The discovery of the mass-energy relation E = mc^{2 }by Einstein was a significant advance in physical theory, and has already had some far-reaching physical applications. It is, of course, entirely consistent with the Reciprocal System of theory. Indeed, this theory provides the explanation of the relation that has heretofore been lacking. It is not always recognized that, in the light of current physical thought, this is a very strange relation. Why should the relation between mass and energy be expressible in terms of speed? Einstein supplied no explanation. He derived the relation from the mathematical expression of his theory of relativity, but a mathematical derivation does not *explain *anything until an *interpretation *of the mathematics gives that derivation a physical meaning. The information that has been missing is now supplied by the Reciprocal System. In the universe of motion defined by that system of theory, mass and energy are both reciprocal speeds, differing only in dimensions, mass being three-dimensional, while energy is one-dimensional. Unit energy is therefore the product of unit mass and the second power of unit speed, the speed of light.

This finding as to the true significance of the mass-energy relation has an important effect on its applicability. It shows that the current belief that a quantity of energy always has a certain mass associated with it is erroneous. Reciprocal speed can exist either as mass, or as energy, but not both simultaneously. A quantity of mass, three-dimensional scalar motion, is equivalent to a quantity of energy, one-dimensional scalar motion, only when three-dimensional motion is actually transformed into one-dimensional motion, or vice versa. In other words, an existing quantity of mass does not correspond to any existing energy, but to the quantity of energy that *would * come into existence if the mass is actually converted into energy.

For this reason, Einstein’s hypothesis of an increase in mass accompanying increased velocity is inconsistent with our findings. The kinetic energy increment could increase the mass only if it were converted to mass by some appropriate process, and in that event it would cease to be kinetic energy; that is, the corresponding velocity would no longer exist. Actually, this hypothesis of Einstein’s is inconsistent with his valid concept of the conversion of mass into energy, regardless of the point of view from which the question is approached. Mass cannot be an accompaniment of kinetic energy, a quantity that increases as the energy increases, and also an entity that can be converted into kinetic energy, a quantity that increases as the energy decreases. The two concepts are mutually exclusive.

In the theoretical universe of motion now being described, the mass-energy relation is applicable only to those processes in which mass disappears and energy appears, or vice versa. The most familiar process of this kind is the interchange between mass and energy that takes place as a result of radioactivity, or similar atomic transformations. As we saw in Chapter 25, the *primary* mass is conserved in these reactions. In the radioactive disintegration Ra^{226} → Rn^{222} + He^{4}, for example, the total primary mass of the original radium atom was 226. The primary mass of the residual radon atom, 222, and that of the ejected alpha particle, 4, likewise add up to 226. Thus any mass-energy conversion involved in atomic transformations of this kind is confined to the *secondary* mass.

Current scientific opinion regards this secondary mass component as the mass which, according to accepted theory, is associated with the “binding energy” that holds the hypothetical constituents of the hypothetical atomic nucleus together. It must be conceded that this “binding energy” concept fits in very well with the prevailing ideas as to the nature of the atomic structure, but it should be remembered that the entire nuclear concept of the atom is purely hypothetical. No part of it has been verified empirically. Even Rutherford’s original conclusion that *most *of the mass of the atom is concentrated in a small nucleus—the hypothesis from which the present-day atomic theory was derived—is not supported except on the basis of the *assumption * that the atoms are in contact in the solid state, an assumption that we now find is erroneous. And every additional step that has been taken in the long series of adjustments and modifications to which the theory has been subjected as a means of extricating it from difficulties has involved one or more further assumptions, as pointed out in Chapter 18. Thus the fact that the “binding energy” concept is consistent with this aggregate of hypotheses has no physical significance. All available evidence is consistent with our finding that the difference between the observed total mass and the primary mass is a secondary mass effect due to motion within the time region, and that the conversion of this secondary mass to energy is responsible for the energy production during radioactivity or other atomic transformations.

