Part Two: The Answer


In Part Three of this work an entirely new theory of gravitation which meets all of the requirements of a complete and comprehensive first order explanation of the gravitational phenomenon outlined in Part One will be developed from some new assumptions as to the basic nature of space and time. These assumptions, however, not only require a rather drastic revision of present-day ideas concerning space-time itself, but also lead to major changes in the theoretical background of almost all branches of physical science. There will, of course, be considerable reluctance to accept any such sweeping revision of current thought, and since the most essential features of the new gravitational theory can be developed from two less general postulates that do not necessarily conflict with the existing theoretical structure of science outside of the gravitational area, it appears advisable to approach the subject from this direction first, leaving the underlying theory for subsequent treatment in Part Three.

By way of establishing a background for the first of these two new postulates, let us consider the currently accepted concept of the progression of time. According to this viewpoint we are presently occupying a location in time which we call “now,” but we regard “now” as continually progressing, so that if we designate the current “now” as x we will be located at point x + 1 in time when another unit of time has elapsed. These lines are being written at a time location which we designate as 1963 A.D. When another year has elapsed we will consider ourselves as occupying time location 1964. We usually think of our own location as remaining stationary with time flowing past us, but the essential point is that in one unit of time a situation in which “now” is at time x changes to a situation in which “now” is at time x + 1. It is clear that this same result would be achieved if time, instead of flowing past us, moves from x to x + 1 in this interval, carrying us with it. In terms of the “River of Time” analogy, we may either visualize ourselves as located on a rock in midstream and measuring the river flow relative to our own position, or we may visualize ourselves as located in a boat floating freely with the stream, in which case we measure the flow by reference to the river bank.

The human race is strongly inclined to regard its own location as fixed and to interpret any relative motion with reference to another object as an actual motion of the other object, and much of the history of science during its first few millennia is concerned with the slow and painful progress toward freeing scientific thought from the handicap of this ingrained error. By this time, however, the scientific world has learned its lesson through costly experience and scientists are now wary of any theory or concept that portrays the abode of man as occupying any fixed or privileged position. The prevailing idea that we remain in a fixed location while time flows past us is actually an anachronism: an isolated corollary of the geocentric theory of the universe that has managed to survive only because it has never been subjected to a serious challenge.

The alternate viewpoint in which the rate of flow or progression of time is independent of us and of our position not only frees this phenomenon from the anthropomorphic aspects of currently popular concepts but also eliminates the necessity of providing an explanation for our motion relative to time. It is, of course, easy to visualize time itself as an entity that has an inherent flow or progression, but it is not so easy to understand why this flow should be a flow past us. This is not implicit in the concept of a progression of time; it is something that is introduced only when we enter the picture, and the mechanism responsible for the motion of time relative to us or, what amounts to the same thing, our motion relative to time, must be connected with us, not with time itself. If we regard time as flowing past us we are therefore faced with the problem of finding some mechanism whereby we can move relative to time. On the other hand, if we adopt the alternative viewpoint that we are being carried along by the flow or progression of time, this problem is eliminated. On this basis we always remain at the same location in time, but this location itself progresses and corresponds to constantly changing coordinates if viewed from the standpoint of an arbitrary reference system that theoretically does not progress.

The first of the postulates of the new theory adopts this latter viewpoint as to the progression of time, and extends the concept to space-time as well. On this basis there exists a progression of space-time such that each location in space-time moves outward from all other locations at a constant velocity. This means, of course, that the observed progression of time is simply one aspect of a more general phenomenon, another aspect of which is a similar progression of space. At first glance this latter concept seems absurd, since we have never recognized any evidence, in our everyday experience, of a progression of space that bears any resemblance to the observed progression of time. As we will see shortly, however, evidence of this kind can be found if we know what to look for.

During one unit of time, according to this postulate, location x not only progresses to x + 1 in time, but also progresses to x + 1 in space, since space-time as a whole is progressing. Any object without independent motion of its own which occupies location x in space at time x will therefore be found at location x + 1 in space at time x + 1, simply because space location x + 1 at time x + 1 is the same space-time location as space location x at time x. The hypothetical object remains permanently at the same location in space-time, but it moves with respect to a coordinate system that does not progress in space or a coordinate system that does not progress in time.

