# CHAPTER 5

# Further Fundamentals

To the earliest thinkers whose ideas are known to us, the directly apprehended world was always inferior to the vast unknown that, they believed, lay beyond it. When so little was known as to the causes of physical phenomena, even the most trivial events could be explained only on the basis of supernatural intervention. In the long march of science from its beginnings more than three thousand years ago to the present era, one after another of these events has been found to be explainable on purely physical grounds. As a result, the pendulum has swung to the other extreme. The currently prevailing opinion not only denies the existence of anything outside the directly apprehended world, but places that world entirely within the limits of the conventional spatio-temporal reference system. According to this present view, the universe exists* in *three-dimensional space, and* in* clock time.

Recognition of the existence of scalar motion makes this view of the universe untenable. Vectorial motion is confined to the conventional reference system because it is, by definition, motion relative to that system. But scalar motion, which has magnitude only, and no inherent relation to the reference system (although, under appropriate conditions, it may *acquire* such a relation by means of an independent process of coupling), is not limited by the reference system. As we saw in the preceding chapter, scalar motion extends into two additional speed ranges beyond the one-dimensional limit at the speed of light to which motion within the reference system is subject. What we will now want to do is to examine the characteristics of motion in these higher speed ranges. As an avenue of approach to this subject we will consider the question of *units*.

It has been found experimentally that electric charge exists only in discrete units. As we saw earlier, charge is simply a name for a one-dimensional distributed scalar motion. It has some properties that are not shared by all one-dimensional scalar motions, but these are properties of the distribution, the variable coupling to the reference system, not inherent properties of the scalar motion itself. From the standpoint of the inherent nature of the motion, all one-dimensional scalar motions are alike. It then follows that the limitation to discrete units applies to *any* one-dimensional scalar motion. Furthermore, there is no distinction between scalar dimensions. Consequently, the limitation applies to scalar motion in general. We thus arrive at this general principle: *Scalar motion exists only in discrete units*.

This conclusion necessarily follows from the observed limitation of electric charge to discrete units. As a necessary consequence of an observed fact, it is itself factual, and does not require confirmation from other sources. Ample confirmation is, however, available. There is substantial evidence for the existence of discrete units of magnetism, two-dimensional distributed scalar motion. The discrete nature of the atoms and particles of matter, the objects that gravitate—that is, experience three-dimensional distributed scalar motion—has been recognized ever since the days of Democritus. The photons of radiation produced by motion of these atoms and particles are likewise discrete units.

The units of charge are *uniform*. The considerations previously discussed in relation to the discrete nature of the units apply with equal force to the uniformity. We may therefore extend the previous statement, and say that scalar motion exists only in * uniform discrete units*.

From one viewpoint, all physical facts have equal standing, inasmuch as a conflict with any one of them brands a theory or belief as invalid, at least in part. However, some of these facts have much more significant consequences than others, and can legitimately be described as *crucial facts*. The existence of distributed scalar motion is one of these. As has been demonstrated in the preceding pages, recognition of this fact opens the door to a wide variety of significant advances in the understanding of important physical phenomena. Furthermore, it sets the stage for recognition of other facts, some of which have consequences that are sufficiently far-reaching to justify including these facts in the crucial category. The existence of multidimensional scalar motion is one of those that is entitled to be so classified. As will be seen in the pages that follow, the fact that we have just recognized—that scalar motion exists in discrete units only also belongs in this same class. It provides the key item of information that we need in order to make it possible to explore the regions of the universe outside (that is, independent of) the region that is capable of representation in the conventional three-dimensional spatial reference system.

