It is generally conceded by those who are in close touch with the situation along the frontiers of physical knowledge that the existing body of physical theory is far from satisfactory. As expressed by Richard Feynman:
Today our theories of physics, the laws of physics, are a multitude of different parts and pieces that do not fit together very well… . We have all these nice principles and known facts, but we are in some kind of trouble.7
Now, why are we in trouble? The truth is that the root of the difficulty is quite generally recognized by those who are on the firing line. The principal obstacle that stands in the way of constructing a more adequate theory of the physical universe is that modern science has not been able to determine just what kind of a thing it is dealing with. Before we can construct an accurate theory of anything we must have at least a reasonably good idea as to the nature of the thing about which we are theorizing. This, physical science does not now have.
For the first hundred thousand years or so of the existence of the human race, the prevailing concept was that of a universe of spirits. The ultimate realities, according to this point of view, are not the physical objects but the demons and spirits that inhabit and control those objects. This “spirit” concept is not entirely dead even today, but the ancient Greeks arrived at a realization that it was not adequate to deal with the new knowledge that they were accumulating in their pioneer efforts along the line of what we now call science, and they initiated a change in thinking that ultimately resulted in the replacement of the concept of a universe of spirits by the concept of a universe of matter: a universe in which the basic entities are elementary particles of matter existing in a setting or background provided by space and time. This is the concept that underlies all of our present-day physical science.
Science was engaged in sketching, bit by bit, the plan of a machine—a gigantic machine identical with the universe. According to the vision thus unfolded, every existing thing was matter, and every piece of matter was a working part of the cosmic technology. (Jacques Barzun)8
Today we are back in the same kind of a situation that confronted Aristotle and his contemporaries. The prevailing concept of the nature of the universe has broken down. Although the fact is not yet generally recognized, mainly because no one wants to face the issue, the “matter” concept of the universe has been completely demolished by the modern discovery that matter can be transformed into non-matter, and vice versa. In the “annihilation” reaction between the electron and the positron, for example, these two particles, which are recognized as material, inasmuch as they possess mass and other material properties, are completely converted into radiation, which is not matter. Obviously, the demonstrated interconvertibility of matter and non-matter is conclusive proof that matter is not basic. There must be some common denominator underlying both matter and non-matter. However reluctant scientists may be to part with it, the concept of a universe of matter is no longer tenable, and sooner or later it will have to be abandoned, along with those portions of existing theory that are wholly dependent on this concept.
Since we are in trouble, and we know why, the next question that arises is: What are we going to do about it? What can be put in the place of this erroneous concept of a universe of matter? Oddly enough, the most likely answer to this question has been known for centuries. It has long been realized that some very substantial advantages would accrue from replacing the “matter” concept with the concept of a universe of motion: one in which the basic entities are units of motion rather than units of matter.
As so many previous investigators have observed, a physical theory based on the “motion” concept could be comprehensive; that is, it could embrace such items as radiation and electrical phenomena which are an acute embarrassment for the present-day “matter” theories, inasmuch as they are neither matter nor part of the background in which matter is presumed to exist. Furthermore, a theory based on the “motion” concept could account for the behavior of physical entities as well as for their existence. When we formulate a theory or a set of theories to explain the existence of such entities on the “matter” basis, we must construct another set of theories to explain how they behave, but a theory based on the “motion” concept can explain not only what these entities are but also what they do. It is beginning to be suspected that modern physical discoveries will force the development of comprehensive theories of this nature. K. W. Ford makes this comment:
There are some new hints that open up one of the most challenging prospects in modern physics, hints that perhaps we are approaching a merger of the description of events and the description of things—that the theory of the behavior of the particles and the theory of the structure and nature of the particles may prove to be one and the same thing.9
The “motion” concept can give us this kind of a merger; the present “matter” concept cannot. Then, too, the “motion” concept brings us appreciably closer to an ultimate understanding of the physical universe. If we postulate a universe of matter, we are immediately confronted with the question, What is matter?, a question that has never been fully or satisfactorily answered. But we think that we have an intuitive understanding of what motion is.
So we are in trouble, we know why, and we know the most promising way out of our difficulties. Why, then, is there no available structure of theory based on the “motion” concept? The answer is that hundreds of years of painstaking effort by competent scientists and philosophers—such men as Eddington, Hobbes, and Descartes, as well as a multitude of less prominent individuals—have been unsuccessful, and no workable theory of a universe of motion has heretofore been constructed. These previous investigators have started with the fundamental premise of the “motion” concept, the premise that we live in a universe of motion—“all things have but one universal cause, which is motion,” says Hobbes unequivocally—and have attempted to build upon this foundation, but they have invariably encountered an obstacle which they have been unable to surmount, or even to identify, and their most strenuous efforts have been fruitless.
