05 Gravitation

CHAPTER 5

Gravitation

Another type of motion that is permitted by the postulates, and therefore exists in the theoretical universe, is rotation. Before rotational motion can take place, however, there must exist some physical object (independent motion) that can rotate. This is purely a matter of geometry. We are still in the stage of the development where we are dealing only with scalar motions, and a single scalar motion cannot produce the directional characteristics of rotation. Like the sine curve of the photon they require a combination of motions: a compound motion, we may say. Thus, while motion is possible without anything moving, rotation is not possible unless some physical object is available to be rotated. The photon of radiation is such an independent motion, or physical object, and it is evident, from the limitations that apply to the kinds of motion that are possible at this stage of the development, that it is the only primary unit that meets the requirement. Simple rotation is therefore rotation of the photon.

In our ordinary experience rotation is a vectorial motion, and its direction (a vectorial direction) is relative to a fixed spatial system of reference. In the absence of other motion, an object rotating vectorially remains stationary in the fixed system. However, any motion of a photon is a scalar motion, inasmuch as the mechanism required for the production of vectorial motion is not yet available at this stage of the development. A scalar motion has an inherent scalar direction (inward or outward), and it is given a vectorial direction by the manner in which the scalar motion appears in the fixed coordinate system.

As brought out in Chapter 4, the net scalar direction of independent motion is inward. The significance of the term “net” in this statement is that a compound motion may include an outward component providing that the magnitude of the inward component of that motion is great enough to give the motion as a whole the inward direction. Since the vectorial direction that this inward motion assumes in a fixed reference system is independent of the scalar direction, the motion can take any vectorial direction that is permitted by the geometry of three-dimensional space. One such possibility is rotation. The special characteristic of rotation that distinguishes it from the simple harmonic motion previously considered is that in rotation the changes in vectorial direction are continuous and uniform, so that the motion is always forward, rather than oscillating back and forth. Consequently, there is no reason for any change in scalar direction, and the motion continues in the inward direction irrespective of the vectorial changes. Scalar rotation thus differs from inherently vectorial rotation in that it involves a translational inward movement as well as the purely rotational movement. A rolling motion is a good analogy, although the mechanism is different. The rolling motion is one motion, not a rotation and a translational motion. It is the rotation that carries the rolling object forward translationally. Similarly, the scalar rotation is only one motion, even though it has a translational effect that is absent in the case of vectorial rotation.

To illustrate the essential difference between rotation and simple harmonic motion, let us return to the automobile analogy. If the car is on a very narrow road, analogous to the one-dimensional path of vibration of the photon, and it runs forward in moving north, then when it reverses its vectorial direction and moves south it also reverses its scalar direction and runs backward. But if the car is on a circular track and starts moving forward, it continues moving forward regardless of the changes in vectorial direction that are taking place.

The vectorial direction of the inward translational movement of the rotating photon, like the vectorial direction of the non-rotating photon, is a result of viewing the motion in the context of an arbitrary reference system, rather than an inherent property of the motion itself. It is therefore determined entirely by chance. However, the non-rotating photon remains in the same absolute location permanently, unless acted upon by some outside agency, and the direction determined at the time of emission is therefore also permanent. The rotating photon, on the other hand is continually moving from one absolute location to another as it travels back along the line of the progression of the natural reference system, and each time it enters a new absolute location the vectorial direction is redetermined by the chance process. Inasmuch as all directions are equally probable, the motion is distributed uniformly among all of them in the long run. A rotating photon therefore moves inward toward all space-time locations other than the one that it happens to occupy momentarily. Coincidentally, it continues to move outward by reason of the progression of the reference system, but the net motion of the observable aggregates of rotating photons in our immediate environment is inward. The determination of the vectorial direction corresponding to “outward” automatically determines the vectorial direction of “inward” in each case, inasmuch as one is the reverse of the other.