In the era of Newton space and time were regarded as independent entities but it has been apparent for the last half century that they are not independent, and that basically we must deal with space-time, not with space alone or with time alone. The currently popular Minkowski concept, which was adopted by Einstein in his work, recognizes this fact and portrays space-time as a four-dimensional continuum made up of three space dimensions and one time dimension. But only time progresses in a Minkowski universe, and hence an object that has no independent motion of its own remains stationary in Minkowski space, whereas the progression of space-time specified by the new gravitational postulate carries such an object outward in space as well as in time. This view of a location in space-time as an entity in motion is something new and unfamiliar but it should not present any serious conceptual difficulties. If we can visualize a progression of time we should certainly be able to visualize a corresponding progression of space. In this connection it should be noted that the concept of a relationship between space and time which is implied by the use of the expression “space-time” naturally suggests motion, since motion is the only relation between space and time of which we have any actual knowledge.

It has been emphasized in the preceding discussion that assumptions of a purely ad hoc nature with no confirmation from independent sources are essentially nothing more than speculations until some confirmation of this kind is forthcoming. The next thing that we will want to do, therefore, is to see what independent confirmation of the postulate of space-time progression can be obtained. If this assumption of a progression of space-time is valid, then we should be able to recognize some phenomena in which identifiable objects without inherent motion of their own are being carried along in space by the progression of space-time. In order to simplify the question of a reference system, let us assume that a large number of such objects originate at the same space-time location, which means that they originate at the same space location simultaneously. Due to the progression of space-time these objects immediately begin moving outward, but outward in space-time is a scalar direction, whereas the corresponding spatial motion is vectorial and can have any direction in three-dimensional space. Inasmuch as there is no reason why any particular direction should be preferred, the motions of the individual objects will be distributed over all possible directions in accordance with the probability principles, hence if the postulate of space-time progression is valid we should observe objects of this kind originating at various spatial locations and moving away from the points of origin in all spatial directions and at a constant velocity.

We do not have to look very far in order to find physical entities, which display exactly this behavior. Throughout the universe there are sources of light or other electromagnetic radiation from which photons emanate in all directions and recede from the points of emission at a constant velocity. Furthermore, these photons, so far as we know, have no motion of their own other than a vibratory motion which, because of the constant reversal of direction, has no net resultant in any spatial direction. Thus these photons not only behave in the manner theoretically appropriate for objects with no inherent motion, but they also answer the description of such objects. The radiation phenomenon therefore provides the definite independent evidence that is necessary in order to demonstrate the reality of the postulated space-time progression.

Further confirmation of the validity of the postulate is provided by the behavior of the very distant galaxies. The galaxies nearest our own have spectra which indicate relatively slow motions of a random character, but outside the local group all galactic spectra indicate that the galaxies are moving away from us at high velocities. Furthermore, these velocities increase with distance, apparently in linear proportion, and at the extreme limits reached by the giant optical telescopes they are in the neighborhood of half of the velocity of light. A reasonable extrapolation of this trend leads to the conclusion that not far (astronomically speaking) beyond the present observational limits the galaxies are receding from us at the velocity of light, which is just what would be expected on the basis of the space-time postulate as stated, providing that these galaxies have no appreciable independent motion of their own in our direction. This is almost certainly true, as our observations indicate that the random velocities of the galaxies are too small to be significant in this connection and at these extreme distances any gravitational motion toward our galaxy would be attenuated to the point where it would be negligible.

Thus the recession of the distant galaxies not only provides us with an additional verification of the postulate of space-time progression but also gives us a clear indication of how gravitation fits into the picture. Gravitation is normally visualized as a force, but in the case of the isolated galaxies, where no opposing forces are present, it is obviously a motion, and since the gravitational motion of each galaxy is directed inward toward all other galaxies, this gravitational motion is directly opposed to the motion of the space-time progression, which carries each galaxy outward away from all others. The gravitational motion evidently must be a property of the matter of which the galaxies are composed, and the second of the two postulates of the new gravitational theory will therefore be that each unit of matter has an inherent motion in the direction opposite to that of the space-time progression. In order to account for both the gravitational attraction at the shorter distances and the recession of the more distant galaxies it will, of course, be necessary to include the assumption that the gravitational motion of any unit of matter toward any other unit is equal to the space-time progression at some finite distance. Since the motion of the progression is constant irrespective of location, the inverse square relationship which applies to gravitation results in a net inward motion at the shorter distances, while beyond the equilibrium point the net notion is outward, increasing toward the velocity of light as the effective gravitational motion weakens.

