CHAPTER VIII

Quasars: The General Picture

The most obvious and most striking feature of the quasars, the point that has focused so much attention on them, is that they simply do not fit into the conventional picture of the universe. They are “mysterious,” “enigmatic,” “surprising,” “baffling,” and so on. Thus far it has not even been possible to formulate a hypothesis as to the nature or mechanism of these objects that is not in open and serious conflict with one segment or another of the observed facts. “We have as yet no real understanding of many of the fundamental physical processes which are operating in the nuclei of galaxies and in QSO’s”²⁵, says G. R. Burbidge. R. J. Weymann makes this comment:

The history of our knowledge of the quasi-stellar sources has been one surprise after another. Indeed, almost without exception, every new line of observational investigation has disclosed something unexpected.²⁶

Ironically, the principal obstacles that have stood in the way of an understanding of the quasar phenomena are not difficult and esoteric aspects of nature; they are barriers that the investigators themselves have erected. In their search for scientific truth, a complicated and difficult undertaking that needs the utmost breadth of vision of which the human mind is capable, these investigators have gratuitously handicapped themselves by placing totally unnecessary and unwarranted restrictions on the allowed thinking about the subject matter under consideration. The existing inability to understand the quasars is simply the inevitable result of trying to fit these objects into a narrow and arbitrary framework in which they do not belong.

Most of these crippling restrictions on thinking result from the widespread practice of generalizing conclusions reached from single purpose theories. This practice is the most serious handicap under which physical science now labors. Many of our present-day theories, both in physics and in astronomy, are in this single purpose category, each of them having been devised solely for the purpose of explaining a single set of facts. This very limited objective imposes only a minimum of requirements that must be met by the theory, and hence it is not very difficult to formulate something that will serve the purpose, particularly when the prevailing attitude toward the free use of ad hoc assumptions is as liberal as it is in present-day practice. This means, of course, that the probability that the theory is correct is correspondingly low. Such a theory, therefore, is not, in the usual case, a true representation of the physical facts; it is merely a model that represents some of the aspects of the particular physical situation. Hence there is very little chance that conclusions drawn from such a theory will be applicable to a totally different phenomenon in some unrelated field. To make matters worse, many currently accepted theories that are utilized as foundations for far-reaching generalizations do not even meet the very modest requirements that are supposed to be applicable.

Relativity theory is a good example. On the basis of this theory, the scientific Establishment has laid down the dictum: “Thou shalt not think of speeds greater than that of light.” Now let us ask, What justification is there for this far-reaching prohibition? Does it have any factual basis? No, the observations merely tell us that no higher speed can be produced by a particular kind of process. These observational results give us no inkling as to whether it is the speed itself or the capabilities of the process that is subject to a limitation. The alleged limitation on speed comes from the theory, not from the observed facts.

But the theory is wide open to serious question. It was developed specifically for the purpose of reconciling the theory of the comparison of velocities with the observed constant velocity of light, and since it does this much it is accepted as a “permanent property of exact science.”¹⁴ Nothing more is required of it, and one of the astounding features of the situation is that it is not required to be consistent with anything else—or even with itself. If we inquire into its logical status we find that its application to motion in general is not required to be consistent with its application to uniform translational motion.

The general theory… discards, in a sense, the conceptual framework of its predecessor. (Peter G. Bergmann)²⁷

It is not required to be consistent with the accepted theory of the structure of matter.

There is hardly any common ground between the general theory of relativity and quantum mechanics. (Eugene P. Wigner)²⁸

It is not required to be self-consistent. The “paradoxes” that result from its application cannot be eliminated without recourse to expedients that conflict with the basic assertions of the theory.

The crucial argument of those who support Einstein (in the clock paradox controversy) automatically undermines Einstein’s own position. (G. J. Whitrow)²⁹

Nor is it required to agree with any extensive set of physical facts.

There is very little experimental evidence about the features of the theory (relativity) which are peculiar to it. (J. R. Oppenheimer)³⁰

Consequently, it is recognized by those who actually face the issue that there is very little scientific justification for acceptance of the theory.

General relativity has hardly been tested yet; only one of its predictions has been experimentally verified… Its acceptance by physicists rests almost entirely on their feeling that it is inherently right but this may be a form of prejudice, rather than a reasoned judgment. (F. D. Kahn and H. P. Palmer)³¹

And there is a growing tendency to define the content of the theory in purely mathematical terms, eliminating the theoretical interpretation on which the speed limitation rests.

Einstein’s original interpretation of the special theory of relativity is hardly ever used by contemporary physicists. (P. K. Feyerabend)³²

Using a theory of this highly questionable nature as the basis for laying down a limiting principle of universal significance is simply absurd, and it is hard to understand why competent scientists allow themselves to be intimidated by anything of this kind. There are a few signs of a coming revolt. Some investigators are beginning to chafe under the arbitrary restrictions on speed, and are trying to find ways of circumventing the alleged limit without actually offering a direct challenge to relativity itself. “Tachyons,” hypothetical particles that move faster than light but have some very peculiar ad hoc properties that enable them to be reconciled with relativity theory, are now accepted as legitimate subjects for scientific speculation and experiment.³³ But such halfway measures will not suffice; what science needs to do is to cut the Gordian knot and to recognize that there is no adequate justification for the assertion that speeds in excess of the speed of light are impossible. The most that can legitimately be claimed on the authority of either relativity theory or the physical observations at high velocities is that they suggest the existence of some kind of a limitation. Stretching this into a positive prohibition of higher speeds is completely unwarranted and constitutes a wholly unnecessary obstacle in the way of understanding new and unfamiliar types of phenomena such as those revealed by the discovery of the quasars.