The nature of the secondary mass was explained in Volume I. The magnitudes of this quantity applicable to the sub-atomic particles and the hydrogen isotopes were also calculated. Some studies were made on the higher elements during the early stages of the investigation, and it was shown in the first edition of this work that there is a fairly regular decrease in the secondary mass of the most abundant isotope of the elements in the range from lithium to iron. Beyond iron the values are irregular, but the secondary mass (negative in this range) remains in the neighborhood of the iron value up to about the midpoint of the atomic series, after which it gradually decreases. and returns to positive values in the very heavy elements. The effect of this secondary mass pattern is to make both the growth process in the light elements and the decay process in the heavy elements exothermic.

From the foregoing, it follows that the secondary mass in the lower half of the atomic series, with the exception of hydrogen, is negative. This conflicts with the general belief that mass is always positive, but our previous development of theory has shown that the observed mass of an atom is the algebraic sum of the mass equivalents of the speed displacements of the constituent rotations. Where a rotation is negative, the corresponding mass component is also negative. The net total mass of a material atom is always positive only because the magnetic rotation is necessarily positive in the material sector of the universe, and the magnetic rotation is the principal component of the total. Just why the minimum in the secondary mass is at or near the midpoint of the atomic series rather than at one of the extremes is still unknown, but a similar pattern was noted in some of the material properties examined in the preceding pages of this and the earlier volume, and it is not unlikely that there is a common cause.

Many investigators have devoted considerable effort to the study and analysis of atomic transformations that might possibly serve as the source of the energy generated in the sun and other stars. The general conclusion has been that the most likely reactions are those in which hydrogen is converted into helium, either directly or through a series of intermediate reactions. Hydrogen is the most abundant element in the stars, and in the universe as a whole. This hydrogen conversion process, if actually in operation, could therefore furnish a substantial supply of energy. But, as brought out in Chapter 25, there is no actual evidence that the conversion of ordinary hydrogen, the H^{1} isotope, to helium is a *naturally *occurring process in the stars or anywhere else. Even without the new information supplied by the investigation here being reported, there are many reasons to doubt that this process is actually operative, and to question whether it would supply enough energy to meet the stellar requirements if it were in operation. It obviously fails by a wide margin to account for the enormous energy output of the quasars and other compact astronomical objects. As one astronomer states the case, the problem of accounting for the energy of the quasars “is widely considered to be the most important unsolved problem in theoretical astrophysics.”^{106}

The catastrophic effect that the invalidation of the hydrogen conversion process as the stellar energy source would otherwise have on astronomical theory, leaving it without any explanation of the manner in which this energy is generated, is avoided by the fact that the development of the Reciprocal System of theory has revealed the existence of not only one, but two hitherto unknown physical phenomena, each of which is far more powerful than the hydrogen conversion process. These newly discovered processes are not only capable of meeting the energy requirements of the stable stars, but also the far greater requirements of the supernovae and the quasars (when the quasar energies are scaled down to the true magnitudes from the inflated values based on the current interpretations of the redshifts of these objects).

Perhaps some readers may find it difficult to accept the thought that there could be hitherto unknown processes in operation in the universe that are vastly more powerful than any previously known process. It might seem that anything of that magnitude should have made itself known to observation long ago. The explanation is that the * results* of these processes *are known observationally.* Extremely energetic events are prominent features of present-day astronomy. What has *not *been known heretofore is the *nature* of the processes* * whereby the enormous energies are generated. This is the information that the theory of the universe of motion is now supplying.

In Chapter 17 we examined one of these processes, the conversion of mass to energy that results when the matter in the interior of a star reaches the destructive thermal limit. This is the long-continuing process that supplies the relatively modest (on the astronomical scale) amount of energy necessary to meet the requirements of the stable stars. It also accounts for the large energy output of one kind of supernova, as we will see in Volume III. At this time we will take a look at what happens when a star arrives at a different kind of a destructive limit.

The destructive limit identified in Chapter 17 is reached when the total of the outward displacements (thermal and electric ionization) reaches equality with one of the inward rotational displacements of the atom, reducing the net displacement of the combination to zero, and destroying its rotational character. A similar destructive limit is reached when the inward displacements (rotation and gravitational charge) are built up to a level that, from the rotational standpoint, is the *equivalent* of zero.

This concept of the equivalent of zero is new to science, and may be somewhat confusing, but its nature can be illustrated by consideration of the principle on which the operation of the stroboscope is based. This instrument observes a rotating object in a series of views at regular intervals. If the interval is adjusted to equal the rotation time, the various features of the rotating object occupy the same positions in each view, and the object therefore appears to be stationary. A similar effect was seen in the early movies, where the wheels of moving vehicles often appeared to stop rotating, or to rotate backward.

