that bear directly on the point at issue, and after subjecting the entire mass of material to his reasoning processes he arrives at certain conclusions. Such a theory, therefore, does not see things as they are; it sees them in the context of existing observational information and existing patterns of thought. We cannot get a quasar out of such a theory until we put a quasar, or something from which, within the context of existing thought, a quasar can be derived, into the theory.
On the other hand, the existing concepts of the nature of astronomical objects cannot be put into an instrument. One cannot tell an instrument what it should see or what it should record, and it sees things as they are, not as the scientific community thinks that they ought to be. If there are quasars, the appropriate instruments see quasars. Every new instrument uncovers many errors in accepted thinking about known phenomena, while at the same time it reveals the existence of other phenomena that were not only unknown, but in many instances wholly unsuspected.
The Reciprocal System of theory is like an instrument in that it, too, is independent of existing scientific thought. Stars and galaxies composed of matter appear in the theory, but neither these objects nor the matter itself are put into the theory; they are consequences of the theory: results that necessarily follow from the only things that are put into the theory, the postulated properties of space and time. These astronomical objects that appear in the theory are subject to the basic physical laws, they exert gravitational forces, they emit radiation, and so on, not because these things were put into the theory, but because they are products of the development of the theory itself. All of the entities and relations that constitute the theoretical universe of the Reciprocal System are consequences of the fundamental postulates of the system. While we can hardly say, a priori, that this system sees things as they are, we can say that it sees things as they must be, if the physical universe is a universe of motion. If there are quasars, then this theory, like an appropriate instrument and independently of any previous theoretical or observational information, sees quasars.
In the preceding chapters we have determined how things theoretically must be in many basic areas. In some instances, the picture of the situation derived from this theory differs very radically from the currently accepted view, but this is what we have to expect from a theory that operates in the manner of an instrument. In every case these answers derived from the theoretical development are in full agreement with all definitely established facts. So far as can be ascertained at this time, therefore, the theoretical universe defined by the new system of theory is a true and accurate representation of the actual physical universe. We may thus approach the astronomical field with confidence that here, too, the conclusions that we derive from the Reciprocal System, the conclusions as to how things must be in a universe of motion, will give us the kind of results that we get from an instrument: an accurate picture of the situation as it actually exists, independent of current thinking in the area.
According to the theory, the course of events in the astronomical world is determined mainly by the outcome, in each individual case, of the basic conflict between gravitation and the space-time progression, and the factor that makes the outcome different in different situations is the variation of the gravitational effect with distance. The progression of space-time originates everywhere and its magnitude is therefore constant irrespective of location, but gravitation originates at the specific location which the gravitating unit happens to occupy (momentarily) and the resulting attenuation of the gravitational effect with distance, as expressed in the inverse square law, results in a change in the relative magnitudes of the inward and outward motion as the distance increases. At unit distance the inward gravitational motion is greater than the unit motion of the space-time progression, but as our reference object moves outward the net balance of inward motion decreases, and ultimately a point is reached at which the inward and outward motions are equal. Beyond this point, the gravitational limit, as we will call it, the net motion is outward, increasing toward unit speed, the speed of light, at very great distances.
For an analogy that may be helpful in visualizing this gravitational situation we may picture a moving belt, traveling outward from a central location and carrying an assortment of cubes and balls. The outward travel of the belt represents the progression of space-time. The cubes are analogous to the photons of radiation. Having no independent mobility of their own, they must necessarily remain permanently in the location on the belt that they occupy initially the same absolute location, in the terms of this work—and they therefore move outward from the point of origin at the full velocity of the belt. The balls, however, can be caused to rotate, and if the rotation is in the direction opposite to the travel of the belt and the rotational velocity is high enough, the balls will move inward instead of outward. These balls represent the atoms of matter, and the inward motion opposite to the direction of travel of the belt is analogous to gravitation. If we decrease the inclination of the belt as the distance from the central point increases, we can incorporate the inverse square relation into the analogy. Under this arrangement the closer balls will still move inward, but at some point farther out there will be an equilibrium, and beyond this point the balls will move outward in the same manner as the cubes, but at a lower speed.
It is now possible to make some further comparisons between the theoretical conclusions and the results of observation. Aggregates of matter in our immediate environment are observed to move inward in space toward each other, conforming to the inverse square relation, as required by theory. Indeed, this inward motion—gravitation is such a prominent feature locally that it is taken for granted in scientific thought that the effect is universal. As stated in a common expression of Newton’s Law, “Every particle of matter in the universe attracts every other particle.” But the powerful optical telescopes and other instruments now available are able to reach out to distances of billions of light years, and at these extreme distances the objects that are observed—galaxies—are not moving very slowly toward us, as they should be according to Newton’s Law. They are moving outward away from us at very high speeds, increasing with the distance, up to a substantial fraction of the speed of light at the present observational limit.