The development of the Reciprocal System has now made it clear that the speed of light is a limit only in a very restricted sense, and that in the universe as a whole speeds in excess of that of light, ultra high speeds, as we will call them in the ensuing discussion, are just as common as those below this level. But even without the benefit of this new information it should be evident that the idea of a speed in excess of that of light is a rational and reasonable concept that is not ruled out by anything that we actually know, and arbitrarily barring it from possible use in the explanation of phenomena that do not fit into the conventional categories is indefensible.

Meanwhile, conclusions derived from other single purpose theories are blocking the astronomers’ view of additional important features of the quasars. The accepted explanation of the high density of the white dwarfs cannot be extended to aggregates of stars, and it therefore stands in the way of a realization that the high density of the quasars results from exactly the same cause. Acceptance of the “big bang” theory of the recession of the distant galaxies, a theory designed to explain one observed fact only, prevents recognition of the scalar nature of motion of the recession type, and leaves the scientific world without any explanation of the absence of quasar blueshifts.

The key to an understanding of all of the matters with which we will here be concerned, the galactic explosions, the radio galaxies, the quasars, and associated phenomena, is a realization that all these are results of reaching the upper destructive limit of matter, and that in general these results are analogous to those which were encountered in our study of the situation at the lower destructive limit. The galactic explosions are analogous to the supernova explosions, the two major components of the galactic explosion products are analogous to the two major products of the supernova explosion, and the unusual properties of the ultra high speed component of the galactic explosion products, the quasar, are analogous to the unusual properties of the ultra high speed component of the supernova explosion products, the white dwarf. The “mysterious” quasars are not so mysterious after all; they are simply the galactic equivalent of the white dwarf stars.

This answer to the quasar problem is so obvious that it should have been recognized immediately, in general if not in detail, when these objects were first discovered. It is commonly understood that the white dwarf star is a product of the supernova explosion, directly or indirectly. In this case, then, the explosion of a star has produced another star with some very peculiar properties. Evidence has recently been found that certain galaxies are also exploding, and almost simultaneously a class of objects of galactic mass with many properties similar to those of the white dwarfs has been discovered. The conclusion that these new objects, the quasars, are white dwarf galaxies follows almost automatically. But however natural this conclusion may be, the astronomers cannot accept it because they are committed to conflicting ideas that have been derived from single purpose theories and have been generalized into universal laws.

The two classes of explosive events differ in a number of details, as a galaxy is quite different from a star, and the results of reaching the upper destructive limit are not identical with the corresponding events at the lower limit, but the general situation is the same in both cases. One component of the explosion products is ejected with a speed less than that of light, and since this is the normal speed in the material sector of the universe, this product is an object of a familiar type, a rather commonplace aggregate of the units of which the exploding object was originally composed. The constituent units of a star are atoms and molecules. When a star explodes it breaks down into these units, and we therefore see a cloud of atomic, molecular, and multi-molecular particles emanating from the site of the explosion. But there is also a second component, a peculiar object known as a white dwarf star, which we identify as a similar cloud of particles that has been ejected with a speed greater than that of light and is therefore expanding into time rather than into space.

Some of the products of the galactic explosion are likewise reduced to particle size, but the basic units of which the galaxy is composed are stars, and hence the material ejected by the explosion comes out mainly in the form of stars. Instead of clouds of gas and dust particles, the galactic explosion therefore produces “clouds” of stars: small galaxies. Here, again, as in the supernova explosion, one of the products of a full-scale galactic explosion acquires a speed in excess of that of light while the other remains below this level. The galaxy traveling at normal speed is also normal in other respects, the only prominent distinguishing feature being the strong radio emission in the early stages. This product is a “radio galaxy.” The high speed product is the quasar.

Motion of an object at right angles to the line of sight—proper motion, as it is known to the astronomers—can be measured, or at least detected, by observation of the change of position of the object with respect to its neighbors. Motion in the line of sight is measured by means of the Doppler effect, the change in the frequency of radiation that takes place when the emitter is moving toward or away from the observer. No proper motion of the quasars or other distant galaxies has been detected, and we may therefore conclude that the random motions of these galaxies are too small to be observable at the enormous distances that separate us from these objects. By reason of the progression of space-time, however, these galaxies are receding from each other and from the earth at high speeds that increase in direct proportion to the distance. The Doppler effect due to these speeds shifts the spectra toward the red in the same proportion. Inasmuch as an approximate value of the relation between redshift and distance (the Hubble constant) can be obtained by observation of the nearer galaxies, the redshift serves as a means of measuring the distances to galaxies that are beyond the reach of other methods.

The most notable feature of the quasars is that their redshifts are fantastically high in comparison with those of other astronomical objects. While the largest redshift thus far measured for a normal galaxy is less than.500, some of the quasar redshifts exceed 2.00, and even the lowest would be relatively high for a normal galaxy. If we assume, as most astronomers now do, that these are ordinary recession redshifts, then the quasars must be by far the most distant objects ever detected in the universe.

