From the standpoint of our accustomed habits of thought, one of the most surprising of the conclusions that were derived by the extrapolation process in Chapter IV is that of a progression of space. The somewhat intuitive impression that we gain from our everyday experience—an impression that has been accepted and formalized by present-day physical science—is that space is an entity that “stays put,” whereas time is an entity that progresses. But now the postulate derived from an extrapolation of the observed space-time relation tells us that space also progresses in exactly the same manner as time.
The origin of the progression is evident as soon as the reciprocal postulate is formulated. If space and time are reciprocally related, then a single unit of space is equivalent to a single unit of time, from the scalar space-time standpoint. When the passage of one additional unit of time causes point A to move forward to A + 1 in time, the equivalence of the unit of time and the unit of space means that point A has also moved forward one additional unit of space, to point A + 1 in space.
The general nature of the progression is not as obvious. Our rather vague psychological impression of the passage of time suggests a unidirectional movement, from the past and toward the future—the River of Time, as it is so often called. But now that we recognize both space and time as progressing, we have an opportunity to see the progression in a much clearer light. As pointed out in Chapter IV, the recession of the distant galaxies is clearly due to the space-time progression, and this phenomenon therefore gives us a visible illustration of the nature of the progression of space and, by extension, the nature of the corresponding progression of time. It is not difficult to get a clear mental picture of the observed situation in which the galaxies are moving directly outward from us in all directions, and we need only to imagine this recession taking place at the velocity of light—which it undoubtedly does somewhere beyond our present observational range—in order to get an understanding of how the locations in space are continually moving away from the location which we happen to occupy.
The corollary to this proposition, the fact that we are likewise moving away from all other galaxies in the same manner and that the location which our galaxy occupies is moving outward in all directions away from all other spatial locations, is somewhat harder to visualize. It is not easy to conceive of motion taking place in all directions simultaneously. But unless we wish to take the position that our galaxy alone, among all of the billions within observational range, occupies a fixed position—a rather fantastic contention—our galaxy must be moving away from all others, and hence must be moving in all directions. A motion in all directions has no specific direction; that is, such a motion is scalar. The movement is simply from A to A + 1 and on to A + n, both in space and in time. To illustrate this phenomenon the astronomers commonly utilize the example of points on the surface of a balloon, which is being inflated. As the inflation proceeds, the distances between the points gradually increase; that is, each point moves away from all other points, and thus moves outward in all directions simultaneously. By visualizing a similar situation in three dimensions we can obtain a mental picture of the recession of the galaxies and of the progression of space which causes the galactic recession.
If we now recognize that time is subject to exactly the same kind of a progression as space, we can get a new concept to replace the familiar idea of a “River of Time” flowing past us unidirectionally. Instead of a river, we should visualize the equivalent of an expanding balloon. Each point in time moves outward from all other points just as each point in the three-dimensional space occupied by the balloon moves outward from all other points. But we should keep in mind that the balloon is an incomplete analogy. The progression of time is different in one important respect: it does not take place in space; it takes place in time. Each location in time is continually moving outward away from all other locations in time.
An important consequence of the progression of space-time is that unit velocity, one unit of space per unit of time, is the condition of rest in the physical universe, the datum from which all activity begins. We are so accustomed to measuring from the mathematical zero that this concept of a finite velocity as the neutral condition will no doubt seem odd on first consideration, but it is not without precedent. There are other physical situations in which the neutral point is at some finite value with meaningful deviations in both directions. For example, there is the hydrogen ion concentration, measured on the pH scale. If we are concerned about alkalinity and we find that two solutions have pH values of 7 and 8 respectively, it might appear to the uninitiated that one solution is slightly less alkaline than the other. The truth is, of course, that the solution with the 7 pH is not alkaline at all, as 7 is the neutral value. This is not an arbitrary point, like the zero on the Centigrade temperature scale; the pH is mathematically related to the actual hydrogen ion concentration, and hence represents an actual physical reality. Unit velocity is a neutral value of the same nature: a true physical datum with a finite magnitude.
In this neutral condition, each unit of space is exactly like all other units of space and each unit of space is equivalent to a unit of time that is exactly like all other units of time. A unit of elapsed time, a unit movement in time, is equivalent to a unit movement in space, hence all locations in space-time are moving away from all other locations at unit velocity. Since space-time is motion, in the most general sense of that term, its measure is speed or, as this speed manifests itself in a spatial or temporal reference system, velocity. Just as we measure space in centimeters, or some similar unit, and time in seconds, we measure space-time in centimeters per second—in velocity terms. Unit velocity is not only the measure of the progression of space-time; it is the measure of space-time itself. Space-time is a motion: a progression. Aside from this ceaseless progression, a universe in the neutral condition would be one vast domain of perfect uniformity in which nothing ever happens and nothing could happen.