Again, as in Chapter 4, it seems advisable to emphasize the purely factual nature of the presentation, even at the risk of seeming unduly repetitious. A number of the conclusions that will be reached by the factual development in the pages that follow are identical with the conclusions reached in the previous theoretical investigation. The discrete unit limitation, for instance, is one of the basic features of the theory of a universe of motion, as set forth in the previous theoretical publications. Consequently, the conclusions reached in this and the subsequent chapters from the application of this limitation derived from factual premises are also produced in the theoretical development of the motion concept. Because of this agreement on results of a decidedly unconventional nature, there may be a tendency to take it for granted that some theoretical considerations must have entered into the present development of thought. This is not correct. The only way in which the theoretical study has entered into the development in this volume is by providing clues as to where to look for the facts. Of course, this is a significant contribution. In looking for previously unrecognized facts, as in looking for buried treasure, it is extremely helpful to have a map. But the status of what we find, in either case, is not affected in any way by the amount of assistance that we were given toward finding it.

The previous investigation was *purely* theoretical. All conclusions were reached entirely by application of logical and mathematical processes to the postulates of the system, without introducing anything from experience. The objective of this present volume, on the other hand, is to present the maximum amount of information regarding the role of scalar motion in the physical universe that can be derived *without* introducing any theoretical considerations, so that the information about scalar motion will be available to all who are interested in the subject matter, whether or not they are ready to go along with a drastic revision of physical fundamentals.

The limitation of scalar motion to discrete units does not mean that this motion proceeds in succession of jumps. A uniform motion is a continuous progression at a uniform rate. Because the motion is *continuous*, there is a progression within each unit, and one unit follows another without interruption. The discrete unit limitation imposes two restrictions. First, the continuity of the progression can be broken only at a junction between units. Fractional units are therefore impossible. Second, any process taking place within a unit cannot carry forward into the next unit.

A chain is an analogous structure. It is composed of discrete units called links, yet it is a continuous entity, not a mere juxtaposition of the links. There are no fractional links. An incomplete link serves no purpose, and is not part of the chain. Properties such as crystal structure do not carry forward from one link to the next. The analogy with scalar motion in this respect could be made even more complete by electrically and thermally insulating the links from each other, as the temperature and electrical conditions existing in each link would then also be independent of those of its neighbors.

The absence of fractional links in the chain does not prevent us from *identifying* different parts of a link, or from utilizing fractions of a link for purposes such as measurement. For example, we can identify the midpoint of a link, and measure a distance of 10½ links, even though there are no half links in the chain. The same principles apply to the discrete units of scalar motion. We can deal with positions and events within a unit on an abstract basis, even though they do not actually exist independently of the unit as a whole.

Scalar motion, as we have seen, has no property other than magnitude. It is a relation between a space magnitude and a time magnitude. Now we further find that these magnitudes occur only in discrete units; that is, we are dealing only with integers. Space and time, so far as they enter into scalar motion, are simply integral numbers of units, reciprocally related, and not otherwise defined. Whether or not they have any other properties in vectorial motion, or in any other connection, is a question that is beyond the scope of this work, which is addressed to scalar motion only. In motion of this type, neither space nor time has any properties other than those appertaining to its status in motion, and time is reciprocally related to space. It follows that the properties of scalar motion are simply the properties of reciprocals. These properties are well known in mathematical terms. All that we need to do, therefore, in order to describe the properties of scalar motion under any particular set of circumstances is to translate the mathematical statement of these properties into the language applicable to motion.

Those who are reluctant to accept the finding that time has the status of reciprocal space in scalar motion, because it conflicts with their ideas as to the inherent nature of time, should realize that those long-standing ideas are not scientifically based. This new finding does not conflict with scientific views as to the nature of time, because there are no such views. The nature of time has always been a mystery to science. About all that is known is that time enters into the equations of physics as a variable, and that in some way it moves by us, or we move through it, from the past, to the present, and on into the future. The familiar expression “the river of time” is a reflection of this subjective impression that we get from experience.