Some of the readers of the first edition found the concept of “inward motion” rather difficult. This was probably due to looking at the situation on the basis of a single reference point. “Outward” from such a point is easily visualized, whereas “inward” has no meaning under the circumstances. But the non-rotating photon does not merely move outward from the point of emission; it moves outward from all locations in the manner of a spot on the surface of an expanding balloon. Similarly, the rotating photon moves inward toward all locations in the manner of a spot on the surface of a contracting balloon. The outward motion is simply the spatial representation of an increasing scalar magnitude, whereas the inward motion is the spatial representation of a decreasing scalar magnitude. If that decreasing magnitude reaches zero, it continues as an increasing negative magnitude; that is, if the object which was moving inward toward a certain location eventually arrives at that location, it continues in motion beyond that point (providing that nothing intervenes).

Since space and time locations cannot be identified by observation, neither inward nor outward motion can be recognized as such. It is possible, however, to observe the changes in relations between the moving objects and other physical structures. The photons of radiation, for instance, are observed to be moving outward from the emitting objects. Similarly, each of the rotating photons in the local environment is moving toward all other rotating photons, by reason of the inward motion in space in which all participate, and the change of relative position in space can be observed. This second class of identifiable objects in the theoretical universe thus manifests itself to observation as a number of individual units, which continually move inward toward each other.

Here, again, the identification of the physical counterparts of the theoretical phenomena is a simple matter. The inward motion in all directions of space is gravitation, and the rotating photons are the physical objects that gravitate; that is, atoms and particles. Collectively, the atoms and particles constitute matter.

As in the case of radiation, the new theoretical development leads to a very simple explanation of a hitherto unexplained phenomenon. Previous investigators in this area have arrived at a reasonably good understanding of the physical effects of gravitation, but they are completely at sea as to how it originated, and how the apparent gravitational effect is propagated. Our finding is that these previous investigators have misunderstood the nature of the gravitational phenomenon.

Except at extreme distances, each unit or aggregate of matter in the observed physical universe continually moves toward all others, unless restrained in some way. It has therefore been taken for granted that each particle of matter is exerting a force of attraction on the others. However, when we examine the characteristics of that presumed force we find that it is something of a very peculiar nature, totally unlike the forces of ordinary experience. As nearly as we can determine from observation, the gravitational “force” acts instantaneously, without an intervening medium, and in such a manner that it cannot be screened off or modified in any way. These observed characteristics are so difficult to explain theoretically that the theorists have given up the search for an explanation, and are now taking the stand that the observations must, for some unknown reason, be wrong.

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 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.

There are many places in accepted scientific thought where the necessity of facing up to clear evidence from observation or experiment is avoided by the use of one or more of the evasive devices that the modern theorists have invented for the purpose, but this gravitational situation is probably the only major instance in which the empirical evidence is openly and categorically defied. While the total lack of any explanation of the gravitational phenomenon that is consistent with the observations has undoubtedly been the primary cause of the flagrantly unscientific attitude that has been taken here, an erroneous belief concerning the nature of electromagnetic radiation has been a significant contributing factor.

The enormous extension of the known range of radiation frequencies in modern times has been accomplished mainly through the generation of these additional frequencies by electrical means, and it has come to be believed that there is a unique connection between radiation and electrical processes, that radiation is the carrier by means of which electrical and magnetic effects are propagated. From this it is only a short step to the conclusion that there must also be gravitational waves, carriers of gravitational energy. “Such (gravitational) waves resemble electromagnetic waves,” says Joseph Weber, who has been carrying on an extensive search for these hypothetical waves for many years. The theoretical development in the preceding pages shows that this presumed analogy does not represent the reality of the universe of motion. In that universe radiation and gravitation are phenomena of a totally different order. But it is worth noting that radical differences between these two types of phenomena are also apparent in the information that is available from empirical sources. That information is simply ignored in current practice because it conflicts with the popular theories of the moment.