In order that there may be events or phenomena in the universe—anything other than the uniform and featureless progression—there must be a deviation from unity: a displacement of space-time from the unit level. There cannot be any such deviation in the space-time velocity, since the equivalence of a single unit of time and a single unit of space holds good for any number of units or any combination of units. The space velocity or the analogous quantity in time may, however, experience displacement because of the directional effects that pertain to space and time individually. If the space direction of the progression, for example, reverses at the end of a unit, the progression of space-time is not affected, since space-time is scalar and has no directional characteristics, but the progression of space now moves back over the same space unit which it just traversed.
On first consideration it may be hard to understand how an object which is moving directly away from us can reverse its direction of motion and still continue moving directly away from us. We realize, however, that inasmuch as the distant galaxies are all moving directly away from us, we must be moving directly away from all of them. Our galaxy M is therefore moving away from galaxy A in the direction AM, whereas it is also moving in the opposite direction BM directly away from some galaxy B which is diametrically opposite to A in our field of vision. It is quite possible, then, for some object to have a motion coinciding with the recession of our galaxy in the direction AM, and then to reverse this spatial direction and move in unison with the recession of our galaxy in the direction BM.
The important point here is that the recession of our galaxy in the direction AM moves the galaxy outward in space away from all other galaxies. Consequently any object whose motion coincides with that of the galaxy is also moving outward away from the distant galaxies; that is, it is moving outward from all other locations in space. But exactly the same thing can be said of any object whose motion coincides with that of the galaxy in the opposite direction BM. This object is also moving outward away from all other locations is space.
The scalar direction of any motion, the inward or outward direction toward or away from all other locations, is thus independent of the spatial direction. In the example we have been discussing, motion in the direction AM may be either inward or outward, from the scalar standpoint. The same is true of motion in the direction BM. This explains how the space-time progression which, in our region of the universe, always proceeds outward, can, under appropriate circumstances, reverse its spatial direction.
No special mechanism is necessary in order to accomplish this reversal. The reciprocal postulate requires the existence of aggregations of n units of space (or time) in association with single units of time (or space) and, as indicated in the foregoing discussion, a change of spatial direction (or temporal direction) is the only means by which such associations can be formed. Deviations from the normal one to one space-time ratio—displacements of space-time, as they are called in this work—therefore must exist, and directional changes must take place wherever such displacements occur.
A directional reversal of this kind is an event—a physical occurrence—and it takes place at a specific spatial or temporal location. All such locations are subject to the progression; that is, a space-time location is a thing in motion. The reversed motion thus becomes detached from the general space-time structure and is carried along by the progression in a direction perpendicular to the direction of the original motion. It now becomes a physical entity: an independent phenomenon pursuing its own course and having a space velocity of its own, the magnitude of which is determined by the relative frequency of reversals of space direction and time direction. Space progresses n units while time progresses m units, and the space velocity is therefore n/m in this particular phenomenon.
Although we have been dealing only with reversals thus far, it will be noted that in making some of the general statements in the preceding paragraphs it was necessary to use the term “change” rather than “reversal” of direction. The reason is that there is no requirement of an immediate reversal. A gradual change of direction by means of a rotational movement will accomplish the same result. However, a direct generation of rotation from the neutral condition, in which nothing exists but the uniform progression of space-time, is impossible simply because there is nothing to rotate. The first effect of a displacement applied to the neutral situation is therefore to cause vibrational motion. The vibrating unit then progresses translationally as has been explained. When this vibrating unit is viewed from a reference system that does not progress, the combination of an oscillation in one dimension with a unidirectional progression in a perpendicular dimension takes the form of a sine curve.
If a number of such oscillating units are generated at the same space-time location—that is, are generated simultaneously at the same space location—their unidirectional progression always takes place in the outward scalar direction, but outward from the scalar standpoint is indeterminate from the standpoint of spatial direction, and the progression of any individual unit can therefore take any spatial direction. Since all directions are equally probable, the mathematical principles of probability, whose validity was assumed as a part of the Second Fundamental Postulate, tell us that the individual progressions of the units will be distributed equally over all spatial directions. The first phenomenon that we develop from the Fundamental Postulates is therefore one in which oscillating space-time units originate at various locations in space-time and move outward in all directions from these locations at unit velocity, one unit of space per unit of time.