In the physical situation, if a rotating combination completes its cycle in a unit of time, each of the displacement units of the combination returns to the same circumferential position at the end of each cycle. From the standpoint of the macroscopic behavior of the motion, the positions at the ends of the time units are the only ones that have any significance—that is, what happens *within *a unit has no effect on other units—and, under the conditions specified, these positions lie in a straight line in the reference system. This means that there is no longer any factor tending to keep the units together as a rotational combination (an atom). Consequently, they separate as linear motions, and mass is transformed into energy. It should be understood, however, that this transformation at the destructive limit has no effect on the motion itself. Scalar motion has no property other than its positive or negative magnitude, and that remains unchanged. What is altered is the coupling to the reference system, which is subject to change at the end of any unit, if the conditions existing at that point are favorable for such a change.

The emphasis on the *ends *of the units of motion in the foregoing discussion is a reflection of the nature of the basic motions, as defined in the fundamental postulates of the Reciprocal System of theory. According to these postulates, the basic units of motion are discrete. This does not mean that the motion proceeds by a succession of jumps. On the contrary, motion is inherently a continuous progression. A new unit of the progression begins at the point where the preceding unit ends, so that continuity, in this sense, is maintained from unit to unit, as well as within units. But since the units are separate entities, the effects of the events that take place in one unit cannot be carried forward to the next (although the combination of the internal and external features of the *same *unit may be effective, as in the case of the primary and secondary mass). The individual units of motion *may *continue on the same basis, but the coupling of the motion to the reference system is subject to change to conform to whatever conditions may exist at the end of a unit. When the atom has returned to the situation that existed at the original zero, as is true if the end of the rotational cycle coincides with the end of the time unit, the motion has reached a new starting point, a new zero, we may say.

For the reasons previously given, the limiting value, the equivalent of zero in each scalar dimension, is eight units of one-dimensional, or four units of two-dimensional, rotational displacement. In the notation used herein, the latter is a 4-4 magnetic combination. However, as indicated in Chapter 24, the destructive limit is not reached until the displacement in the electric dimension also arrives at the equivalent of the last magnetic unit. A rotational combination (atom) is therefore stable, at zero magnetic ionization, up to 4-4-31, or the equivalent 5-4-(1), which is element 117. One more step reaches the limit at which the rotational motion terminates.

If the rotational limit is reached in atoms whose individual magnetic ionization is above the general level in the aggregate of which these atoms are constituents, the effect of approaching the limit is that the atoms become radioactive, and eject portions of their masses in the form of alpha particles, or other fragments. This prevents the building of elements heavier than number 117, but it does not result in destruction of primary mass such as that which occurs at the destructive thermal limit. Thus the radioactivity is a means of avoiding the destructive effects of reaching the limiting value of the magnetic displacement.

This situation is analogous to a number of others that are more familiar. For example, we saw in Chapter 5 that the limiting value of the specific heat of a solid is reached at a relatively low temperature. Beyond this limit the atom. or molecule, enters the liquid state. The transition requires a substantial energy input, and since the lower energy states are more probable in a low energy environment, the atom avoids the need to provide the energy increment by changing to a different thermal vibration pattern, if it has the capability of so doing. The atoms of the heavier elements make several changes of this kind as new limiting values of the specific heat are encountered at successively higher temperatures. Eventually, however, a point is reached at which no further expedients of this kind are available, and the atom must pass into the liquid state. Similarly, the probabilities favor the continued existence of the combination of motions that constitutes the atom, as long as this is possible. The destructive effects of arriving at the displacement limit are therefore avoided by the ejection of mass. But here, too, as in the case of the specific heat, a point is eventually reached where the level of magnetic ionization tending to *increase *the atomic mass prevents further ejection of mass from the atom, and arrival at the destructive limit can no loner be avoided.