The key that finally opened the door to the construction of an accurate and comprehensive physical theory based on the “motion” concept was the identification of the obstacle that blocked the efforts of these previous investigators. The reason why they all arrived at a dead end before they advanced very far, we now find, is that they all failed to realize that switching from a universe of matter to a universe of motion requires a change in the definition of space and time. The usual definition of matter, as employed in present-day physical science, does not define space and time. Consequently, when we specify that matter is the basic constituent of the universe we must define space and time independently. This is what has been done. In the absence of any factual information on the subject, some assumptions have been made, based mostly on the impressions of space and time gained from casual observation, and the definitions have been set up accordingly. There is much difference of opinion regarding the details, particularly with respect to space—whether or not space is absolute and immovable, whether such a thing as empty space is possible, whether space and time are interconnected, and so on—but the essential thought has remained the same: space and time, as seen by scientists and laymen alike, are the setting or background in which physical phenomena take place.
While fields and particles come and go, space and time lie inert, providing the stage upon which the actors play their roles. (K. W. Ford)10
But when we specify that the basic constituent of the universe is motion, we can no longer set up independent definitions of space and time in this manner, because in defining motion we are also, at the same time and by the same act, defining space and time. Motion is defined as a relation between space and time, and is measured as speed or velocity, the mathematical expression of that relation. The equation of motion in its simplest form is v = s/t. As can be seen from this equation, the standard definition of motion in terms of space and time is also a definition of space and time in terms of motion; that is, in motion, space and time are the two reciprocal aspects of that motion, and nothing else.
In a universe of matter, the fact that space and time have only this limited significance with respect to motion does not preclude them from possessing other aspects in connection with phenomena of a different character, as present-day theory assumes that they do. But in a universe of motion, where all physical entities and phenomena are manifestations of motion, the role of space and time in motion is their role in the universe as a whole. Since there is nothing but motion, they cannot have any properties or any significance that they do not have in motion. In particular, they cannot constitute a setting or background for motion, because motion is not a background for itself. Everywhere in a universe of motion, space and time are the two reciprocal aspects of that motion, and they have no other significance anywhere.
This is where the previous investigators made the mistake that prevented them from accomplishing their objectives. To Eddington and the other early adherents of the “motion” concept, the units of motion that would take the place of particles of matter as the ultimate constituents of the universe would still be located in the same kind of a space-time framework that formed the background for the hypothetical universe of matter, and they were unable to see that this is incompatible with their definition of motion. It is interesting to note that some of these investigators did actually reach the point of realizing that the conventional views of the relations between space, time, and motion would have to be modified. Eddington‘s views were influenced rather strongly by those of one of his predecessors, W. K. Clifford, and he noted that “Clifford was convinced that matter and the motion of matter were aspects of space-curvature and nothing more.” Here we see a recognition of the fact that going to the concept of a universe of motion requires a direct and intimate connection between space, time, and motion rather than the independence that exists in the “matter” universe, but Clifford and Eddington were still unable to get entirely away from the concept of space as a container or setting for physical events—something that could be “curved.”
When we finally do make a clean break with the “matter” concept, and accept the definition of space and time that is required by the concept of a universe of motion, the first consequence that we note is that on the basis of this “motion” concept there is a general reciprocal relation between space and time. Here is an idea that is manifestly absurd in the context of the prevailing pattern of thought. In the light of currently accepted views of the nature of things, the reciprocal of space is simply inconceivable. But the truth is that these accepted views are simply creatures of the “matter” concept. When it is postulated that the ultimate constituents of the universe are “elementary units” of matter, then there must be a setting or framework in which this matter exists, and it has been assumed that space and time constitute such a framework. Current ideas as to the nature of space and time are thus dictated by the prevailing concept of the kind of a universe with which we are dealing. When we replace the “matter” concept with the concept of a universe of motion, and as a consequence find that we must redefine space and time as simply the two reciprocal aspects of motion, that which was previously inconceivable now becomes inevitable. In speed, the measure of motion, more space is the equivalent of less time and vice versa.