Present-day science accepts this vague subjective impression as the definition of time for scientific purposes “without examination,”^{61} as Richard Tolman puts it. R. B. Lindsay admits that the “notions of space and time” employed by science are “primitive, undefined concepts,” but contends that “more precisely defined constructs”^{62} can be developed, in some unspecified way, farther down the line. Vincent E. Smith is indignant at the suggestion that scientists should be required to define these concepts before using them. “Surely,” he says, “mathematical physicists are exempted from defining such realities as space and time and free to concentrate on only their mathematical aspects.”^{63} Other investigators are beginning to realize that this uncritical acceptance of a “primitive, undefined concept” of time as one of the cornerstones of physical science is incompatible with good scientific practice, and are expecting some changes. The following are typical comments:

And perhaps as the domain (of our experience) is broadened still further we may well have to modify our conceptions of time (and space) yet more to enrich them, and perhaps to change them radically.”

^{64}(David Bohm)Perhaps we are here on the edge of the discovery of a new law of physics that determines how the other fundamental laws depend on time. !t is my feeling that such a law must obviously contain time as one of its basic elements.

^{65}(G. L. Verschuur)

It is true that space and time appear to be very different. In contrast to the continuing movement that characterizes time, as we observe it, space appears to be an entity that stays put. But the clarification of the relation between space and time in scalar motion throws a new light on the meaning of these observations. The key factor in the situation is the status of unit speed.

The magnitude of a unit of scalar motion is one unit of space per unit of time; that is, unit speed. And since scalar motion exists only in units, its magnitude (speed) on an individual unit basis is *always *unity. However, this magnitude may be either positive or negative, and it is therefore possible to generate net speeds differing from unity by periodic reversals of the scalar direction. As noted in Chapter 1, a continuous and uniform change of direction is just as permanent as a continuous and uniform change of position.

In order to arrive at a negative speed, the reversal of direction must apply to only one component (space or time). Coincident reversals of both components would leave the quotient, the speed, positive. Thus a negative scalar motion is inward either in space or in time, not both. Introduction of reversals of scalar direction in time reduces the net time magnitude without altering the space magnitude, and thus increases the speed, the ratio of space to time. Similarly, introduction of reversals of scalar direction in *space* reduces the net space magnitude without altering the time magnitude, and thus increases the ratio of time to space, the *inverse speed*.

From the foregoing it follows that the minimum amount of space that can be traversed in one unit of time is one unit. Anything less than one unit would involve an integral number of units of time per unit of space. This is not speed, but inverse speed, and it cannot be produced by the kind of a process, reversal of scalar direction in time, that produces speed. The minimum speed is therefore unity. Similarly, the minimum inverse speed is likewise unity. In the familiar vectorial type of motion, on the other hand, the minimum speed is zero. Here the condition of rest is zero speed, and effective vectorial speeds are measured from this zero level. Now we see that in a reciprocal speed system the condition of rest, the condition from which effective scalar speed (or inverse speed) magnitudes extend is unity, not zero.

Unit speed is thus the *natural reference level* for scalar motion, the reference level to which the scalar motion of the universe actually conforms. In other words, the reference system for scalar motion is not our stationary spatio-temporal reference system, but a system that is moving at unit speed relative to that stationary system. Both space and time are moving. While “now” moves forward in the manner to which we are accustomed, “here” is moving forward in exactly the same manner. There is no distinction between reciprocal integers.

What this means in practice is that any object that has no capability of independent motion, and is not acted upon by any outside agency, so that it must remain in its original position, retains its position in the natural reference system, the system recognized by nature, not in the conventional fixed coordinate system, which is a purely arbitrary system selected by human beings for their own convenience. Such an object is carried outward at unit speed relative to the fixed reference system by the motion of the natural system of reference. We are not conscious of the outward progression of space, as we are of the progression of time, because the spatial movement is ordinarily masked by an opposing gravitational motion of the aggregate of matter from which we are doing our observing, but any object that is * not* subject to an appreciable gravitational effect, such as a photon, or a galaxy at an extreme distance, is observed, or deduced by extrapolation, to be moving outward at unit speed (which we can identify as the speed of light), as required by the conclusion that we have just reached from purely factual premises.