The various entities that emerge as constituents of the theoretical RS universe as the development proceeds will, of course, appear without labels, but it will not usually be difficult to identify the corresponding feature of the observed physical universe. In this case it is obvious that the oscillating units which we have been describing are photons of light or other electromagnetic radiation. The process of emission and movement of these photons is known as radiation, the space-time ratio of the oscillation is the frequency of the radiation, and unit velocity is the velocity of electromagnetic radiation or, as it is more commonly termed, the velocity of light, customarily represented by the symbol c.
Here, then, is the first of those Outstanding Achievements of the Reciprocal System, which deserve special emphasis. The foregoing description of the nature of the photon furnishes a complete and logical explanation of the seemingly paradoxical behavior of radiation in which it sometimes acts as a particle and sometimes as a wave—one of the most baffling enigmas of modern physics: “the vexed antinomy of ’corpuscles versus waves’ which contemporary physics faces and which the term “complementarily” merely hides without removing,”78 as Capek describes it. The photon acts as a particle in emission and absorption because it is a single independent unit; it travels as a wave because the combination of a linear oscillation and a translatory movement in a perpendicular direction produces a wave-like motion.
One of the most significant features of the Reciprocal System is that the explanations, which it produces for basic physical phenomena, are extremely simple. Instead of explaining why seemingly complicated phenomena are complex and perplexing, this system removes the complexity and reduces the phenomena to simple terms. The space-time progression and the galactic recession, which it produces, occur because one unit of space is equivalent to one unit of time. The photon originates by a periodic reversal of the direction of one of the components of space-time. Both of these are about as simple as any physical explanation can be. Now we find that the answer to the seemingly insoluble wave-particle problem is equally simple. To the question: Is the photon a wave, a particle, some hybrid that could be called a “wavicle“, or is it one of the ghostly denizens of the half-world of the quantum theories?, we are able to reply: The photon is a particle (that is, a discrete physical entity) which travels as a wave. On this basis the reason why radiation can have wave-like properties such as that of polarization even though it consists of discrete particles is obvious.
The same simple explanation of the nature of the photon can also be credited with Outstanding Achievement Number Two: the answer to the problem of how the energy of radiation is transmitted from one object to another distant object without any connecting medium between the two. Such answers must be innovations; if they could be obtained from existing lines of thought there would be no problems. Furthermore, if they are to be simple answers to problems of long standing, they must have some rather surprising aspects, as it is not at all likely that answers within the bounds of accepted thinking would have remained hidden so long, particularly in view of all of the effort that has been applied to searching for them. In the case of the wave-particle problem, no one has previously realized that the photon, as observed, might be more than a photon; that is, it might be a photon in conjunction with something else. But as soon as we look at the situation in this light, it is apparent that we have arrived at a simple solution of the difficulty.
The innovation that solves the problem of how radiation is transmitted through empty space is one of an even more surprising character. The answer here is that radiation is not transmitted at all. The photon remains permanently in the same space-time location in which it originates, but space-time itself progresses, carrying the photon with it, and the photon is therefore able to act on any objects which are not carried along by the progression and which are therefore encountered en route. For an explanation of the nature of these objects, let us now return to the subject of rotation.
Once the photon has come into being, the previous obstacle to the existence of rotational motion has been eliminated, since there is now an “object” that can rotate, and our next step in the development of the theoretical RS universe will be to examine the characteristics of this rotation. First, let us bear in mind that the photon, the object which we are going to rotate, is itself a motion, so that when we rotate the photon what we are actually doing is generating a compound motion. We cannot do this by simple addition, as a total magnitude exceeding that of the progression would result in a directional reversal, and would give rise to vibration rather than rotation. The photon can, however, rotate in the opposite scalar direction or, strictly speaking, since rotation has no meaning from a scalar standpoint, it can rotate in space or time in such a manner that the corresponding space-time movement is in the scalar direction opposite to that of the progression. Inasmuch as the space-time progression is linearly outward in space, this means that the scalar effect of the rotational motion is linearly inward in space.
Another requirement is that the magnitude of the rotational motion must be greater than that of the progression. One unit of inward motion would simply cancel the one unit outward movement of the progression and create the rotational equivalent of nothing at all. Less than one unit is not possible, as fractional units do not exist. Hence the magnitude of the rotational motion must be greater than unity. We find, then, that when the photon acquires a rotation it reverses its space-time direction and travels backward along the line of the progression, moving inward from its own location toward all other spatial locations.
Again we have no difficulty in identifying the corresponding phenomena in the observed physical universe. The rotating photons, with the exception of certain incomplete units that we will discuss later, are atoms. Collectively the atoms constitute matter, and their inward movement is gravitation.