Furthermore, this is not merely a mathematical relation; it is a general relation. The equation v = s/t, which says that the speed is equal to space divided by time, could equally well be written in the reciprocal form, which would assert that the reciprocal speed is equal to time divided by space. Either of these two forms is equally as valid a representation of the relationship as the other—there is nothing in the definition of motion that can distinguish between the two—and it is thus evident that space and time are similar entities, differing only in that they stand in a reciprocal relation to each other. Any property that may apply to one likewise applies, in the reciprocal form, to the other.
At first glance, this statement may seem to be a direct contradiction of experience, as the observed properties of space do not resemble the observed properties of time at all. But we will find as we proceed with the theoretical development that these differences in the way in which space and time appear under observation are not due to any actual dissimilarity between the two, but are a result of our particular position in the universe, which gives us a different view of one than of the other. For example, time appears to be essentially a progression, whereas space seems to “stay put,” but we will find that our view of space is distorted by our special position, and that space actually progresses in the same manner as time.
Likewise, we recognize three dimensions of space, but time appears to be one-dimensional: a linear progression from the past to the present and on into the future. This view of time seems to be confirmed by the equations of motion, such as v = s/t, in which s is a vector quantity while t is a scalar quantity. But the one-dimensionality does not, in fact, follow from the scalar character of the term. What current thought has overlooked is that speed or velocity in the context of present-day usage always refers to speed or velocity in space (the existence of motion in time is not recognized at all) , and the equations as ordinarily expressed are therefore space velocity equations. In such an equation any term representing time is necessarily scalar, irrespective of how many dimensions time may have, inasmuch as time has no spatial dimensions. Whatever dimensions it has are dimensions of time, not dimensions of space. The scalar nature of the time term thus has no implications with respect to the dimensions of time. The fact that we are able to observe only one time dimension likewise does not preclude the existence of other dimensions that are not directly observable.
We are thus on sound ground in postulating that motion is three dimensional. This is the first of a few assumptions that we will have to make about the properties of space and time, in their capacity as aspects of motion, in order to complete the foundations for a general physical theory based on the concept of a universe of motion. Only one more physical assumption is required: the assumption that motion, and hence space and time, exist only in discrete units. As already pointed out, the “motion” concept itself establishes a reciprocal relation between space and time. Together with three assumptions as to the mathematical behavior of the universe, the foregoing items constitute the Fundamental Postulates of the new system of theory, the Reciprocal System, as it has been named, because of the key position of the reciprocal space-time relation in the theoretical structure.
From these postulates as premises, the entire structure of theory has been developed deductively, without introducing any further assumptions of any kind, and without the use of any information derived from observation. In the case of the objects that are the principal subjects of the discussion in this present volume, the quasars and the pulsars, both the existence and the properties of these objects have been derived theoretically from the postulated properties of space and time, and from these properties only, without resort to assistance from any other source. The postulates may be expressed as follows:
First Fundamental Postulate: The physical universe is composed entirely of one component, motion, existing in three dimensions, in discrete units, and with two reciprocal aspects, space and time.
Second Fundamental Postulate: The physical universe conforms to the relations of ordinary commutative mathematics, its magnitudes are absolute, and its geometry is Euclidean.
The objective of the presentation in the pages that follow will be to demonstrate that the quasars, the pulsars, and the astronomical phenomena with which they are associated are implicit in these postulates.
From the very first, a question has existed as to the terminology in which the postulates should be expressed; specifically, whether the basic constituent of the universe should be called “space-time” or “motion.” The original conclusion, as stated in New Light on Space and Time, was in favor of using the term “space-time”:
It seems advisable to select those terms which will be most understandable in the context of existing thought and which will facilitate explaining the new theoretical structure to individuals who are familiar with previously accepted ideas. We will therefore say that the universe has only one component, and for the present, we will call this component space-time, with the understanding that this term is equivalent to motion, when motion is taken in the most general sense.
In the meantime, additional experience, both in the clarification of the details of the theory, and in the presentation of the theory to college audiences, has indicated the desirability of laying more emphasis on motion, and the wording of the First Postulate has been changed accordingly. No change in the substance of the postulate is involved.
One of the factors that enters into this situation is a widespread inability to conceive of the existence of motion which is not motion of anything, the kind of basic motion that is synonymous with space-time. A major reason for reversing the original decision with respect to terminology and replacing “space-time” with “motion” is that it is absolutely essential, for an understanding of the theoretical development, to recognize that the relation between space and time that is represented by the expression “space-time” is a motion, not, as current theory assumes, some kind of a super-space in which time plays a quasi-spatial role. Any relation between space and time is motion.