Our theoretical development indicates that from the standpoint of distance in space this conclusion is erroneous. In the context of the Reciprocal System of theory the recession redshift cannot exceed 1.00, as this value corresponds to the speed of light, the full speed of the progression, the level that is reached when the effect of gravitation becomes negligible. Even without any detailed consideration it is therefore evident that the observed quasar redshift includes another component in addition to the recession shift. From the previous account of the origin of the quasar it can readily be seen that this excess over and above the redshift due to the normal recession is a result of the extremely high speed imparted to the quasar by the galactic explosion, a speed that exceeds unity (the speed of light) and therefore has characteristics that differ significantly from those of speeds below unity, the normal range in the material sector of the universe.

In order to examine this situation in detail, let us turn back to Figure 4, in which the various basic combinations of unidirectional motion are shown in our triangular motion diagrams. As explained in Chapter V, diagram a represents the normal motion in the material sector, the kind of motion that we encounter in our daily life. Here the two inactive dimensions of a unidirectional motion have zero space velocity. In what we have called the cosmic sector of the universe, the sector in which the normal speeds exceed that of light, the normal pattern is that shown in diagram e, where there is zero time velocity in the two inactive dimensions. To change a motion of type a to motion of type e it is necessary to convert the two inactive dimensions from zero motion in space to zero motion in time by way of a sequence such as that shown in Figure 4, going from left to right. However, the interactions in the region beyond the neutral point (diagram c) reduce the inverse speed and accomplish the change from condition c to condition e automatically. It is only necessary, therefore, to provide enough space displacement (energy) to reach the neutral point. This requires the addition of two units of motion (equivalent to 2.00 redshift), one in each of the two inactive dimensions.

Inasmuch as the condition of zero motion in space which exists in each inactive dimension of unidirectional motion in the material sector is the result of a negative (inward) motion acting in opposition to the inherent progression in this dimension, the effect of the motion generated by the explosion, so far as this dimension is concerned, is to cancel the effect of the negative motion and permit the progression to take place unchecked. The added motion due to the explosion is therefore, in effect, another progression, an outward scalar motion, similar to the progression in the active dimension, and, to the extent that the motions are coincident, the redshifts are additive. Since all of this progression is outward, there are no blueshifts.

The supernova explosion is not energetic enough to give the constituent particles of the white dwarf the necessary speed to reach situation c, and that star therefore retains the zero spatial speed in the inactive dimensions, absorbing the additional energy by increasing the speed in the active dimension to a level above the speed of light (in terms of the diagram, changing T to S). As the white dwarf loses energy by interaction with other objects it ultimately reverts back to the normal less-than-unit speed. A full-scale galactic explosion, however, is far more powerful than the supernova, and it gives the quasar enough speed to meet the two-unit requirement for entry into the cosmic sector. But this change does not take place immediately, as the speed generated by the explosion, the explosion speed, as we will hereafter call it, is subject to gravitational effects in the same manner as the normal progression, and the quasar therefore remains as a visible object in the material sector until its net explosion speed reaches two units (equivalent to a 2.00 addition to the recession redshift).

During this interval, while the net explosion speed of the quasar is below the two-unit level, the spatial speed in the inactive dimensions must remain at zero (that is, an object cannot move translationally in space in more than one direction at a time), and the effective portion of the explosion speed (the addition to the recession) must therefore take the form of a scalar addition to the unit recession speed. Beyond unity, motion takes place in time rather than in space, but because of the reciprocal relation, this motion in time has a space equivalent, and it is that equivalent motion in space that determines the size of the addition to the normal recession redshift that is contributed by the explosion speed.

Unit speed in time and unit speed in space are coincident; they are both defined as one unit of space per unit of time. The one-dimensional separation between zero speed in space and zero speed in time is therefore two space-time (motion) units. But inasmuch as space and time are three-dimensional, the total separation amounts to 23 or 8 units. Any intervening speed can thus be expressed in either of two ways: as x units measured from zero speed in space or as 8-x units measured from zero speed in time. This is the situation that we often encounter in chemistry, where, for example, an element such as iodine has a negative valence of 1, but a positive valence of 7. In the present instance, we have found that the motion generated by the explosion must take place in time, and one unit of this motion, the smallest amount that can exist, is equivalent to seven units measured from the spatial zero, the way in which this speed in time manifests itself in the phenomena of the material sector.

The spatial equivalent of a motion in time has no dimensional limitations, as time dimensions are not related in any way to space dimensions, and the seven units are therefore divided equally (by the operation of probability) between the two spatial dimensions that are now active. The component of the explosion speed in the recession dimension is thus 3.50. If the motion of the quasar continued on this basis up to the point where the normal recession reaches unit value—that is, the point where the recessional speeds are no longer being reduced by gravitation—the total speed in the dimension of the normal recession, and the total redshift (which has the same numerical value) would be 1.00 + 3.50 = 4.50. Since only one dimension of the explosion speed is coincident with the normal recession, the excess redshift of the quasar at any shorter distance is proportional to the square root of the recession redshift. Thus, where the recession shift is z, the added redshift is z^½ times the 3.5 value that corresponds to unit normal redshift. The excess quasar redshift at this point is therefore 3.5 z^½ and the total redshift of the quasar is z + 3.5 z^½.