We will want to follow the presentation of this evidence that space has the characteristic property of time, the constant progression, with evidence that time has the characteristic property of space, extension into three dimensions. This will require development of another of the consequences of the reciprocal speed relation, and before beginning discussion of this new subject matter it will be desirable to give some further consideration to the question of the nature of reference systems, which has already been introduced.

The reference system in general use, both by scientists and by the public at large, is an arbitrary system. This arbitrary spatio-temporal system recognizes the scalar progression of time, and treats time as continually moving forward at a rate indicated by a clock. The observable spatial motions are mainly motions relative to some particular object, or set of objects, and, for convenience, these objects are treated as stationary for definition of the reference system. The surface of the earth is taken as stationary in most common usage. For other purposes, the center of the earth is assumed to be stationary, while the astronomers find it convenient to use still other arbitrary fixed points.

The justification for the use of an arbitrary reference system of this kind is that the only significant magnitudes under the circumstances of observation are the deviations from the condition taken as a base for the reference system. In dealing with motion on the surface of the earth, for example, we are not concerned with the movement of the earth around the sun, or the movement of the solar system around the center of the galaxy, in which all objects on the earth’s surface are participating. These motions are irrelevant because they do not change the relative positions of the objects in which we are interested. When we undertake to analyze fundamental motions, the situation is quite different. In order to evaluate these motions, we must have a reference system relative to which an isolated object with no inherent motion does not move.

The orthodox doctrine at present is that there is no such reference system, because, it is contended, motion is relative, rather than being a specific deviation from some motionless absolute base. “There is no meaning in absolute motion,”^{66} is the assertion of those who follow Einstein in this respect. But this view encounters serious difficulties. The fixed stars do provide a background to which observations can be referred. Indeed, those who attempt to explain away the various “paradoxes” to which relativity theory is subject often call upon “acceleration relative to the fixed stars”^{67} as a way out of their difficulties. Richard Feynman likewise resorts to astronomy to provide a fixed reference system, as in the following statement:

We cannot say that all motion is relative. That is not the content of relativity. Relativity says that uniform velocity in a straight line relative to the nebulae is undetectable.

^{68}Werner Heisenberg offers this comment:

This is sometimes stated by saying that the idea of absolute space has been abandoned. But such a statement has to be accepted with great caution…. The equations of motion for material bodies or fields still take a different form in a “normal” system of reference from another one which rotates or is in a non-uniform motion with respect to the “normal” one.^{69}

The key to an understanding of this rather confused situation is a recognition of the place of scalar motion in the picture. As long as “motion” is taken to be synonymous with “vectorial motion,” all motion is, by definition, relative to something arbitrary, and no absolute reference system can be defined. But the assumption that all motion is vectorial motion is not valid. Scalar motion does exist, and it does have an absolute datum level, or effective zero, at unit positive (outward) speed. When a negative scalar motion at unit speed is superimposed on the basic unit positive speed, the net result is a speed that is *mathematically* equal to zero (as distinguished from unit speed, which is the physical datum, or condition of rest, the physical zero, we might say). A set of objects with speeds of zero (mathematically) constitutes a reference system that is absolute in nature, and is appropriate for use by the inhabitants of the sector of the universe in which we live, although as indicated earlier, such a reference system is capable of representing only a very limited portion of the total physical universe. The distant astronomical objects, whose vectorial motions are negligible because of the great distances intervening, constitute such a stationary system.

For analytical purposes, we need to recognize that the zero datum of this fixed system is a composite, and that the datum level of the *natural* reference system is defined by the one-to-one space-time ratio (speed) of the fundamental units. As seen in the context of the fixed spatial coordinate system, the natural reference system appears as a uniform outward progression of space coinciding with a uniform increase in the registration on a clock. Thus, when no physical interaction is taking place, all objects that appear stationary in a fixed reference system are, in fact, moving inward at unit speed. Objects such as photons, that have no capacity of independent motion and must remain in the same absolute location (the same location in the natural reference system) in which they originate, are carried outward relative to the fixed reference system, at this same unit speed, by the progression of space.