A consideration of the situation existing at this equilibrium point shows how the concepts of gravitational force and gravitational motion are related. At this point there is no apparent motion in either direction. According to the gravitational postulates both the gravitational motion and the motion of the space-time progression actually exist, but there is no net resultant as one cancels the other. It is also possible, however, to consider both gravitation and the space-time progression as forces tending to cause motion, and to take the stand that no motion actually exists because the opposing forces are equal and there is no net force in either direction. The concept of force is quite legitimate and it is very convenient for many applications, but it has certain limitations simply because it is not exactly a true representation of the physical facts. One of the postulates of Einstein’s General Theory, for instance, is the so-called “Principle of Equivalence” which asserts that a gravitational force is equivalent to an accelerated motion. Actually, on the basis of the theory now being presented, gravitation is not equivalent to motion; it is motion. Under most circumstances these two concepts amount to the same thing, but the boundary conditions are different and Einstein’s formulation leads to erroneous results under some conditions: a situation which will be discussed in detail in the pages to follow.

From a space-time standpoint gravitation, as defined in this new system, is a uniform motion. This uniform motion is, however, distributed equally in all spatial directions in accordance with the probability principles, and the fraction of the total motion, which is directed toward any specific point in space, is therefore inversely proportional to the square of the intervening distance. In spite of the fact that it is uniform in space-time, the gravitational motion is thus an accelerated motion in space.

For present purposes it is not actually necessary to inquire into the question of the origin of the gravitational motion, but it is quite evident from the foregoing discussion that a rotational motion of the units of matter—the atoms—in, the direction opposite to that of the space-time progression would produce just such a result. From a spatial standpoint rotational motion produces no net effect as the motions in the different directions cancel each other, but since the space-time aspect of this rotational motion is scalar (that is, it is outward only, without any other directional specification), the rotational motion of the atoms can have a constant space-time direction and for present purposes a constant space-time direction opposite to that of the space-time progression will be assumed. The theoretical necessity for this constant direction will be demonstrated in Part Three. Unlike the space-time progression, which originates everywhere here and thus has a constant magnitude irrespective of location, the rotational motion of an atom originates at the specific location which that atom happens to occupy. Since the direction in space corresponding to an inward motion in space-time is indeterminate, the rotational motion is distributed over all spatial directions, and the magnitude of the effective component of this motion directed toward any other unit of matter therefore decreases with distance, following the inverse square law.

The two gravitational assumptions may now be expressed as follows:

  1. There exists a progression of space-time such that each location in space-time moves outward from all other locations at the velocity of light.
  2. Each atom of matter has an inherent motion of rotational origin opposite to the motion of the space-time progression in direction and equal in magnitude at a finite distance.


Let us now see what kind of a gravitational picture will result from these two assumptions. First, we note that on this basis gravitation is not an action of one mass upon another; it is a relation between each mass individually and the general space-time structure. In the absence of gravitation, each mass would move outward from all other masses by reason of the ever-present progression of space-time. Gravitation, being opposite in direction and greater in magnitude than the progression inside the equilibrium distance, reverses this behavior and causes each mass to move inward toward all other masses.

Here we have a situation in which each mass appears to be exerting a force of attraction on all other masses (within the distance limit) but in reality each is pursuing its own course completely independent of the masses with which it appears to be interacting. Under these circumstances the apparent force of attraction is exerted instantaneously, no medium is necessary, and there is obviously no way in which the effect could be screened off or modified by anything interposed between the masses. This is just the kind of behavior that is indicated by observation: a behavior which previous gravitational theories have been unable to account for.