On this basis, the excess redshift reaches 2.00 when the recession shift is 0.3265 and the total quasar redshift is 2.3265. (In the ensuing discussion the last figure will be dropped, as the redshift measurements are not currently carried to more than four significant figures.) The 2.00 explosion speed is sufficient to permit the quasar to convert to the neutral level (Figure 4c) in the two inactive dimensions. When this conversion occurs, the gravitational effect in space disappears, and the full explosion speed (3.5) plus the full recession speed (1.0) become available to take the quasar past the neutral point and into the inverse, or cosmic, sector of the universe. The 2.326 redshift therefore constitutes a limit which cannot be exceeded (under normal conditions, at least).

Up to the current year no redshift exceeding the theoretical limiting value by any significant amount had appeared, but quite recently the rather startling figure of 2.877 was reported for the quasar 4C 05.34. This is not necessarily in conflict with the theory, as there could conceivably be some kind of interference that would delay the conversion process that normally cuts the redshift off at the 2.00 level rather than continuing on the 3.5 z½ basis. For the time being, however, it will probably be advisable to regard the 2.877 figure with some degree of skepticism, particularly in view of the large margin by which it exceeds any other measured redshift.

The radiation of the quasar, like its motion, is divided between the two dimensions that are active in the ultra high speed range, and it thus has a two-dimensional distribution rather than a three-dimensional distribution such as that which takes place in three-dimensional space. Instead of following an inverse square relation, therefore, the radiation from a quasar theoretically decreases in proportion to the inverse first power of what we may call the “quasar distance,” the distance corresponding to the excess redshift. Observational data to show that the quasar radiation does, in fact, follow this theoretical first power relation will be presented in Chapter IX.

The idea of a two-dimensional distribution of radiation will no doubt create conceptual difficulties for some readers in view of the long-standing habit of looking upon space as a setting or container, even though that idea has been expressly repudiated in setting up the basic framework of the Reciprocal System. It seems advisable, therefore, to discuss the nature of this two-dimensional distribution in some detail before proceeding further with the theoretical development.

As brought out in Chapter III, the inherent relationship between location A and location B is scalar only. As a scalar quantity it can be represented one-dimensionally—that is, by a line—but in reality it has no dimensions at all. It is simply a magnitude. The expanding balloon analogy that was utilized earlier can be of considerable assistance in clarifying this situation. If points A and B are located on the balloon surface, the only inherent relation between the two is a scalar quantity expressing the separation, a quantity that changes as the balloon expands. This quantity can be represented by a line, a one-dimensional construct, but the line adds nothing to our knowledge of the situation. As long as we consider the two locations A and B only, without bringing in any kind of a reference system, the only property of the line AB is its length, a scalar magnitude. This is the same quantity as that which expressed the separation between the two locations, and we are thus right back to where we were before we started thinking in terms of the line concept.

In order to give the relation between location A and location B any significance other than that expressed by a scalar magnitude, it is necessary to introduce a reference system, and the nature of the further relationship now perceived between the two locations depends on the particular reference system selected; that is, it is essentially a property of the reference system rather than a property of the two locations. The effect of a change of reference system on the indicated motions of the spots on the balloon surface was discussed in detail in Chapter III. As brought out there, such changes not only alter the direction attributed to a particular motion but may also affect the magnitude, even to the extent, under some circumstances, of depicting that motion as non-existent.

For reference purposes we ordinarily select a three-dimensional coordinate system; that is, we pass three perpendicular axes through point A and refer the line AB to the spatial system thus defined. What we see, then, is not things as they are in themselves, but as they appear in the context of our three-dimensional reference system. Instead of seeing location B as being related to location A merely by a magnitude representing the distance AB, we see the line AB as having a direction; that is, we locate B somewhere on the surface of a sphere with radius AB. Any motion that has no directional characteristics of its own is thus assigned a direction by our reference system. Inasmuch as this directional assignment is purely by chance, in any case where many separate motions of this nature are involved, as where photons of radiation emanate from a source in three-dimensional space, these motions are distributed over all possible directions. Under these conditions the portion of the total radiation received at point B from source A is inversely proportional to the square of the intervening distance AB.

But some motions do have directional characteristics of their own. For example, light may be emitted as a beam rather than in random directions. If this is a perfect beam (something that is hard to achieve in practice, but is theoretically possible) the amount of light received at B is independent of the distance AB. All of the emission takes place in this one direction. Obviously there is another possibility intermediate between the beam and the three-dimensional distribution. It is possible that light may be emitted under such conditions that the distribution is two-dimensional. This is the situation that theoretically exists when radiation originates in the region of ultra high speeds, where physical action takes place only in two scalar space-time dimensions and not in three-dimensional space or time. In this case all points on the circumference of a circle with radius AB are equally probable targets of the photons emanating from A, and the amount of radiation received at location B is inversely proportional to the first power of the distance AB. In a two-dimensional universe point B will always be in the plane of the radiation, but in a three-dimensional universe this plane may have any orientation in the third dimension, and the probability that point B will be located in the plane of the radiation is also inversely proportional to the first power of the distance AB.