The consequences of reaching this rotational displacement limit at the equivalent of zero are qualitatively identical with those of reaching the thermal displacement limit at zero. The various rotational components cancel out, and the motion reverts to the linear basis. This transforms mass into kinetic energy, most of which is imparted to the residue of the atoms, or to other matter in the environment. The remainder goes into electromagnetic radiation. From a quantitative standpoint, there are some significant differences between the two phenomena. The thermal limit applies only to the heaviest element that is present in the aggregate in a significant quantity, and the rate at which this element arrives at the limit is regulated by a process that will be discussed in Volume III. The elements lower in the atomic series are not affected. Furthermore, the conversion of rotational to linear displacement (mass to energy) at the thermal limit does not necessarily apply to more than one of the magnetic displacement units of the atom, and a large part of the atomic mass may therefore remain intact, either as a residual atom or a number of fragments.

Consequently, the thermal limit has no catastrophic effect until the temperature reaches the destructive limit of an element, iron, that is present in relatively large quantities. On the other hand, arrival at the magnetic displacement limit affects the entire mass of each atom, and the only portion of the mass of an aggregate that remains intact is that in the outer portions of the aggregate where the magnetic ionization level is lower than in the deeper interior. There is no process that limits the rate of disintegration at this destructive limit. The resulting explosion, known as a Type II supernova, is therefore much more powerful (relative to the mass of the exploding star) than the Type I supernova that occurs at the thermal limit, although its full magnitude is not evident from direct observation, for reasons that will be explained in Volume III.

While the thermal disintegration process is operative in every star, it does not necessarily proceed all the way to destruction of the star. The extent to which the mass of the star, and consequently the temperature, increases depends on its environment. Some stars will accrete enough mass to reach the temperature limit and explode; others will not. But the increase in the magnetic ionization level is a continuing process in all environments, and it necessarily results in arrival at the magnetic destructive limit when sufficient time has elapsed. This limit is thus essentially an *age *limit.

A process related to those that have been described in the foregoing paragraphs is the sequence of events that counterbalances the conversion of three-dimensional motion (mass) into one-dimensional motion (energy) in the stars. The energy that is generated by atomic disintegration leaves the stars in the form of radiation. According to present-day views, this radiation moves outward at the speed of light, and most of it eventually disappears into the depths of space. The theory of the universe of motion gives us a very different picture. It tells us that inasmuch as the photons of radiation have no capability of independent motion relative to the natural datum, they remain stationary in the natural reference system, or move inward at the speed of the emitting object. Each photon therefore eventually encounters, and is absorbed by, an atom of matter. The net result of the generation of stellar energy by atomic disintegration is thus an increase in the thermal energy of other matter. As will be explained in Volume III, the matter of the universe is subject to a continuing process of aggregation under the influence of gravitation. Consequently, all matter in the material sector, with the added thermal energy, is ultimately absorbed by one of the giant galaxies that are the end products of the aggregation process.

When supernova explosions in the interior of one of these giant galaxies become frequent enough to raise the average particle speed above the unit level, some of the full units of speed thus made available are converted into rotational motion, creating cosmic atoms and particles. This cosmic atom building, which theoretically operates on a very large scale in the galactic interiors, has been observed on a small scale in experiments, the results of which were discussed in Volume I. In the experiments, the high energy conditions are only transient, and the cosmic atoms and particles that are produced from the high level kinetic energy quickly decay into particles of the material system. Some such decays no doubt also occur in the galactic interiors, but in this case the high energy condition is quasi-permanent, favoring continued existence of the cosmic units until ejection of the quasar takes place. In any event, the production of these rotational combinations has increased the amount of existing cosmic or ordinary matter at the expense of the amount of existing energy, thus reversing the effect of the production of energy by disintegration of atoms of matter.

In concluding this last chapter of a volume dealing with the properties of matter, it will be appropriate to call attention to the significant difference between the role that matter plays in conventional physical theory, and its status in the theory of the universe of motion. The universe of present-day physical science in a universe of matter, one in which the presence of matter is the central fact of physical existence. In this universe of matter, space and time provide the background, or setting, for the action of the universe; that is, according to this view, physical phenomena take place *in * space and *in *time.