This is the background pattern of the scalar motions of the universe. The development that follows, in which independent physical activity will be introduced, will proliferate rapidly into a wide variety of significant conclusions, and unless the successive steps in the development of thought are specifically noted, it may be hard to believe that so many consequences would necessarily follow from such a limited set of factual premises. It therefore needs to be emphasized at the outset that all of these conclusions are so derived, without bringing in any assumptions or theories, and that they all have the factual status.

The fundamental physical action of the universe is a result of the existence of independent units of scalar motion, the net effect of which is to oppose the outward progression of the natural reference system. If that outward motion continues unimpeded, there can be no interaction between units. Nor can any interaction result from independent motion in the outward direction superimposed on the outward progression, as this, if possible, would merely accelerate the dispersal of the units. But independent motion in the inward scalar direction is capable of bringing the units close enough together to permit interaction. The requirement that the net motion of the independent units must be directed inward means that the *basic* independent scalar motion must have the inward scalar direction. This basic motion can be identified as gravitation.

A gravitating object, moving outward by reason of the progression of the natural reference system, and inward by reason of gravitation, may acquire additional independent motions of a different character. As indicated earlier, the net resultant of a combination of motions may be either a *speed*, which, on a one-dimensional basis, is one unit of space per n units of time, or an *inverse speed*, n units of space per unit of time (intermediate values are produced by combination with units having the full one-to-one space-time ratio.) A speed, 1/n, decreases the amount of space per unit time below the normal unit ratio, thus causing a change of position in space, while the time progression continues at the normal rate. Such motion is* motion in space*.

An important feature of a reciprocal system is that it is symmetrical around the unit level. The temporal relations in scalar motion are therefore subject to the same general considerations as the spatial relations, but recognition of this fact has been blocked by erroneous ideas as to the relation of space and time. Up to about the beginning of the present century it was generally believed that space and time are independent. The increase in knowledge since then has revealed that this is incorrect, and that there is actually some kind of a connection between the two. The current opinion is that one dimension of time joins with three dimensions of space in some manner to form a four-dimensional space-time continuum. The role of time in this hypothetical four-dimensional structure is vague. In order to constitute an added dimension of the spatial structure, time must be some kind of a quasi-space, but just how its spatial aspect is supposed to differ from ordinary space is not specified in current theory. Actually, it is difficult to see how one dimension of an n-dimensional structure could differ from another in *any* way other than in magnitude, if the results of calculations involving different dimensions are to have any meaning.

In any event, the discrete unit limitation leads to a quite different view of the space-time relation, as we have seen. Like the theory that calls for the propagation of the gravitational effect through a medium-like space, and the other theories that are in conflict with the *facts* disclosed by the scalar motion investigation, the four-dimensional space-time concept will therefore have to be discarded. It should be noted, however, that neither this nor the modifications of current thought required by the findings reported in the earlier chapters amount to a wholesale rejection of present-day physical theory. The fabric of that theory is such that there is only a minimum amount of connection between its various parts. As described by Feynman, “the laws of physics are a multitude of different parts and pieces that do not fit together very well.”^{32} This absence of positive connections is, of course, a weakness in the body of theory, but it is nevertheless advantageous in the present instance, as it enables excluding those aspects of existing thought that are in conflict with the factual results of the scalar motion investigation without affecting much of the remainder of accepted theory.

Because of the symmetry around the unit speed level, the conclusions that were reached with respect to scalar motion with speed 1/n also apply, in inverse form, to motion with inverse speed 1/n, equivalent to speed n/1. This inverse speed increases the amount of space per unit time; that is, it alters positions in time while the space progression takes place at the normal rate. Motion at inverse speeds is thus *motion in time*.