It has already been recognized that there are aspects of the quasar radiation that are indicative of a distribution in less than three dimensions. Many investigators have suggested that this radiation might be concentrated as a beam, and in his review article on pulsars, A. Hewish refers to “beaming in two coordinates,”³⁴ the same concept that we have derived theoretically. Hence even though the concept of a two-dimensional distribution of radiation seems rather strange in the light of current thinking, it is not entirely unprecedented. In the final analysis the validity of such a concept must be demonstrated by showing that it produces the right answers, and this will be done in the pages that follow, but an unfamiliar idea sometimes seems more palatable if it is understood that there has been previous thinking aimed in the same general direction.

If we assume that the population of ordinary galaxies is uniform in space, from the large-scale standpoint, as required by the Reciprocal System of theory, the total number of such galaxies in a volume of radius d is proportional to d³. Inasmuch as the luminosity varies as 1/d², it then follows that the distribution of visible galaxies in distance is proportional to d^1/5. The quasars also originate in three-dimensional space, and their number is also proportional to d³. Because of the two-dimensional distribution of their radiation, their luminosity varies as l/d rather than 1/d², but, as brought out in the preceding discussion, by reason of the random orientation of the two-dimensional radiation only l/d of the total number is visible from any specific location in space. The distribution of the visible quasars in distance therefore follows the same d^1/5 relation as the distribution of ordinary galaxies.

In this situation where we are examining the question as to where the visible objects are located in space, it is immaterial whether an object is invisible because its magnitude is reduced below the visibility limit by the inverse square relation or because it cannot be seen at all by reason of the orientation of the plane of the radiation. The d^1/5 relation therefore holds good in both cases. When we examine the question as to the relation of the number of quasars to luminosity, however, this equivalence no longer exists. If we increase the power of our instruments, the object that was previously just below the visibility limit becomes visible, but the object that was dimensionally inaccessible remains inaccessible.

If all galaxies were equally luminous, so that the observed differences in magnitude could be attributed to distance alone, the 1.5 power relation between number and distance would result in a -1.5 power relation between number N and luminosity S. It can be shown mathematically that this relation also holds good even if the luminosity is variable, as long as the variations are random. Current studies of this relationship, the log N-log S relation, as it is generally called because the pertinent data are usually shown in logarithmic form, are therefore based on the premise that the slope of the log N-log S curve will be -1.5 in a uniform Euclidean universe.

But this premise assumes a three-dimensional distribution of the radiation. In the case of the ordinary galaxies, where this assumption is valid, the total number of galaxies that are actually visible is the same as the number potentially visible; that is, sufficiently luminous to be visible. A total number proportional to d^1/5 is distributed in distance in proportion to d^1/5. Where there is a two-dimensional distribution in a three-dimensional universe, however, the number potentially visible is proportional to d³, but the number actually visible is less because in some instances the radiation is not directed toward the given location. For this reason the distribution of the visible objects in distance is proportional to d^1/5, as previously indicated. Under these circumstances the number of visible objects to any limiting magnitude is inversely proportional to the geometric mean of these two values, and the slope of the log N-log S curve for the quasars should therefore be -2.25. This theoretical conclusion is confirmed by a study of the quasars included in the 3C (Third Cambridge) catalog which arrived at a value of -2.2.³⁵

A great deal of attention has been paid to this relation because of its presumed relevance to cosmological issues, particularly the active contest between the “evolutionary” and “steady-state” theories of the universe. There are very few solid facts that have any relevance for cosmology, and the choice between these rival theories has had to be made largely on non-scientific grounds. In its present form the steady-state theory conflicts with the conservation laws by postulating that matter is created out of nothing, and for this reason it is philosophically unacceptable to those who regard conservation as fundamental. On the other hand, the evolutionary theories involve the existence of one or more singularities in the evolution of the universe that are beyond the reach of scientific investigation and are therefore repugnant to those who dislike mixing metaphysics with science. The counts of radio sources have consequently been hailed with enthusiasm as providing some firm support for the evolutionary theories, and for a time the steady-state advocates were in full retreat, although more recently they are beginning to reform their ranks.

These radio source counts have consistently yielded values of the log N-log S slope that exceed the -1.5 value, the most recent data indicating that the slope for all radio sources is about -1.8. Thus there are more faint sources than should be present in a steady-state universe, on the basis of a normal three-dimensional distribution of the radiation from these sources. The contention of the supporters of the evolutionary theories is that this discrepancy is an evolutionary effect, an indication that the state of affairs in the universe was different billions of years ago when the radiation that we are now receiving from the most distant objects originated. But this argument is completely dependent on the assumption that the radiation distribution is three-dimensional, and there is now ample evidence to show that this assumption is not valid in application to the quasars. Our finding that the slope of the curve for the quasars is -2.25 deprives the -1.8 value of any cosmological significance. The fact that the slope of the curve for all radio emitters is above the normal -1.5 value is now nothing more than an indication that a substantial proportion of objects of the quasar type is included in the total, which is something that we already know from observation.