As a rough analogy, we may visualize 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 at whatever location on the belt they occupy initially, and they therefore move outward from their 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.
The analogy is, of course, incomplete. It cannot portray a strictly scalar motion, and consequently the mechanism whereby the rotation of the balls causes them to move inward translationally is not the same as that which causes the inward motion in the actual atomic situation. The analogy is also unable to demonstrate movement in all directions. Nevertheless, it does show quite clearly that under appropriate conditions a rotational motion can cause a translational displacement, and it also gives us a rough picture of the general relations between the space-time progression, gravitation, and the travel of the photons of radiation.
Unlike the space-time progression, which originates everywhere, and therefore remains constant irrespective of location, the gravitational motion originates at the location, which the atom happens to occupy. Since the atom is moving in opposition to the space-time progression it is continually passing from one space-time unit to another. The spatial direction corresponding to this scalar inward motion is indeterminate, and inasmuch as this direction is continually being redetermined because of entry into another unit of space-time, the effect of the probability laws is to distribute the motion equally over all directions. The fraction of the total motion directed toward any area A at distance d is then determined by the ratio of this area to the total surface area of a sphere of radius d. This ratio is inversely proportional to d2, hence the gravitational motion decreases with distance in accordance with the familiar inverse square law.
As the foregoing discussion indicates, gravitation is a movement of the atom inward toward all space-time locations other than the one, which it occupies (momentarily). Thus it is inherently a motion of the individual atom or material aggregate relative to the general space-time framework. However, the only way in which we can recognize such a motion is by reference to some observable aggregate of matter, and since that aggregate also has a similar gravitational motion inward in space-time, what we actually observe is that the two material aggregates are moving inward toward each other. Quite naturally this has been interpreted as indicating that the two masses are exerting forces of attraction upon each other, and the great problem of gravitation has been to account for the observed characteristics of these “forces,” which are most extraordinary and totally unlike those of forces encountered elsewhere in the physical realm. How can it be possible for one mass to exert a force upon another distant mass instantaneously, without an intervening medium, and in such a manner that the force cannot be screened off or modified in any way?
The total inability of modern science to make any headway toward an answer to this question has been so discouraging to the scientific profession that it no longer tries to find the answer. The current practice is to ignore the observations and to base gravitational theory on assumptions which are in direct contradiction to the observed facts. Even though all practical gravitational calculations, including those at astronomical distances, are carried out on the basis of instantaneous action, without introducing any inconsistencies, and even though the concept of a force which is wholly dependent upon position in space being propagated through space is self-contradictory, the theorists take the stand that since they are unable to devise a theory to account for instantaneous action, the gravitational force must be propagated at a finite velocity, all evidence to the contrary notwithstanding. And even though there is not the slightest independent evidence of the existence of any medium in space, or the existence of any medium-like properties of space, the theorists also insist that since they are unable to devise a theory without a medium or something that has the properties of a medium, such an entity must exist, in spite of the negative evidence.
As usually happens when men are driven, in the depths of their frustration, to the desperate step of denying the facts, all this has accomplished nothing. Gravitation is still an “enigma” or a “mystery” to the present-day scientist, and there is no indication that it is becoming any less enigmatic or less mysterious. Nor is any blue sky visible on the far horizon. Sir John Cockcroft summarizes the current (1964) outlook as follows: “It will probably be a long time before we can bring the gravitational forces within a general theory, since there is at present no progress in this direction.”79
The answer, which the Reciprocal System now provides for this difficult gravitational problem is Outstanding Achievement, Number Three. The explanation in the preceding paragraphs not only tells us how gravitation originates and why it is an inherent property of matter, but also accounts for all of the seemingly strange properties of gravitation in the exact form in which they are observed. And here again a surprising innovation emerges. The new system does not explain how one mass can exert a force on another distant mass instantaneously and without an intervening medium; it tells us that the reason for all of these peculiar properties is that gravitation is not an action of one mass upon another at all. Each mass unit is pursuing its own individual course entirely independent of all other masses, and the phenomenon that appears to be a mutual attraction is actually the result of the inherent nature of the individual motions. The gravitational motion of each mass is an inward scalar motion in opposition to the space-time progression, and it carries the mass inward in space-time. Since all other masses are similarly moving inward in space-time, each mass moves toward all other masses. Such a motion needs no medium, nor does it require a finite time for propagation; the inward motion is an inherent property of the atoms and there is no propagation.