It is true that no evidence of such a property of time is now known to science. However, all that this means is that the existing evidence is not currently recognized as such. As we saw in

Chapter 2, it has been found that there is a serious discrepancy between the “time” that is registered on a clock and the “time” that enters into the equations of motion. Now we further find that the clock registers only the time of the progression of the natural reference system, while the total time involved in motion from one location to another includes the separation in time between the locations. This separation is negligible at low speeds, but is significant at high speeds. Here is the alternative that Einstein overlooked when he concluded that “there is no other way” of meeting the situation disclosed by the measurements at high speeds but to abandon the concept of absolute magnitudes.

Inasmuch as the universe is three-dimensional (a fact of observation), position in space is position in three-dimensional space. The position in time that is altered by motion in time is the same kind of a position, differing only in its reciprocal nature. Motion in time has no direction in space, but it has a property that corresponds to spatial direction, and can logically be called direction in time. Position in time is therefore position in *three-dimensional time*.

Here, then, we have demonstrated the other half of the proposition, stated earlier in this chapter, that each of the components of motion has the principal property of the other. The findings previously discussed showed that the principal characteristic of time, its continual progression, is likewise a property of space. Now, by deduction from factual premises, it has been shown that the principal characteristic of space, its three-dimensional extension, is also a property of time.

Because of the particular location from which we view physical events, the two situations *appear *quite different. We observe the time progression directly, and detect the independent motion in time only by its effect on the magnitudes of certain physical quantities. In the spatial situation the reverse is true. We observe the independent motion in space directly, and detect the space progression only by its effect on some physical quantities. The reason for this difference is that we who are observing these phenomena exist in a sector of the universe in which changes of position take place in space. In this *material sector*, as we will call it, all material objects are, as we know from observation, moving inward gravitationally in space. This inward gravitational motion counterbalances the outward progression of the natural reference system, and leaves us approximately at rest relative to a fixed spatial coordinate system. From this vantage point we are able to detect the independent motion in space, but we cannot observe the space progression directly.

An important consequence of the existence of motion in three-dimensional time on a basis coordinate with that of motion in three-dimensional space is that there is an inverse sector of the universe, the *cosmic sector*, we will call it, similar to our own material sector, but differing in that space and time are interchanged. If there are observers in this sector, they can observe the space progression and the independent motion in time directly, but they can detect the time progression and the independent motion in space only by their effect on the magnitudes of certain physical quantities.

This is a region of the universe of the kind mentioned earlier, one that is not capable of representation in the conventional spatial reference system. One dimension of the motion in this cosmic sector could, however, be represented in a temporal reference system analogous to the spatial system. Such a reference system would consist of a three-dimensional pattern of time coordinates, in which changes of position in time take place during the continuous outward progression of space, measured by a device analogous to a clock.

In this present discussion we are dealing with scalar motion only, but it can be deduced that at least some of the vectorial motions that take place within our familiar spatial reference system are duplicated in the cosmic sector. Without extending the investigation to the details of vectorial motion, which, as matters now stand, is not feasible without a theoretical analysis, we cannot say that *all* of the vectorial phenomena of the material sector are so duplicated, but in view of the reciprocal relation between space and time in scalar motion, we can say that this is true of all scalar motion phenomena, including gravitation. The existence of gravitation requires the existence of matter in corresponding amounts. Thus matter, too, is duplicated in the cosmic sector. Inasmuch as the probability of a deviation in the temporal direction, speed n/1 , from the scalar speed datum, 1/1 , is equal to the probability of a deviation in the spatial direction, speed 1/n, the quantities of all of these entities that do exist in the cosmic sector are commensurate with the quantities of the corresponding entities in the material sector. The cosmic sector is thus coextensive with the material sector, whether or not it is an exact duplicate (another point that requires a theoretical analysis). Here, then is a second full-scale division of the universe.