Many individuals are very emphatic in the assertion that motion is necessarily motion of something, and that anything else is impossible. But those who are so positive on this score are laying down a principle that is valid only in application to a universe of matter, and has no place in a universe of motion. If the basic entities of the universe are material “things,” and motion is a property of those “things” then, of course, the objectors are correct; matter is logically prior to motion, and there can be no motion that is not motion of something. But if this is a universe of motion, in which matter is a complex of motions, then motion is logically prior to matter, and there must be simple motions before there can be matter or motion of matter. Hence the existence of these simple motions is not only logical but essential in a universe of motion. It should be noted, in this connection, that the mathematics of motion of matter are equally applicable to the simple motions, since an equation such as v = s/t has no term representing the “something” even if it refers to a motion of something.
Many other features of the new theoretical system will no doubt seem strange, perhaps even incredible, on first consideration, but it should be realized that this initial reaction is a result of trying to fit the new ideas into the pattern of existing thought, a pattern that is based on the “matter” concept, whereas in order to arrive at an understanding of the theory it is necessary to view each of the details in the context of the “motion” concept. This will require a certain amount of mental reorientation, to be sure, but it is hardly possible to make a significant advance in physical understanding without upsetting some previous beliefs, and the greater the advance the more dislocation of existing thought will be required.
It should also be realized that the development described herein is unprecedented in that it is wholly theoretical. All previous physical laws and theories are composite structures that include empirical as well as purely theoretical elements. The theorist begins with observed facts, and the nature of his activities has been described in this manner:
Faced with the facts of physical observation and experiment, the theoretical physicist applies the abstract relationships of mathematics to connect these facts and predict new facts.12
The “matter” that enters into Newton‘s law of gravitation is one of these “facts of physical observation,” not a theoretically defined entity. It is the matter that is actually encountered in the physical world, an entity whose precise nature is still a subject of considerable difference of opinion. Similarly, the photon of light that enters into the theory of the photoelectric effect and various optical relations is not a theoretically defined entity; it is an observed phenomenon whose real nature is understood only vaguely. This mingling of theory and observation cannot be avoided as long as physical science is still in the stage where a great many observed phenomena must be treated as unanalyzable, and hence it has come to be regarded as a characteristic of all theories. It is important to note, therefore, that the Reciprocal System is not a composite theory of the usual type; it is a purely theoretical structure that includes nothing of an empirical nature.
For example, the “space” with which this system deals is not physical space; it is theoretical space. Of course, the exact correspondence between the theoretical and observed universes that will be demonstrated in the course of the development means that the theoretical space is a true and accurate representation of the actual physical space, but it is important to realize that what we are dealing with in the development of theory is the theoretical entity, not the physical entity. The significance of this point is that while physical “space,” like “matter” and other physical items, cannot be defined with precision and certainty, as there can be no assurance that our observations give us the complete picture, we do know exactly what we are dealing with when we talk about theoretical space. Here, there is no uncertainty whatever. Theoretical space is just what we have defined it to be—no more, no less.
The same is true of all of the items that enter into the subsequent theoretical development. Inasmuch as the basic elements of the theoretical system are explicitly defined, and their consequences are deduced by sound logical and mathematical processes, the conclusions that are reached are unequivocal. Of course, there is always a possibility that some error may have been made in the chain of deductions, particularly if it is a very long chain, but aside from this possibility, which is at a minimum in the early stages of the development, there is no question as to the true nature and characteristics of any theoretical entity or phenomenon that emerges.
Unlike Newton, who was unable to determine why the matter that he observed conformed to the gravitational law that he formulated, we know exactly why our theoretical atom of matter gravitates. There is no doubt as to either the structure or the properties of this theoretical atom, because both are consequences that we are able to derive from our basic assumptions as to the properties of space and time. Such certainty is impossible in the case of any theory that contains empirical elements. The currently popular theory of the atom has undergone a long series of changes since the time that it was first formulated by Bohr and Rutherford, and there is no assurance that the modifications are at an end. On the contrary, a general recognition of the weaknesses of the theory as it now stands has stimulated an intensive search for ways and means of bringing it into a closer correspondence with reality, and current literature is full of proposals for revision
Theories of this kind are particularly vulnerable to what we may call involuntary changes, modifications that are not initiated by efforts to improve the theory, but are forced by reason of new experimental or observational discoveries. The purely theoretical Reciprocal System, on the other hand, contains no empirical elements, and it is therefore unaffected by any change in empirical knowledge. This is a point that should be clearly understood before any attempt is made to follow the development of theory in the subsequent pages. The theory therein described is a single integrated unit that stands or falls as a whole. It is not subject to any change or adjustment, other than the correction of any errors that have been made, and addition of new items due to the extension of the theory into other areas. Once the postulates have been stated, the entire character of the resulting theoretical universe has been defined, down to the most minute detail.