As an aid in visualizing this gravitational situation, let us assume that a violent explosion has taken place and that we are looking at the results shortly thereafter without any knowledge of what has happened. We will see a cloud of flying particles apparently exerting a force of repulsion upon each other, and with a reasonable amount of ingenuity we can formulate a mathematical expression to represent the magnitude of this force. But we will find it very difficult to account for the origin of the force and to explain how it operates, as long as we remain under the Impression that it is a force exerted by one particle upon another, since we will find that this hypothetical force has some very peculiar characteristics: it acts instantaneously, without an intervening medium, and in such a manner that it cannot be screened off or modified in any way.

Judging by past experience, we can expect our leading physicists to deny the validity of the results of our observations of these happenings, on the grounds that they imply action at a distance, and to contend that there must be some kind of propagation of the repulsive force between the particles of debris, notwithstanding the physical facts that testify to the contrary.

Of course it can be anticipated that the foregoing statement will be taken as merely a bit of pleasantry; the idea that anyone would react to the situation in such a manner seems absurd in this case. But actually these are the conclusions which the great majority of the theoretical physicists of the present day have reached with respect to gravitation, on the strength of an almost identical set of observed facts. It is true that gravitation acts in the opposite direction—inward rather than outward, but it should not take much of a mental effort to visualize an explosion in reverse.

This new concept of gravitation not only explains the mechanism of the apparent attraction of one mass toward another, but also explains the unusual characteristics of the gravitational action at the same time, and eliminates the necessity of postulating phenomena or behavior characteristics for which there is no experimental or observational evidence: deformation of space, a finite propagation velocity, etc. The most impressive feature of this performance is that the entire theoretical structure is an integral unit; the same assumptions that lead to the existence of gravitation also define the characteristics of the gravitational action and no supplementary or collateral assumptions are required.

Furthermore, these assumptions also account for the general behavior of electromagnetic radiation and for the recession of the distant galaxies, as already indicated. The first of the three major deviations from the normal gravitational pattern which were discussed in Part One, that which is observed at extreme distances, is thus explained. Then when we turn our attention to the second area of deviation, the unexpectedly great distances between the stars, we find that this is simply another manifestation of exactly the same combination of factors that is responsible for the galactic recession.

Since the gravitational assumptions specify that the inward-directed gravitational motion of each atom is equal to the outward-directed motion of the space-time progression at a finite distance, this distance constitutes a gravitational limit for the atom, a limit within which the gravitational motion exceeds that of the progression, and beyond which the motion of the progression is the greater. Where a number of atoms are associated in a material aggregate the total gravitational motion, or force, increases proportionately with the mass, and since the space-time progression is constant this means that the gravitational limit moves outward as the mass increases. Each mass aggregate therefore has an individual gravitational limit that depends on the magnitude of the mass. The gravitational limit of a large spiral galaxy such as our own or M 31 has been found empirically to be in the neighborhood of a million light years. The Magellanic Clouds, which are about 200,000 light years distant from the Milky Way, are therefore within the gravitational influence of our galaxy and have a small gravitational motion in our direction; M 31 and M 33, the principal exterior members of our local group of galaxies, are outside our gravitational limit and therefore have a small outward motion due to the net space-time progression. The velocities of these local galaxies due to the net excess of gravitation or progression are so small that they can easily be masked by the random motions which the galaxies have acquired in the course of their development, but all other galaxies beyond the local group have a relatively large outward velocity due to the excess of the progression over the gravitational motion: a quantity which increases with distance, as has been explained.

Aside from the globular star clusters, which for present purposes can be considered as junior size galaxies, the next smaller independent unit of mass is the star. Since the only difference between the galactic aggregate and the stellar aggregate from a gravitational standpoint is in magnitude, the points that were brought out with reference to the gravitational behavior of the galaxies also apply to the stars. Here again there is a gravitational limit, within which there is a net inward motion and beyond which there is a net outward motion. From Newton’s relationship between mass, distance and gravitational force, we find that if the gravitational limit of a galaxy whose mass is equal to that of the Milky Way is approximately one million light years, the gravitational limit for a mass equal to that of the sun is about two light years. This, then, is the explanation of the immense distances between the stars. All matter within the gravitational limit of an existing star is pulled in to the star by the gravitational forces, and this prevents the accumulation of enough material to form a new star. If there ever was a “creation” period, and if some different situation prevailed at that time so that stars did come into existence within the gravitational limits of other stars, such new stars have long since consolidated with their predecessors or formed multiple star systems. Any star initially outside the gravitational limit of another star can never get inside, as the net motion in the region beyond the limit, is outward.