Although the question as to whether we live in a steady-state or evolutionary universe is not directly involved in the chain of reasoning leading to an explanation of the quasars and associated phenomena that constitutes the primary subject matter of this volume, it may be of interest at this point to note that the development of the consequences of the postulates of the Reciprocal System leads to a universe of the steady-state type, but one that differs from the current version in that it is cyclical. Thus there is no violation of the conservation laws by creation of matter ex nihilo. In this cyclical universe the products of the destruction of the galaxies that reach the age limit are the raw material from which the new galaxies are eventually constructed. The new development also overcomes the other major difficulties that face the steady-state theory in its present form. It provides for the complete removal of the oldest galaxies from the system, not merely disappearance “over the time horizon,” a concept that is subject to some serious criticisms, and it also provides the explanation of the recession of the galaxies that is required when the “big bang” is repudiated. Current steady-state theory suggests that the appearance of new matter creates a “push” that forces the older galaxies outward, but it is totally silent as to how such a push could be accomplished.

This is a serious weakness, as present-day theory is not even able to explain how one galaxy can exert a thrust against another, or how a fragment of a galaxy could be ejected. As pointed out in Chapter VI, the prevailing theories of the structure of galaxies provide no means whereby any kind of a “push” can be exerted against a stellar aggregate in which the constituent units are separated by distances on the order of light years. Consequently, the question as to the mechanism whereby ejection of galactic fragments takes place either has to be ignored or answered by means of some far-fetched ad hoc assumptions. Our finding that the stars in a galaxy or an independent cluster occupy equilibrium positions and that, as a result, the stellar aggregate has the general characteristics of a liquid now clarifies the situation and identifies the ejection mechanism.

Addition of any substantial amount of energy to the molecular motion in a liquid would, of course, result in converting a portion of the liquid to the gaseous state, a condition in which the molecules no longer maintain their original equilibrium positions but move independently and, if confined, exert a pressure on their container. The mechanism of the galactic explosion can readily be understood if it is realized that the effect of the explosion of a number of stars in the interior of the galactic aggregate is to create what we might call a bubble of “star gas,” a situation in which the stars that have absorbed energy from the explosion have left their equilibrium positions and are moving independently in the manner of gas particles, exerting a pressure on the portions of the galaxy that surround them.

At their equilibrium points the stars are moving outward at the speed of the recession (the speed of light) and at the same time moving inward gravitationally at the same speed. The energy imparted to them by the explosions therefore increases the outward speed to a level above the recession speed, and since speeds above unity are in time rather than in space, these stars move outward in time. The pressure that is built up against the overlying material is a pressure in time, and when this pressure reaches a high enough level it blows out a section of the overlying structure, just as an explosion in a building might throw a section of the wall out into the street. The ejected fragment is thrown outward in time, but by reason of the reciprocal relation between space and time this outward motion in time has a spatial equivalent, as pointed out earlier, and this spatial equivalent is the “quasar distance” that enters into the discussion. The energy imparted to the galactic fragment that becomes a quasar is, of course, shared between the motion of the individual stars within the fragment and the motion of the object as a whole. Indeed, a considerable portion of this energy is communicated to the constituent stars during the build-up of the explosion forces before the ejection actually takes place. We may deduce, therefore, that a substantial number of the stars in the quasar are individually moving at speeds in excess of the speed of light, and the quasar is consequently expanding in time, which means that it is contracting in equivalent space. Hence, like the white dwarfs, which are abnormally small stars, the quasars are abnormally small galaxies.

This is the peculiarity that has given them their name. They are “quasi-stellar” sources of radiation, mere points like the stars, rather than extended sources on the order of the normal galaxies. Some dimensions are beginning to emerge from recent measurements with the aid of special techniques, but this information merely confirms the fact that as galaxies they are extremely small objects. The most critical issue in the whole quasar situation, as seen in the context of current thought, is “the problem of understanding how quasars can radiate as much energy as galaxies while their diameters are some thousand times smaller.”³⁶

But this is not a unique problem; it is a replay of a record with which we are already familiar. We know that there is a class of stars, the white dwarfs, which radiate as much energy as ordinary stars while their diameters are some thousand times smaller. Now we find that there is a class of galaxies, the quasars, that has the same characteristics. All that is needed for an understanding is a recognition of the fact that these are phenomena of the same kind. It is true that the currently accepted theory of the small dimensions of the white dwarfs cannot be extended to the quasars, but the obvious conclusion from this fact is that current thought in this area is wrong. In the Reciprocal System of theory the abnormally small dimensions are due to the same cause in both cases. Ultra high speeds introduce displacement in time which has the effect of reducing the equivalent space occupied by the object in question. As pointed out earlier, the quasars might well be called white dwarf galaxies.

The brightness of the quasars, another of their special characteristics, is also a result of their abnormally small size. Because of the decrease in the amount of equivalent space occupied by the quasar, the spatial area from which its radiation originates is much smaller than that of a normal galaxy of equivalent mass. Although the underlying cause—the introduction of time displacement into the structure—is the same as that which is responsible for the brightness of the white dwarf stars, the mechanism is somewhat different. Stars radiate from their entire surface, and the relatively high rate of radiation of the white dwarfs per unit of surface area is due to a high surface temperature which, in turn, is an indirect result of the high density. In a galaxy the stars are so far apart that the total radiation from the galaxy is nearly equal to the sum of the radiations from the constituent stars. Here the concept of surface temperature has no meaning, and the brightness is not a temperature phenomenon but a result of concentration of more stars into a smaller equivalent volume.