Just because of the postulated properties of space and time a theoretical entity that has the same properties as the observed entity known as matter must exist, and this theoretical matter must exist in the form of atoms. Because of the postulated properties of space and time there must be different kinds of atoms, and these different kinds must form a series in which each member, or element, differs from the one preceding by a single unit of motion. Because of the postulated properties of space and time the theoretical elements must have certain characteristics that divide the series into groups. Because of the postulated properties of space and time each theoretical element must have certain physical properties, the magnitudes of which are characteristic of the particular element and can be calculated from the basic factors that apply to each element by virtue of its position in the atomic series and group. Because of the postulated properties of space and time each theoretical element must be able to combine in certain specific ways with certain other elements, and these theoretical combinations, or compounds, must have specific properties of the same nature as those appertaining to the individual elements, and capable of being calculated in a similar manner.
For the purposes of this present volume it will not be necessary to carry the discussion of matter and its properties beyond the point of establishing the nature of the atomic structure and the limitations to which it is subject. Similarly, our consideration of other physical areas—radiation, electrical and magnetic phenomena, radioactivity, etc: will be limited to those issues that have a direct bearing on the specific objective of this work, but it should be understood that in each of these areas the development of the consequences of the postulated properties of space and time produces an exact theoretical counterpart of the observed pattern of phenomena in the area, just as it does in the case of the properties of matter.
Furthermore, the theoretical behavior of large aggregates of matter is determined by these same basic postulates. The postulated properties of space and time account for the existence of theoretical stars, star clusters, and galaxies, for theoretical pulsars and quasars, and for the interrelations between these and other features of the theoretical astronomical universe. The same properties of space and time that determine the structure of the smallest theoretical atom also determine the structure of the largest theoretical galaxy. Thus there is no leeway for adjustment or modification anywhere in the system. The theoretical universe, all the way from atom to galaxy and from photon to quasar, is specifically defined by the basic postulates.
Of course, if this theoretical universe were only a completely integrated, self-consistent theoretical system, and nothing more than this, it would be merely an interesting intellectual exercise, similar to some of the more abstruse systems of mathematics or geometry that have engaged the attention of the mathematicians in recent years. But there is one very important fact that gives the theoretical universe an altogether different significance. The features of this universe derived from theory have been checked against the corresponding features of the observed physical universe in thousands of separate cases in many different physical fields, and in no instance has there been any conflict. Wherever sufficient observational or experimental information has been available to enable a meaningful comparison to be made, there has been agreement, or at least no inconsistency. In total, these comparisons have been numerous enough and diversified enough to reduce the probability of a conflict between the two systems in any respect to a negligible level, thereby justifying the assertion that the theoretical universe of the Reciprocal System is a true and accurate representation of the actual physical universe.
Because of their semi-empirical nature, the general run of physical theories cannot be used with any degree of confidence outside the range for which they have been specifically verified. Extrapolation into other areas may give the right results, or it may not; it is always risky. Thus the area of coverage of these theories is essentially coextensive with the range of the observational facilities. The big advantage of an accurate and potentially complete picture of the universe such as that supplied by the Reciprocal System is that it is not subject to these limitations. This theoretical picture not only gives us a clear view of those situations in which the observational data are inadequate and confusing—particle physics, for example—but also reveals the existence of significant features of the universe, such as the progression of space, that have not hitherto been recognized at all.
Much of what the new theoretical system has to offer is still a potentiality rather than a finished product. The answers that it is capable of furnishing do not come automatically; tracing out the detailed consequences of the basic postulates requires a great deal of careful and painstaking work, and a long period of investigation and study lies ahead. But because the theoretical development is completely independent of any data from observation, the theoretical conclusions regarding the areas that are observationally unknown, or only partially known, can be just as accurate as those that reflect well-known phenomena. This can appropriately be compared to the coverage of an aerial map, which portrays the geographical features of an area inaccessible to surface exploration just as accurately as the features of the accessible areas. Absence of the limitations to which observations are subject is especially significant when we undertake to examine the theoretical status of such objects as quasars and pulsars.