We do not observe a “recession of the stars” similar to the recession of the galaxies, but this is obviously due to the fact that the stars, unlike the galaxies, are under the gravitational control of larger aggregates. The stars in the vicinity of the sun, for example, are moving outward from the sun and from each other but at the same time they are being pulled inward toward the center of the galaxy by the gravitational force of the galaxy as a whole. The net result is an equilibrium in which the stars maintain reasonably constant relative positions just outside the gravitational limits of their neighbors.

The globular star clusters provide a particularly interesting example of this kind of equilibrium. The structural relationships in these clusters have long been a major astronomical problem. It seems quite obvious that each cluster is held together by gravitational forces, but if current gravitational ideas are valid some counter force must be operative to maintain the existing distances between the stars and prevent collapse of the structure. Unfortunately for the theorists it has not been possible to find such a force. From analogy with other astronomical systems it is natural to think of rotation in this connection, but all available evidence indicates that there is little or no rotation of the clusters. An attempt has been made to formulate an alternative theory on a basis somewhat similar to the kinetic theory of the motion of gas particles, but here again the observed facts prove to be recalcitrant. Such an explanation would require a high random velocity of the individual stars and frequent collisions or near collisions, neither of which is substantiated by observation.

Again, as in the case of the galactic recession, the new theory provides a ready answer in terms of gravitation in conjunction with the space-time progression. There is a force of repulsion between the individual systems (separate stars and multiple star systems) because each is outside the gravitational limits of its neighbors. The cluster is held together by the gravitational effect of the total mass on the individual units but the local repulsion between these individual units prevents the star density from exceeding a certain limiting value. This theory based on the two gravitational assumptions of this work thus requires just the kind of a situation which, according to the observations, actually exists.

The mere existence of clusters of this kind is a powerful argument in support of the new theory, as this is a case where the consequences of the basic assumptions of this theory see in sharp contrast to the results obtained from any other gravitational theory. No theory heretofore proposed could explain the existence of structures with the characteristics of these globular clusters, but they do exist and they are not freak phenomena; they exist in enormous numbers. One galaxy (M 87) is estimated to have over a thousand associated clusters. The abundance of these objects in the visible universe is a strong point in favor of the only theory, which explains why they hold together but do not collapse.

Likewise, the fact that individual stars or multiple star systems are never observed less than one or two light years distant from each other, either in the clusters or elsewhere, strongly supports the conclusions of this work to the effect that a closer approach is impossible and that any astronomical theory which postulates stellar collisions or near misses is erroneous.


The most striking fact about the gravitational theory outlined in the foregoing description is that it sidesteps the dilemma that has hitherto seemed inescapable; that is, it explains the gravitational effect without postulating either a medium or action at a distance, and without any “semantic trick” such as that employed by Einstein to create the appearance of having eliminated the medium without actually doing so. It is now apparent that this dilemma was not inherent in the gravitational problem itself, as had been thought; it was introduced by means of a totally unnecessary assumption that slipped into the line of reasoning without being recognized for what it actually is.

It is generally understood that the existence of concealed assumptions in a line of reasoning is one of the serious hazards that attends any attempt to apply logic to a problem, and great care is customarily taken to avoid introducing such assumptions. Unfortunately, however, it is usually necessary to formulate some kind of a theoretical viewpoint before a physical question can be approached at all and it is always possible that the concepts which enter into this viewpoint may contain some kind of a hidden assumption that is totally or partially erroneous, and this may invalidate the entire chain of thought, just as has happened in the gravitational case. The assertion that the gravitational effect is an action of one mass upon another is not a fact of observation, as has been believed; it is purely an assumption, and recognition of this fact opens the way to a clarification of the whole situation.