As Newton saw them, space and time were permanent and unchanging, independent of each other and of the physical activity taking place in them. Space was assumed to be Euclidean (“flat” in the jargon of present-day mathematical physics), and time was assumed to flow uniformly and unidirectionally. All magnitudes, both of space and of time, were regarded as absolute; that is, not dependent on the conditions under which they are measured, or on the manner of measurement. A subsequent extension of the theory, designed to account for some observations not covered by the original version, assumed that space is filled with an imponderable fluid, the *ether, *which interacts with physical objects.

Einstein’s relativity theories, which have replaced Newton’s theory as the generally accepted view of the theoretical physicists, retain Newton’s concept of the general nature of space and time. To Einstein these entities constitute a background for the action of the universe, just as they did for Newton. Instead of being a three-dimensional space and a one-dimensional time, independent of each other, as they were for Newton, they are amalgamated into a four-dimensional space-time in Einstein’s system, but they still have exactly the same function; they form the framework, or container, within which physical entities exist and physical events take place. Furthermore, these basic physical entities and phenomena are essentially identical with those that exist in Newton’s universe.

It is commonly asserted that Einstein eliminated the ether from physical theory. In fact, however, what he actually did was to eliminate the *name “*ether,” and to apply the name “space” to the concept previously called the “ether.” Einstein’s “space” has the same kind of properties that were formerly assigned to the ether, as he admits in the following statement:

We may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there still exists an ether.

^{25}

The downfall of Newtonian physics was due to a gradual accumulation of discrepancies between theory and observation, the most critical being the results of the Michelson-Morley experiment and the measurements of the advance of the perihelion of Mercury, neither of which could be explained within the limits of Newton’s system. Some modification of that system was obviously necessary. The question, as it stood around the end of the nineteenth century, was what form the revision of Newton’s ideas should take.

As brought out in Chapter 13, in order to qualify as “theory,” in the full meaning of the term, the treatment of a physical phenomenon must cover not only its mathematical aspects, but also its physical aspects; that is, it must provide a conceptual understanding of the entities and relations to which the mathematics refer. However, the general tendency in recent years has been to concentrate on the mathematical development and to omit the parallel conceptual development, substituting conceptual interpretations of the individual mathematical results. Richard Feynman describes the present situation in this manner:

Every one of our laws is a purely mathematical statement in rather complex and abstruse mathematics.

^{56}

In his attack on the problem of revising Newton’s theory, Einstein not only adopted this policy of widening the latitude for theory construction by restricting his development to the mathematical aspects of the subject under consideration, and thereby avoiding any conceptual limitations on his basic assumptions, but went a step farther, and loosened the normal mathematical constraints as well. He first introduced a high degree of flexibility into the numerical values by discarding “the idea that co-ordinates must have an immediate metrical meaning [an expression that he defines as the existence of a specific relationship between differences of coordinates and measurable lengths and times].”^{36} As C. Moller describes this theoretical picture:

In accelerated systems of reference the spatial and temporal coordinates thus lose every physical significance; they simply represent a certain arbitrary, but unambiguous, numbering of physical events.

^{107}

Along with this flexibility of physical measurement, which greatly increased the latitude for making additional assumptions, Einstein introduced a similar flexibility into the geometry of spacetime by assuming that it is distorted or “curved” by the presence of matter. The particular aim of this expedient was to provide a means of dealing with gravitation, a key issue in the general problem. One textbook explains the new view in this manner:

What we call a gravitational field is equivalent to a “warping” of time and space, as if it were a rubbery sort of material that stretched out of shape near heavy bodies.

^{108}

The basis for this assertion is an* assumption, * the assumption that, for some unspecified reason, space and matter exert an influence upon each other. “Space acts on matter, telling it how to move. In turn, matter acts on space, telling it how to curve.”^{109 }(Misner, Thorne, and Wheeler) But neither Einstein nor his successors have given us any explanation of *how *such interactions are supposed to take place—*how *space “tells” matter, or vice versa. Nor does the theory explain inertia, an aspect of the gravitational situation that has given the theorists considerable trouble. As Abraham Pais sums up this situation:

It must also be said that the origin of inertia is and remains

themost obscure subject in the theory of particles and fields.^{110}

Today there is a tendency to call upon Mach’s principle, which attributes the local behavior of matter to the influence of the total quantity of matter in the universe. Misner, Thorne, and Wheeler say that “Einstein’s theory identifies gravitation as the mechanism by which matter there (the distant stars) influences inertia here.”^{111 }But, as indicated in the statement by Pais, this explanation is far from being persuasive. It obviously gives us no answer to the question that baffled Newton: How does gravitation originate? Indeed, there is something incongruous about the acceptance of Mach’s principle by the same scientific community that is so strongly opposed to the concept of action at a distance.