Radiation is a process whereby energy is transferred from a material aggregate at some particular location in space (or time) to other spatial (or temporal) locations. Each photon has a definite frequency of vibration and a corresponding energy content; hence these photons are essentially traveling units of energy. The emitting agency loses a specific amount of energy whenever a photon leaves. This energy travels through the intervening space (or time) until the photon encounters a unit of matter with which it is able to interact, whereupon the energy is transferred, wholly or in part, to this matter. At either end of the path the energy is recognizable as such, and is readily interchangeable with other types of energy. The radiant energy of the impinding photon may, for instance, be converted into kinetic energy (heat), or into electrical energy (the photoelectric effect), or into chemical energy (photochemical action). Similarly, any of these other types of energy, which may exist at the point of emission of the radiation, can be converted into radiation by appropriate processes.

The gravitational situation is entirely different. Gravitational energy is not interchangeable with other forms of energy. At any specific location with respect to other masses, a mass unit possesses a definite amount of gravitational (potential) energy, and it is impossible to increase or decrease this energy content by conversion from or to other forms of energy. It is true that a change in location results in a release or absorption of energy, but the gravitational energy which the mass possesses at point A cannot be converted to any other type of energy at point A, nor can the gravitational energy at A be transferred unchanged to any other point B (except along equipotential lines). The only energy that makes its appearance in any other form at point B is that portion of the gravitational energy which the mass possessed at point A that it can no longer have at point B: a fixed amount determined entirely by the difference in location.

Radiant energy remains constant while traveling in space, but can vary almost without limit at any specific location. The behavior of gravitation is the exact opposite. The gravitational effect remains constant at any specific location, but varies if the mass moves from one location to another, unless the movement is along an equipotential line. Energy is defined as capability of doing work. Kinetic energy, for example, qualifies under this definition, and any kind of energy that can be freely converted to kinetic energy likewise qualifies. But gravitational energy is not capable of doing work as a general proposition. It will do one thing, and that thing only: it will move masses inward toward each other. If this motion is permitted to take place, the gravitational energy decreases, and the decrement makes its appearance as kinetic energy, which can then be utilized in the normal manner. But unless gravitation is allowed to do this one thing which it is capable of doing, the gravitational energy is completely unavailable. It cannot do anything itself, nor can it be converted to any form of energy that can do something.

The mass itself can theoretically be converted to kinetic energy, but this internal energy equivalent of the mass is something totally different from the gravitational energy. It is entirely independent of position with reference to other masses. Gravitational, or potential, energy, on the other hand, is purely energy of position; that is, for any two specific masses, the mutual potential energy is determined solely by their spatial separation. But energy of position in space cannot be propagated in space; the concept of transmitting this energy from one spatial position to another is totally incompatible with the fact that the magnitude of the energy is determined by the spatial location. Propagation of gravitation is therefore inherently impossible. The gravitational action is necessarily instantaneous as Newton’s Law indicates, and as has always been assumed for purposes of calculation.

It is particularly significant, therefore, that the theoretical characteristics of gravitation, as derived from the postulates of the Reciprocal System, are in full agreement with the empirical observations, strange as these observations may seem. In the theoretical universe of motion gravitation is not an action of one aggregate of matter on another, as it appears to be. It is simply an inward motion of the material units an inherent property of the atoms and particles of matter. The same motion that makes an atom an atom also causes it to gravitate. Each atom and each aggregate is pursuing its own course independently of all others, but because each unit is moving inward in space, it is moving toward all other units, and this gives the appearance of a mutual interaction. These theoretical inward motions, totally independent of each other, necessarily have just the kind of characteristics that are observed in gravitation. The change in the relative position of two objects due to the independent motions of each occurs instantaneously, and there is nothing propagated from one to the other through a medium, or in any other way. Whatever exists, or occurs, in the intervening space can have no effect on the results of the independent motions.

One of the questions that is frequently asked is how this finding that the gravitational motion of each aggregate is completely independent of all others can be reconciled with the observed fact that the direction of the (apparent) mutual gravitational force between two objects changes if either object moves. On the face of it, there appears to be a necessity for some kind of an interaction. The explanation is that the gravitational motion of an object never changes, either in amount or in direction. It is always directed from the location of the gravitating unit toward all other space and time locations. But we cannot observe the motion of an object inward in space; we can only observe its motion relative to other objects whose presence we can detect. The motion of each object therefore appears to be directed toward the other objects, but, in fact, it is directed toward all locations in space and time irrespective of whether or not they happen to be occupied. Whatever changes appear to take place in the gravitational phenomena by reason of change of position of any of the gravitating masses are not changes in the gravitational motions (or forces) but changes in our ability to detect those motions.