Furthermore, the distribution of matter in the universe is altogether different from that which would be expected on the basis of Newton’s Law. As expressed by A. C. B. Lovell:
The application of Newton’s theory of gravitation, in which the attraction between bodies varies inversely as the square of the distance apart, to the large-scale structure of the universe would require that the universe had a centre in which the spatial density of stars and galaxies was a maximum. As we proceed outwards from this centre the spatial density should diminish, until finally at great distances it should be succeeded by an infinite region of emptiness.20
Einstein expresses the same thought in these words: “The stellar universe ought to be a finite island in the infinite ocean of space.”21 But this is not the way things are at all. So far as can be determined from the information now available, the distribution of matter in the universe is fairly uniform from a large scale standpoint. In order to reconcile the observed situation with present-day theory some extraordinary ad hoc assumptions have had to be made: first, the assumption of an explosion of the universe as a whole, one that has hurled the galaxies into space at the enormous speeds that are now observed, and second, the assumption that space itself is distorted by the matter than it contains.
The need for any such far-fetched and fanciful assumptions is eliminated by the development of the Reciprocal System. The significant fact revealed by this theoretical development is that there are two factors involved in the distribution of matter, not just gravitation alone. The progression of space-time acts in opposition to gravitation, and by reason of the attenuation of gravitation with distance while the progression remains constant, there is a net inward motion at the shorter distances and a net outward motion at the greater distances. This accounts for both the recession of the distant galaxies and the observed distribution of matter. Within the gravitational limits matter is moving inward and aggregating into galaxies. Each of these galaxies is just what Einstein said that Newtonian gravitation in Euclidean space should produce. It is a finite island in the ocean of space within its own gravitational limits. But these galaxies—these finite islands—are receding from each other because the net motion outside the gravitational limits is outward.
The explosion theory of the origin of the galactic recession—the “big bang” theory, as it is somewhat irreverently called—provides a good example of the way in which the lack of a comprehensive general theory, and the consequent proliferation of theories of very limited scope, has prevented recognition of important aspects of physical phenomena. If we overlook a certain implausibility, the “big bang” provides an adequate explanation of the recession of the galaxies as an isolated phenomenon without relation to, or connection with, anything else. But it does not give us any inkling of a significant fact that our development of a comprehensive theory now reveals: the fact that the recession is a general phenomenon; that every unit of matter which is outside the gravitational limit of another unit is receding from that other unit. This is not apparent from observation because all units smaller than galaxies are subject to the gravitational forces of larger aggregates, and the ultimate result therefore is an equilibrium rather than a continued outward motion. Meanwhile, acceptance of a theory of limited range as an explanation of the galactic recession has prevented any theoretical investigation that might have revealed the true situation.
The recession of the smaller units accounts for a number of otherwise inexplicable relationships. The globular cluster problem is a conspicuous example. These huge aggregates of stars are obviously held together by gravitational forces, but why do the stars remain separated by immense distances on the order of light-years? Astronomy has no answer, because it cannot identify any force of the required magnitude acting in opposition to gravitation. The Reciprocal System identifies this force, and arrives at a very simple explanation of the great distances. Each star of the cluster is outside the gravitational limits of its neighbors, and it is therefore receding from them. But it cannot continue the outward motion, in the manner of the galaxies, because it is subject to the gravitational force (that is, the inward motion) of the cluster as a whole. It therefore moves outward only to a point of equilibrium where the total forces (motions) add up to zero.
This same equilibrium between the recession of the individual stars and the gravitational attraction of the aggregate also provides an explanation for the immense distances between the stars of the galaxies, a phenomenon that has hitherto not only remained unexplained, but has not even been recognized as needing an explanation. Aside from the members of multiple star systems, which theoretically have a common origin, there is no indication that any star ever comes even moderately close to another. The entire range from the relatively short separations in the multiple systems, comparable to planetary distances, out to distances measured in light-years, is completely empty. Such a wildly improbable condition cannot exist by chance. It must have an explanation, and that is what the new theoretical system provides.
But even though the stars, single and multiple, are destined to remain far apart, they do not exist in complete isolation from each other, as currently assumed. On the contrary, the fact that they are occupying equilibrium positions means that the structure of a cluster or galaxy of stars is analogous to that of a liquid. There is a certain amount of freedom of movement in the cluster, just as there is in the liquid, but any disturbance of the equilibrium conditions, either by motion of the constituent units or by outside influences, meets with resistance. Current astronomical thought does not recognize this situation. Fred Hoyle, for instance, makes these comments about possible collisions of galaxies:
Think of the stars as ordinary household specks of dust. Then we must think of a galaxy as a collection of specks a few miles apart from each other, the whole distribution filling a volume about equal to the Earth. Evidently one such collection of specks could pass almost freely through another.22
According to our findings, such a collision would be more like the impact of a stream from a fountain on the surface of the pool into which it falls. There will be a certain amount of penetration in each case, while the incoming kinetic energy is being absorbed, but in both cases the moving mass meets a wall, not a passageway. Passage of one galaxy through another is simply impossible.