Because of the diversity of the processes that are occurring in the quasars the frequencies of the emitted radiation extend over a wide range. As explained in previous publications, thermal and other processes affecting the linear motions of atoms generate radiation which is emitted principally at wavelengths relatively close to unit space (0.456×10^-5 cm), whereas processes such as radioactivity that alter the rotational motions of the atoms generate radiation that is mainly in wavelengths far distant from unit space. Explosions of stars or galaxies, especially the latter, cause readjustments of both the material and cosmic types, and hence these events generate both very long wave radiation (radio) and very short wave radiation (x-rays and gamma rays) as well as thermal and inverse thermal radiation. When the facilities for observation of the very short wave radiation have been improved to the level of the present radio facilities it should be possible to determine quite accurately just what is going on at any particular location by analyzing the radiation mix. In fact, some results of this kind are already possible on the basis of the optical and radio radiation alone, as will be demonstrated in Chapter X.

The question as to the origin of the large amount of energy radiated from the quasars has been a major problem ever since their discovery, but our finding that this radiation is distributed two-dimensionally rather than three-dimensionally simplifies the problem very materially. For example, if we find that we are receiving the same amount of radiation from a quasar as from a certain nearby star, and the quasar is a billion times as far away as the star, then if the quasar radiation is distributed over all three dimensions of space, as currently assumed, the quasar must be emitting a billion billion times as much energy as the star. But on the basis of the two-dimensional distribution that takes place in the theoretical universe of the Reciprocal System the quasar is only radiating a billion times as much energy as the star, and the problem of accounting for the energy production is simplified accordingly. Even in astronomy, where extremely large numbers are commonplace, a reduction of the energy requirements by a factor of a billion is very substantial. An object that radiates the energy of a billion billion (10¹⁸) stars is emitting a million times the energy of a giant elliptical galaxy, the largest aggregate of matter in the known universe (about 10¹² stars), and attempting to account for the production of such a colossal amount of energy is a hopeless task, as matters now stand. On the other hand, an object that radiates the energy of a billion (10⁹) stars is equivalent, from the energy standpoint, to no more than a rather small galaxy.

While the new theory is thus drastically scaling down the amount of energy to be accounted for, it is at the same time providing an immense source of energy to meet the reduced requirements. The disintegration of the atom at the upper destructive limit results in complete conversion of the atomic mass into energy, and inasmuch as the magnetic ionization of the matter of which a star is composed is uniform throughout the mass, because of the mobility of the charged neutrinos, the explosion of a star at the upper limit is theoretically able to convert the greater part of the mass of the star into energy. It should also be noted that the quasar is not called upon to provide its own initial supply of energy. The kinetic energy that accelerates both the quasar as a whole and its constituent stars to ultra high speeds is provided by the giant galaxy from which the quasar is ejected, and all that the quasar itself has to do is to meet the subsequent energy requirements.

A point that has given considerable trouble to those who have been attempting to put the observational data on the quasars into some coherent pattern is the existence of relatively large fluctuations in the output of radiation from some of these objects in relatively short times. This imposes some limits on the sizes of the regions from which the radiation is originating, and thereby complicates the already difficult problem of accounting for the magnitude of the energy being radiated. Additional study will be required before the mechanism of these variations is understood in detail, but the theoretical conclusions reached in the preceding paragraphs make some substantial contributions toward this end by (1) drastically reducing the energy requirements, (2) showing that the quasars are very small by reason of their inherent nature, (3) revealing that motions are taking place within the quasars at speeds in excess of the speed of light, and (4) identifying the primary source of energy as a large number of separate explosions in individual stars. Each of these items helps to simplify the problem of explaining the variations, and in total they should reduce this problem to manageable dimensions. It should be noted that item (4) is sufficient, in itself, to account for the existence of the variations.

One further property of the quasars that we will want to consider at this time, because it will enter into the quantitative development in the next chapter, is the effect of the explosion speed in causing change of position in space. Here the significant factor is gravitation. In the region of speeds below 1.00, the speed of light, the effect of gravitation on a material object is to alter the spatial speed, and

Table 1

	Galaxy	Quasar A	Quasar B	Quasar C
Observed redshift	0.050	0.832	1.081	1.560
Motion in space
Recession speed	1.000	1.000	1.000	1.000
Gravitational speed	0.950	0.950	0.919	0.840
Net redshift	0.050	0.050	0.081	0.160
Motion in equivalent space
Explosion speed		1.000	1.000	1.400
Gravitational speed		0.218	0	0
Net redshift		0.782	1.000	1.400

hence the spatial position, of that object. An object which, in the absence of gravitation, would move outward at unit speed by reason of the space-time progression is slowed down by gravitation to some lower speed 1.00-X. Column 1 of Table I shows the values of these speeds (in natural units) for a galaxy with redshift 0.050. This galaxy is carried outward by the recession (progression) at unit speed, but there is an inward gravitational speed of 0.950, and the resultant net spatial speed is 0.050, as indicated by the redshift.