Let us assume a mass unit X occupying location a, and moving gravitationally toward locations b and c. If these locations are not occupied, then we cannot detect this motion at all. If location b is occupied by mass unit Y. then we see X moving toward Y; that is, we can now observe the motion of X toward location b, but its motion toward location c is still unobservable. The observable gravitational motion of Y is toward X and has the direction ba.

Now if we assume that Y moves to location c, what happens? The essence of the theory is that the motion of X is not changed at all; it is entirely independent of the position of object Y. But we are now able to observe the motion of X toward c because there is a physical object at that location, whereas we are no longer able to observe the motion of X toward location b, even though that motion exists just as definitely as before. The direction of the gravitational motion (or force) of X thus appears to have changed, but what has actually happened is that some previously unobservable motion has become observable, while some previously observable motion has become unobservable. The same is true of the motion of object Y. It now appears to be moving in the direction ca rather than in the direction ba, but here again there has been no actual change, other than the change in the position of Y. Gravitationally, Y is moving in all directions at all times, irrespective of whether or not that motion is observable.

The foregoing explanation has been presented in terms of individual mass units, rather than aggregates, as the basic question with respect to the effect of variable mass on the gravitational motion has not yet been considered. The discussion will be extended to the multiple units in the next chapter.

As emphasized in Chapter 3, the identification of a second general force, or motion, to which all matter is subject, provides the must needed “antagonist,” to gravitation, and enables explaining many phenomena that have never been satisfactorily explained on the basis of only one general force. It is the interaction of these two general forces that determines the course of major physical events. The controlling factor is the distance intervening between the objects that are involved. Inasmuch as the progression of space and time is merely a manifestation of the movement of the natural reference system with respect to the conventional stationary system of reference, the space progression originates everywhere, and its magnitude is always the same, one unit of space per unit of time. Gravitation, on the other hand, originates at the specific locations which the gravitating objects happen to occupy. Its effects are therefore distributed over a volume of extension space the size of which varies with the distance from the material object. In three-dimensional space, the fraction of the inward motion directed toward a unit area at distance d from the object is inversely proportional to the total area at that distance; that is, to the surface of a sphere of radius d. The effective portion of the total inward motion is thus inversely proportional to d2. This is the inverse square law to which gravitation conforms, according to empirical findings.

The net resultant of these two general motions in each specific case depends on their relative magnitudes. At the shorter distances gravitation predominates, and in the realm of ordinary experience all aggregate of matter are subject to net gravitational motions (or forces). But since, the progression of the natural reference system is constant at unit speed while the opposing gravitational motion is attenuated by distance it accordance with the inverse square law, it follows that at some specific distance, the gravitational limit of the aggregate of matter under consideration, the motions reach equality. Beyond this point the net movement is outward, increasing toward the speed of light as the gravitational effect continues to decrease.

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 the natural reference system. The cubes are analogous to the photons of radiation. Having no independent mobility of their own, they must necessarily remain permanently at whatever locations on the belt they occupy initially and they therefore move outward from the point of origin at the full speed 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 speed 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 the travel of the belt is analogous to gravitation.

We could include the distance factor in the analogy by introducing 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 analogy is incomplete, particularly in that 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 of the atoms. Nevertheless, it does show quite clearly that under appropriate conditions a rotational motion can cause a translational displacement, and it gives us a good picture of the general relations between the progression of the natural reference system, gravitational motion, and the travel of the photons of radiation.

All aggregates of matter smaller than the largest existing units are under the gravitational control of larger aggregates; that is, they are within the gravitational limits of those larger units. Consequently, they are not able to continue the outward movement that would take place in the absence of the larger bodies. The largest existing aggregates are not limited in this manner, and on the basis of the principles that have been stated, any two such aggregates that are outside their mutual gravitational limits recede from each other at speeds increasing with the distance.