The liquid-like structure of the stellar aggregate also explains why stars or groups of stars can be ejected from an aggregate by explosive forces. This is another item that current theory fails to explain.
Explosions are sudden releases of energy that “push things apart” or show as sudden increases in luminosity. It is difficult to explain the “pushing” of stars. (Page and Page)23
When it is understood that a star cluster offers the same kind of resistance to applied forces as a viscous liquid, this “pushing” is no longer a problem, a point that will be of importance in connection with some of the items to be discussed later.
Within the range of effectiveness of the gravitational forces all units of matter move inward toward each other, and if given sufficient time must join. Various factors control the nature of the combinations; the relative directions of movement may result in orbital motion rather than actual consolidation, or the outward progression of the individual units may prevent any close approach, but inside the gravitational limits all aggregates eventually reach gravitational equilibrium. Within these limits, therefore, the aggregates of matter are continually growing. Atoms join together as particles, the particles gather into clouds, the clouds condense into stars, the stars increase in size and form groups and clusters. These aggregations grow into small galaxies, and the small galaxies become large galaxies.
In the earlier stages of this process the matter is cold, but as the dust cloud begins to contract, potential energy is gradually transformed into kinetic energy of the molecules, and the temperature of the aggregate begins to rise. At some point in this process, probably somewhere in the range in which a dense dust cloud is becoming a very diffuse star, the central temperature of the mass reaches the lower destructive limit of the heaviest atom present, and generation of energy by atomic disintegration begins.
When the star reaches gravitational equilibrium and contraction ceases, one of the two sources of energy is eliminated. The heavy element content of the star is, however, roughly proportional to the total stellar mass, which means that the production of energy from the destruction of these elements is a function of the third power of the diameter. The loss of energy by radiation, on the other hand, is a function of the surface area; that is, the second power of the diameter. The stellar temperature therefore rises as the accretion of mass continues, and this makes successively lighter elements available as fuel for the conversion process.
Since none of the heavier elements is present in more than a relatively small quantity in the usual case, the availability of an additional fuel supply due to reaching the destructive limit of one more element is not normally sufficient to cause any major change in the energy balance of the star. When the temperature corresponding to the destructive limit of the nickel-iron group of elements is reached, however, the situation is quite different. These elements are not limited to small amounts; they are present in concentrations which represent an appreciable fraction of the total mass of the star. The sudden arrival of this large quantity of material at the destructive limit activates a potential source of far more energy than the star is able to dissipate through the normal radiation mechanism. The initial release of energy from this source therefore blows the whole star apart in a tremendous explosion. Because of the relatively large amount of the nickel-iron elements in the central core of the star, the explosion takes place as soon as the first portions of this material are converted into energy, and the remainder, together with the overlying lighter matter, is dispersed by the explosion-generated velocities.
This explosion which theoretically occurs when the star reaches the destructive limit of the nickel-iron group can obviously be identified with the observed phenomenon known as a supernova. One product of the explosion, the most visible product, is an expanding cloud of dust and gas propelled outward from the explosion site. From the standpoint of our ordinary experience, this can be regarded as a perfectly normal result, the kind of a thing that we expect as the result of any explosion. But this stellar explosion is not just another ordinary explosion; it is an explosion of a special type. At the extremely high temperatures prevailing in the interior of the star before the explosion the atoms of matter are already moving with extremely high velocities, and when the explosion adds a large amount of kinetic energy to that already existing, the velocities of some of the atoms—a considerable fraction of the total mass in the usual case—are increased to levels beyond unity.
The nature of the resulting product can be best understood by first taking a look at what happens to the explosion products that are expanding outward in space. Ultimately the forces of expansion are overcome by gravitation and encounters with interstellar particles, and contraction then begins under the influence of the ever-present gravitational forces. In due course the cloud of particles regains the status of a star. At the stage when it first becomes visible, this star, a red giant, is still extremely diffuse. It has been picturesquely described as a red hot vacuum. But this does not mean that the matter of which it is composed is any different from the matter in the stars of the so-called “main sequence,” and no one ever suggests any such thing. It is recognized that the special characteristics of the red giant, the enormous size, the relatively low surface temperature, and the extremely low density, are all due to the existence of a large amount of empty space between the particles of matter.