We must now qualify the previous statement that the magnitude of the rotational motion of the atom is greater than that of the space-time progression by noting that this statement applies specifically to the situation at unit distance. Within this distance the net inward motion (or equivalent) becomes still greater because of the effect of the inverse square relation, outside this distance the net inward motion decreases for the same reason, and at some point in this outer region an equilibrium between the inward gravitational motion and the outward motion of the space-time progression is reached. Beyond this point the net movement is outward, the outward excess increasing as the distance becomes greater. Where an aggregate of matter is involved rather than a single atom, the gravitational motion is proportional to the mass, for reasons that will be explained in Chapter XII, and the point of equilibrium, the gravitational limit, as we will call it, is therefore a function of the mass.
We could include the distance factor in the analogy of the moving belt by devising some means of varying the speed of rotation of the balls with the distance from the central point. Under this arrangement the closer balls would still move inward, but at some point farther out there would be an equilibrium, and beyond this point the balls would move outward.
The reason for the great difference between the view that we get of time and the view that we get of space in our everyday experience is now evident. The progression of time is unchecked in our local environment and this progression so far overshadows any other change in time location that it is the only aspect of time, which we observe. Space actually progresses outward at the same rate as time, but the outward motion which the space progression imparts to objects existing in this local environment is more than counterbalanced by the inward movement due to gravitation, and the net result is that what we seem to see is a stationary space in which most physical objects, aside from the photons of radiation, have relatively low velocities of a random character. Gravitation is thus the controlling factor in our view of the universe. In the local region where it overpowers the progression, we get a picture of a relatively stable environment; at great distances where the gravitational motion is small and the progression is dominant we get an entirely different picture: one in which all objects are moving apart at enormous speeds.
In view of the important role, which the galactic recession plays in cosmology, we are justified in characterizing the explanation of this recession that is provided by the new system as Outstanding Achievement Number Four. However, the existence of a gravitational limit, within which there is a net inward gravitational motion and outside of which there is a net outward progression, explains a great deal more than the recession of the distant galaxies. For one thing, it reconciles the seemingly uniform distribution of matter in the universe with Newton’s Law of Gravitation and Euclidean geometry. One of the strong arguments that has been advanced against the existence of a gravitational force of the inverse square type operating in a Euclidean universe is that on such a basis “The stellar universe ought to be a finite island in the infinite ocean of space,”80 as Einstein puts it. Observations indicate that there is no such concentration. As far as we can tell, the galaxies are distributed uniformly or nearly uniformly throughout the immense region now accessible to observation, and this is currently taken as a definite indication that the geometry of the universe is non-Euclidean.
It is now clear that the flaw in this argument is that it rests on the assumption that gravitation is effective throughout space. This present work shows that this assumption is incorrect, and that there is a net gravitational force only within the gravitational limit of the particular mass under consideration. On this basis it is only the matter within the gravitational limit that should agglomerate into a single unit, and this is exactly what occurs. Each galaxy is a “finite island in the ocean of space” within its gravitational limit. The existing situation is thus entirely consistent with Newtonian gravitation operating in an Euclidean universe, which is the situation envisioned by the Reciprocal System.
The existence of the gravitational limit also solves the problem of how the galaxies could form in the first place, a question, which the cosmologists have been unable to answer. As Gold and Hoyle describe the situation: “Attempts to explain both the expansion of the universe and the condensation of galaxies must be very largely contradictory so long as gravitation is the only force field under consideration. For if the expansive kinetic energy of matter is adequate to give universal expansion against the gravitational field it is adequate to prevent local condensation under gravity, and vice versa.”81 In the RS universe gravitation is not the only force involved, and the existence of an equilibrium point within which the motion of matter is inward and beyond which it is outward accounts in an easy and natural way for both the aggregation of matter into galaxies and the recession of the distant galaxies.
The answer to the dilemma described by Gold and Hoyle could well be considered another of the outstanding achievements of the new system, but the limitations which have had to be imposed on the scope of this volume will prevent going into sufficient detail to clarify the nature of the process of galaxy formation, as it occurs in the RS universe, and this subject will therefore be omitted from the list. It should be understood in this connection that this list is not intended as a complete catalog of the major achievements of the Reciprocal System; it is merely a selection of the most significant items from among those included in the subject matter of this particular volume.
A full development of the other consequences of the existence of gravitational limits is also beyond the scope of this present volume, but it should be mentioned that these limits apply to all aggregates of matter and not only to the galaxies. Inasmuch as the smaller aggregates are under the gravitational control of the larger units such as the galaxies, the effect of the gravitational limits is somewhat modified in application to the smaller masses, but nevertheless, the existence of these limits has many significant results, some of which have been explored in previous publications.