In the observed physical universe, the largest aggregates of matter are galaxies. According to the foregoing theoretical findings, the distant galaxies should be receding from the earth at extremely high speeds increasing with distance up to the speed of light, which will be reached where the gravitational effect is reduced to a negligible level. Until quite recently, this theoretical conclusion would have been received with extreme skepticism, as it conflicts with what was then the accepted thinking, and there was no way in which it could be subjected to a test. But recent astronomical advances have changed this situation. Present-day instruments are able to reach out to distances so great that the effect of gravitation is minimal, and the observations with this improved equipment show that the galaxies are behaving in exactly the manner predicted by the new theory.

In the meantime, however, the astronomers have been trying to account for this galactic recession in some manner consistent with present astronomical views, and they have devised an explanation in which they assume, entirely ad hoc, that there was an enormous explosion at some singular point in the past history of the universe which hurled the galaxies out into space at their present fantastically high speeds. If one were to be called upon to decide which is the better explanation—one which rests upon an ad hoc assumption of an event far out of the range of known physical phenomena, or one which finds the recession to be an immediate and direct consequence of the fundamental nature of the universe—there can hardly be any question as to the decision. But, in reality, this question does not arise, as the case in favor of the theory of a universe of motion is not based on the contention that it provides better explanations of physical phenomena, a contention that would have to depend, in most instances, on conformity with non-scientific criteria, but on the objective and genuinely scientific contention that it is a fully integrated system of theory which is not inconsistent with any established fact in any physical area.

Another significant effect of the existence of a gravitational limit, within which there is a net inward motion, and outside of which there is a net outward progression, is that 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,”39 as Einstein stated the case. Observations indicate that there is no such concentration. So 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.

From the points brought out in the preceding pages, it is now clear that the flaw in this argument is that it rests on the assumption that there is a net gravitational force effective throughout space. Our findings are 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 major galaxy is a “finite island in the ocean of space,” within its gravitational limit. The existing situation is thus entirely consistent with inverse square gravitation operating in a Euclidean universe, as the Reciprocal System requires.

The atoms, particles, and larger aggregates of matter within the gravitational limit of each galaxy constitute a gravitationally bound system. Each of these constituent units is subject to the same two general forces as the galaxies, but in addition is subject to the (apparent) gravitational attraction of neighboring masses, and that of the entire mass within the gravitational limits acting as a whole. Under the combined influence of all of these forces, each aggregate assumes an equilibrium position in the three-dimensional reference system that we are calling extension space, or a net motion capable of representation in that system. So far as the bound system is concerned, the coordinate reference system, extension space, is the equivalent of Newton’s absolute space. It can be generalized to include other gravitationally bound systems by taking into account the relative motion of the systems.

Any or all of the aggregates or individual units that constitute a gravitationally bound system may acquire motions relative to the fixed reference system. Since these motions are relative to the defined spatial coordinate system, the direction of motion in each instance is an inherent property of the motion, rather than being merely a matter of chance, as in the case of the coordinate representation of the scalar motions. These motions with inherent vectorial directions are vectorial motions: the motions of our ordinary experience. They are so familiar that it is customary to generalize their characteristics, and to assume that these are the characteristics of all motion. Inasmuch as these familiar vectorial motions have inherent directions, and are always motions of something, it is taken for granted that these are essential features of motions; that all motions must necessarily have these same properties. But our investigation of the fundamental properties of motion reveals that this assumption is in error. Motion, as it exists in a universe composed entirely of motion, is merely a relation between space and time, and in its simpler forms it is not motion of anything, nor does it have an inherent direction. Vectorial motion is a special kind of motion; a phenomenon of the gravitationally bound systems.