It should be emphasized that the new gravitational theory not only resolves this long-standing dilemma, but also agrees with all of the observed characteristics of the gravitational phenomenon; something that no other theory has ever done. All previous theories have had to assume that the gravitational observations do not mean what they seem to mean; that they are misleading and that the true characteristics of gravitation are something other than what the observations would indicate. This present work offers, for the first time, a system in which the theoretical characteristics of gravitation are in full agreement with the picture that we get from observation; that is, gravitation acts instantaneously, without an intervening medium or any substitute for a medium, and in such a way that it cannot be screened off or modified.

This is only one of several instances where the new theory provides simple and logical explanations of items for which no plausible explanations have been forthcoming on the basis of previous theories. The globular cluster problem previously discussed is another striking example. No previous theory has been able to explain, in any way that is consistent with the observed facts, why these clusters hold together but do not collapse into one massive aggregate.

The general situation involved in accounting for the extraordinary magnitude of the minimum distance between stars (or multiple star systems) is a case where previous theories have not only failed to supply an explanation, but have been unable to provide enough insight into the situation to enable recognition of the fact that there is an anomaly here which requires an explanation. Serious consideration is currently being given to many theories involving collisions or near collisions of stars, both in the clusters and elsewhere, although even the most elementary analysis indicates that if the stars were free to approach each other to within collision distance, there would necessarily be a distribution of stars throughout the zone extending from this collision distance outward, whereas observations indicate that there is an immense region out to a radius of one or two light years completely devoid of stars. The observed star distribution is thus totally inconsistent with current astronomical thought and in this instance, therefore, the new theory supplies the answer to a problem before the scientific community has recognized that such a problem exists.

Summarizing the foregoing, for three hundred years it has been accepted as an incontrovertible fact that there are only two possible explanations of the gravitational phenomenon: action at a distance or propagation of the effect at a finite velocity through something with the properties of a medium (ether, field or deformable space). This work has now presented a third alternative that has been completely overlooked by previous investigators: a process analogous to the inverse of an explosion, in which the individual mass units merely act as if they are exerting attractive forces on each other, whereas in truth each is pursuing its own course completely independent of all others. The mere fact that this development lies produced an entirely new concept of a logical and self-consistent nature in a field, which has been exhaustively studied for centuries by the best scientific minds, is, in itself, a noteworthy achievement. But this is much more than just another hypothesis comparable to the original two, neither of which is at all satisfactory. This new theory meets all of the requirements of a complete and satisfactory explanation of the gravitational mechanism.

Furthermore, the explanation provided by the new development is not the difficult and esoteric concept that might be expected in view of the fact that it remained undetected for three hundred years; it is something readily intelligible in terms of ordinary human experience. The gravitational action as explained by this new theory is the very essence of simplicity. There is no action at a distance, no medium, no propagation of a force, no distortion of space; simply an inherent motion of the atoms of matter in the direction opposite to the ever-present outward progression of space-time. These atoms appear to exert mutual forces of attraction only because they are in constant motion toward each other. Such an explanation seems quite strange on first acquaintance, to be sure, but this is merely because it is unfamiliar; anyone can visualize the behavior of the particles of debris that seem to be exerting a “force of repulsion” on each other after an explosion, and no great feat of the imagination is required in order to envision an inverse process. We could even get a visual demonstration of a process somewhat analogous to gravitation by taking a motion picture of an explosion and then running it backward.

Then, additionally, this same simple hypothesis which explains the general nature and mechanism of gravitation also explains the observed characteristics of this phenomenon, including not only the curious, but well-known, properties that have been so difficult to account for in terms of previous theories, but also the gravitational behavior in other fields such as the recession of the galaxies where the role of gravitation has hitherto been largely a matter of conjecture.

In spite of these achievements, however, the theory as here set forth cannot claim to be anything more than an explanation of the second order, on the basis of the classification set up in Part One, since it still leaves the question of the origin of the gravitational motion unanswered. Part Three, which follows, will answer this question, and in so doing will also supply the additional information that we need in order to clear up the gravitational situation in the atomic region: the only one of the regional gravitational anomalies that is being left unexplained in Part Two.

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