The fact is that neither Newton’s theory nor Einstein’s theory tells us anything about the “mechanism” of gravitation. Both take the existence of mass as something that has to be accepted as a given feature of the universe, and both require that we accept the fact that masses gravitate, without any explanation as to how, or why, this takes place. The only significant difference between the two theories, in this respect, is that Newton’s theory gives us no reason why masses gravitate, whereas Einstein’s theory gives us no reason why masses cause the distortion of space that is asserted to be the reason for gravitation. As Feynman sums up the situation, “There is no model of the theory of gravitation today, other than the mathematical form.”^{56}

The concept of a universe of motion now provides a gravitational theory that not only explains the gravitational mechanism. but also clarifies its background, showing that mass is a necessary consequence of the basic structure of the universe, and does not have to be accepted as unexplainable. This theory is based on a new, and totally different, view of the status of space and time in the physical universe. Both Newton and Einstein saw space and time as the container for the constituents of the universe. In the theory of the universe of motion, on the other hand, space and time *are *the constituents of the universe, and there is no container. On this basis, the space of the conventional spatio-temporal reference system is just a reference system—nothing more. Thus it cannot be curved or otherwise altered by the presence or action of anything physical. Furthermore, since the coordinates of the reference system are merely representations of existing physical magnitudes, they automatically have the “metrical meaning” that Einstein eliminated from his theory to attain the flexibility without which it could not be fitted to the observations.

The theory of the universe of motion is the first physical theory that actually *explains *the existence of gravitation. It demonstrates that the gravitational motion is a necessary consequence of the properties of space and time, and that the same thing that makes an atom an atom, the rotationally distributed scalar motion, also causes it to gravitate. Additionally, the same motion is responsible for inertia.

Of course, this return to absolute magnitudes and mathematical rigidity invalidates the conceptual interpretations of Einstein’s solutions of the problems raised by the observed deviations from the consequences of Newton’s theory, and requires finding new answers to these problems. But these answers have emerged easily and naturally during the course of the development of the details of the new theory. In most case no changes in the existing formulation of the mathematical relations have been required. While Einstein’s modification of Newton’s theory was almost entirely mathematical, our modification of the Newton-Einstein system is primarily conceptual, because the errors in currently accepted theory are nearly all in the conceptual interpretation of the observations and measurements; that is, in the prevailing understanding of the *meaning *of the mathematical terms and the relations between them.

The changes that the new theory makes in the conceptual aspects of the gravitational situation do not affect any of the valid mathematical results of Einstein’s theory. For example, most of the mathematical consequences of the general theory of relativity that have led to its acceptance by the scientific community are derived from one of its postulates, the Principle of Equivalence, which states that gravitation is the equivalent of an accelerated motion. In the theory of the universe of motion, gravitation *is *an accelerated motion. It follows that any conclusion that can *legitimately *be drawn from the Principle of Equivalence, such as the existence of gravitational redshifts, can likewise be derived from the postulates of the theory of the universe of motion in exactly the same form.

The agreement between the two theories that exists in these subsidiary areas, and in the mathematical results, does not extend to the fundamentals of gravitation. Here the theories are far apart. The theoretical development reported in the several volumes of this work shows that the attempt to resolve physical issues by mathematical means—the path that has heretofore been followed in dealing with fundamental physics—precludes any significant conceptual* *changes in theory, whereas, as our findings have demonstrated, there are major errors in the basic assumptions upon which the mathematical theories have been constructed.

Until comparatively recently it was not feasible to locate and correct these errors, because access to a large amount of factual information is indispensable to such an undertaking, and the available supply of information was simply not adequate. Continued research has overcome this obstacle, and the development of the theory of the universe of motion has now identified the “machinery,” not only of gravitation, but of physical processes in general. We are now able to identify the common denominator of all of the fundamental physical entities, and by defining it, we define the entire structure of the physical universe.

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