The net resultant of the scalar motions of any object—the progression of the reference system and the various gravitational motions—has a vectorial direction when viewed in the context of a stationary reference system, even though that direction is not an inherent property of the motion. The observed motion of such an object, which is the net resultant of all of its motions, both scalar and vectorial, thus appears to be simply a vectorial motion, and is so interpreted in current practice. One of the prerequisites for a clear understanding of basic physical phenomena is a recognition of the composite nature of the observed motions. It is not possible to get a true picture of activity in a gravitationally bound system unless it is realized that an object such as a photon or a neutrino which is traveling at the speed of light with respect to the conventional frame of reference does so because it has no capability of independent motion at all, and is at rest in its own natural system of reference. Similarly, the behavior of atoms of matter can be clearly understood only in the light of a realization that they are motionless, or moving at low speeds, relative to the conventional reference system because they possess inherent motions at high speed which counterbalance the motion of the natural reference system that would otherwise carry them outward at the speed of the photon or the neutrino.

It is also essential to recognize that the scalar motion of the photons can be accommodated within the spatial reference system only by the use of multiple reference points. Photons are continually being emitted from matter by a process that we will not be prepared to discuss until a later stage of the theoretical development. The motion of the photons emitted from any material object is outward from that object, not from the instantaneous position in some reference system which that object happens to occupy at the moment of emission. As brought out in Chapter 3, the extension space of our ordinary experience is “absolute space,” for vectorial motion and for scalar motion viewed from one point of reference. But every other reference point has its own “absolute space,” and there is no criterion by which one of these can be singled out as more basic than another. Thus the location at which a photon originates cannot be placed in the context of any general reference system for scalar motion. That location itself is the reference point for the photon emission, and if we choose to view it in relation to some reference system with respect to which it is moving, then that relative motion, whatever it may be, is a component of the motion of the emitted photons.

Looking at the situation from the standpoint of the photon, we may say that at the moment of emission this photon is participating in all of the motions of the emitting object, the outward progression of the natural reference system, the inward motion of gravitation, and all of the vectorial motions to which the material object is subject. No mechanism exists whereby the photon can eliminate any of these motions, and the outward motion of the absolute location of the emission, to which the photon becomes subject on separation from the material unit, is superimposed on the previously existing motions. This, again, means that the emitting object defines the reference point for the motion of the photon. In a gravitationally bound system each aggregate and individual unit of matter is the center of a sphere of radiation.

This point has been a source of difficulty for some readers of the first edition, and further consideration by means of a specific example is probably in order. Let us take some location A as a reference point. All photons originating from a physical object at A move outward at unit speed in the manner portrayed by the balloon analogy. Gravitating objects move inward in opposition to the progression, and can therefore be represented by positions somewhere along the lines of the outward movement. Here, then, we have the kind of a situation that most persons are looking for: something that they can visualize in the context of the familiar fixed spatial coordinate system. But now let us take a look at one of these gravitating objects, which we will call B. For convenience, let us assume that B is moving gravitationally with respect to A at a rate which is just equal to the outward progression of the natural reference system, so that B remains stationary with respect to object A in the fixed reference system. This is the condition that prevails at the gravitational limit. What happens to the photons emitted from B?

If the expanding system centered at A is conceived as a universal system of reference, as so many readers have evidently taken it to be, then these photons must be detached from B in a manner which will enable them to be carried along by progression in a direction outward from A. But the natural reference system moves outward from all locations; it moves outward from B in exactly the same manner as it does from A. There is no way in which one can be assigned any status different from that of the other. The photons originating at B therefore move outward from B. not from A. This would make no difference if B were itself moving outward from A at unit speed, as in that case outward from B would also be outward from A, but where B is stationary with respect to A in a fixed coordinate system, the only way in which the motions of the photons can be represented in that system is by means of two separate reference points. Thus there is a sphere of radiation centered at A, and another sphere centered at B. Where the spheres overlap, the photons may make contact, even though all are moving outward from their respective points of origin.

It has been suggested that the theoretical conclusion that the unit outward motion of the photon is added to the motion imparted to the photon by the emitting object conflicts with the empirically established principle that the speed of radiation is independent of the speed of the source, but this is not true. The explanation lies in some aspects of the measurement of speed that have not been recognized. This matter will be discussed in detail in Chapter 7.

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