Column 2 gives the corresponding data for Quasar A, a fragment recently ejected from the galaxy of column I. This quasar is subject to the normal recession, and to the gravitational motion in the dimension of the recession, in the same manner as the galaxy of origin, and its speed (redshift) includes a component 0.050, equal to the net outward speed of the galaxy. But the quasar also has an additional outward motion component, the motion generated by the explosion. Because this motion takes place at ultra high speed, the retardation by gravitation is overcome much more rapidly in the dimension of the quasar motion than in the dimension of the normal recession, and while the gravitational speed opposing the recession of Quasar A is still 0.950, that in opposition to the explosion speed is already down to 0.218. The net explosion speed is then 0.782. and the total redshift is 0.782 + 0.050 = 0.832.

Inasmuch as the motion generated by the explosion takes place in time it has no effect, in itself, on the spatial position of the moving object. However, gravitation does have a spatial effect, and where a portion of the explosion speed is applied to overcoming the speed due to gravitation, the elimination of this gravitational effect modifies the net spatial speed and thus changes the spatial position of the object involved. In the case of Quasar A, an amount 0.218 of the total explosion speed is required for this purpose, and the net effective outward speed is reduced by this amount, but in the process of neutralizing gravitation this 0.218 component changes the spatial position of the quasar (something that the net effective speed, which is in time, does not do). It can readily be seen that the spatial effect of this nature is at a maximum at the shorter distances, and it decreases as the quasar moves outward to more distant locations where gravitation is weaker. Thus we arrive at the rather surprising conclusion that the faster the quasar moves (as indicated by its redshift) the less spatial distance it travels.

Mathematical confirmation of a theoretical conclusion of this kind, one that is manifestly absurd on the basis of conventional theory, is highly significant. It does not necessarily establish the validity of the theory from which the conclusion was derived, as we cannot exclude the possibility that there may be other theories which lead to the same mathematical results, but it is positive proof that conventional theory is wrong in some essential respect. The mathematical verification of this conclusion with respect to the quasar motion that will be presented in Chapter IX, utilizing two independent lines of evidence, therefore strikes a devastating blow at the foundations of the prevailing concept of the nature of motion.

From the 3.5 z/2 relation between the quasar redshift and the redshift due to the normal recession we find that when the recession redshift reaches 0.081 the gravitational effect on the explosion speed is down to zero, and the excess quasar redshift is 1.00, as shown by the data for Quasar B, in column 3 of Table I. From this point on, the excess redshift of the quasar is the full equivalent of the motion in time. In the case of Quasar C, column 4, this amounts to 1.40. The absence of any gravitational effect beyond 1.00 excess redshift means that in this range the spatial speed of the quasar, relative to our location, is zero, and as we see the situation, it remains at its point of origin until the limiting 0.326 recession speed is reached. From probability considerations we can deduce that half of these spatially motionless objects will appear in front of the galaxy of origin. In this position the radiation of the quasar will overpower that of the galaxy, and the quasar will appear to be alone. The other half will be behind the heavily populated galactic centers from which, according to theory, they originate, and in this case the quasar radiation will be absorbed and reradiated.

As a consequence of this occlusion, the number of quasars beyond 1.00 excess redshift should be only half that which would be expected on the basis of the relation of number to distance at the lower redshift levels. Observational data confirming this point will be included with the quantitative material that will be presented in Chapter IX. Another observable consequence should be the existence of a class of galaxies in which the nuclear regions are abnormally bright by reason of the reradiated quasar emission. We can expect to find a few such objects even where the quasars do have a small motion in space, as a certain proportion of them will be moving radially outward merely by chance. Most of the galaxies that are occluding quasars should, however, appear between the 1.00 level, where spatial motion ceases, and the 2.00 level, beyond which the quasar disappears. The corresponding recession redshifts are 0.08 and 0.326, and the theoretical objects of this class should therefore appear only in the range between these two values, except for the few chance coincidences not far below 0.08.

An observed class of galaxies, the so-called N type, fits the foregoing description, and can tentatively be identified with the theoretical associates of the occluded quasars.³⁷ These N-type galaxies have the kind of abnormally bright nuclei that theoretically result from reradiating the energy received from the quasar, and have been given the “N” designation for this reason. Their spectral characteristics have many points of similarity to those of the quasars; they are distributed throughout the range of redshifts from 0.08 to 0.326 in which they should theoretically occur, with none over 0.326 and only a few at distances shorter than 0.08; and the number of such galaxies thus far identified is consistent, when due allowance is made for their lower visibility, with the number of quasars missing because of the change in the relation of number to distance above 1.00 excess redshift. While these points are by no means conclusive, they add up to a rather strong suggestion that the N galaxies should be identified with the galaxies that are theoretically occluding the missing quasars.

In any event, regardless of the specific manner in which the N type galaxies fit into the general picture, they are undoubtedly related to the quasars in some manner. The fact that the most distant N galaxy now known has a redshift of 0.306 is therefore highly significant. Galaxies can be, and have been, located at greater distances, and in view of the intensive search that has been made for objects with quasar-like characteristics it is quite probable that the failure to observe any N-type galaxies at distances beyond 0.306 is due to the existence of a distance limit somewhere in this vicinity. This, of course, is right in line with the theoretical conclusion that the spatial distance limit for all objects with quasar characteristics, including the quasars themselves, is 0.326.