Neither the mass nor the volumetric characteristics of the atoms of matter has been changed by the expansion in space. But when we measure the density, m/V, of the giant stars we include in V, because of our method of measurement, not only the actual equilibrium volume of the atoms but also the empty three-dimensional space between them, and the density of the star calculated on this basis is something of a totally different order from the actual density of the matter of which it is composed.
The situation with respect to the component of the explosion products that is moving faster than the speed of light is exactly the same, except that in this case the outward motion does not take place in space. As brought out in Chapter V, after the speed of light is reached any further increase in space displacement, or its equivalent, results in a motion in time. The particular pattern that such motion will take depends on the magnitude of the added space displacement. If this is relatively small, the speed in the two inactive dimensions remains at the spatial zero, and the motion in time is a scalar addition to the motion in space, as shown in diagram b, Figure 4. If the added displacement is large enough to carry the total speed beyond the neutral level, the inactive dimensions convert to zero motion in time, and the moving object leaves the material sector, eventually reaching the situation shown in diagram e.
An object in the condition indicated by diagram b remains in the same spatial location that it would occupy at unit speed, and any further motion is not in space, but in equivalent space, the spatial equivalent of the scalar motion in time. It therefore remains as an identifiable object in space, distinguished from other objects only by a size that is abnormally small for the class of objects to which it belongs, and by the effects that accompany this reduced size: high density, high temperature, etc. While we do not have, at this stage of the development of theory, any quantitative method of evaluating the increment of speed that is acquired by the products of a supernova explosion, and thus determining theoretically whether these products will remain in the condition of diagram b or will continue on to that of diagram e, it is clear from observation that we can identify them as having the b status; that is, their motion in time is not sufficient to reach the neutral level.
The second component of the explosion products is thus similar to the first component in that it, too, is a cloud of dust and gas expanding outward, but it differs from the first component in that it is expanding outward in time rather than in space. The result of this expansion is a star in which the particles of matter are separated by empty time rather than by the empty space that separates the particles of the ordinary dust cloud or red giant star.
In this star the deviations from normal are just the opposite of those that we observe in the red giant. Because of the reciprocal relation between space and time, more time is equivalent to less space, hence introducing more time between the particles of matter has the same effect as decreasing the space between these particles. When we measure the volume occupied by the star in the usual manner, the results that we obtain include the effect of the reduced equivalent space, just as similar measurements of the volume of the red giant include the effect of the large amount of space between the particles. Thus, even though the actual density of the matter of which a star is composed is the same in all cases, aside from the normal effects of temperature and pressure, the measured density of the star is highly dependent on the nature of the separation between the constituent particles. The star that has expanded into time, a white dwarf, is characterized by an abnormally small volume, a very high density, and since it is radiating from a surface that is small in proportion to its mass, a high surface temperature.
When judged by terrestrial standards, the calculated densities of the white dwarfs are nothing less than fantastic, and they were originally accepted with great reluctance and only after all of the alternatives that could be conceived had been ruled out for one reason or another. In the light of the foregoing information, however, it is clear that this very high density is no more out of line than the very low density of the giant stars. The magnitude of the effect is essentially the same in both cases. In the extreme red giant the density of the star is less than the equilibrium density of matter by a factor of 105 or 106. In the extreme white dwarf the density of the star is greater than the equilibrium density by approximately the same factor. The expansion of the cloud of particles outward in time has thus accomplished the exact opposite of an expansion outward in space.
This is one of the most significant consequences of the reciprocal relation between space and time that exists in a universe of motion, as it removes the principal obstacle that has hitherto stood in the way of an understanding of some of the most important recent discoveries in astronomy. Most of these puzzling discoveries are concerned with objects that are abnormally compact when judged by familiar standards. The white dwarf star was unique in this respect when it was first discovered, but it is now only one of many, inasmuch as a wide variety of compact objects have appeared on the scene one by one as astronomical knowledge has widened. In the case of the white dwarf, it was found possible to devise an explanation of sorts for the high density within the boundaries of conventional basic physical theory, but in order to do so it was necessary to make some extraordinary, and in some respects quite illogical, ad hoc assumptions. This merely compounded the difficulties and blocked the way to a theory of compact objects in general, as a highly artificial construct of this kind is inherently incapable of application to any situation other than that to which it was specifically fitted.
The increase in density due to outward motion in time is not limited in this manner. Any object composed of particles or other units will expand and decrease in density if those constituent units move outward spatially. Similarly, any such object will expand in time, a process that is equivalent to a contraction in space and therefore increases the density, if the constituent units move outward in time by reason of a speed in excess of that of light. Thus the same process that is responsible for the high density of the white dwarf is available to explain abnormally high density wherever we find it—in quasars, in pulsars, in galactic cores, and so on. We will make much use of this process in the subsequent pages.