This is a far-reaching conclusion of great importance, one that, at a single stroke, doubles the size of the universe. The general reaction to a new idea of this magnitude is one of considerable skepticism, but the existence of an “antiuniverse” is clearly suggested by a number of recent additions to physical knowledge, and has been the subject of numerous speculations. As expressed by Asimov:

Somewhere, entirely beyond our reach or observation, there may be an anti-universe made up almost entirely of antimatter.

^{70}

The results of the investigation reported herein have now identified the reality behind these speculations. The existence of this “anti” (actually inverse) sector of the universe is a necessary consequence of the facts about scalar motion that have been ascertained in the course of an intensive investigation, and presented in the preceding pages. Furthermore, the key conclusions in this factual line of development are corroborated by observational evidence. Direct observation of the inverse phenomena is not possible because the cosmic sector is almost entirely outside our observational range. The reason for this is that the entities and phenomena of that sector are distributed throughout three-dimensional time. The various physical processes to which matter is subject alter positions in space independently of positions in time, and vice versa. As a result, the atoms of a material aggregate, which are contiguous in space, are widely dispersed in time, while the atoms of a cosmic aggregate, which are contiguous in time, are widely dispersed in space.

It should be noted that the dispersion takes place in the space and time of the respective three-dimensional reference systems, and does not alter the position in the space-time progression (the outward motion of the natural reference system). The limitation of the concentration of matter to either space or time, not both, effectively separates the material (space) sector of the universe from the cosmic (time) sector. We of the material sector are moving through three-dimensional time in one scalar dimension—a one-dimensional line of progression—and as a consequence, only a relatively small proportion of the cosmic phenomena come within the range that is accessible to us. Furthermore, since the components of cosmic aggregates are contiguous in time, not in space, the cosmic phenomena that we do encounter are not in the forms in which they can be recognized as counterparts of the known phenomena of the material sector. Physical phenomena are primarily interactions of aggregates, or of concentrated radiation from aggregates, and the aggregates of one sector are not recognizable as such in the other.

We can, however, deduce the forms in which certain phenomena of the cosmic sector will appear in our reference system, and we can then compare these deductions with the results of observation. We can deduce, for instance, that electromagnetic radiation is being emitted from an assortment of sources in the cosmic sector, just as it is here in the material sector. Radiation moves at unit speed relative to both types of fixed reference systems, and can therefore be detected in both sectors regardless of where it originates. Thus we receive radiation from cosmic stars and other cosmic objects just as we do from the corresponding material aggregates. But these cosmic objects are not aggregates in space. They are randomly distributed in the spatial reference system. Their radiation is therefore received in space at a low intensity and in an isotropic distribution. Such a background radiation is actually being observed. It is currently attributed to remnants of the Big Bang, but there is no real evidence as to how it originates. The significant fact in the present connection is that the consequences of the existence of scalar motion in discrete units * require* a radiation of this nature.

The same considerations also account for the apparent absence of “antimatter” in the expected quantities. All current physical theories (including the theory of a universe of motion) incorporate symmetries from which it can be concluded that matter in the ordinary form and in some “anti” form should exist in approximately equal quantities. There is no observational evidence of the existence of * any* antimatter aggregate, and the question, “Where is the antimatter?”, has become a serious issue for the physicists and the astronomers. This present development supplies the answer. The matter of the cosmic sector is inversely related to the matter of the material sector; it is the missing antimatter. Since the cosmic sector is the inverse of the material sector, and coextensive with it, cosmic matter is just as plentiful in the universe as a whole as ordinary matter, but because it is aggregated in time rather than in space, we do not meet it in the form of stars, or galaxies, or even small lumps. We meet it only one atom at a time, and because of the very small portion of the three-dimensional expanse of time that ever comes within our observational range, we encounter only a limited number of these atoms. These are the cosmic rays. The answer to the antimatter question then is: It exists, but most of it is outside our range of observation.

Antimatter itself is accepted as a reality. All current physical theories define the structure of matter in such a way that the units atoms and particles—of which the material aggregates in our environment are composed are paralleled by a series of similar units of an “anti” nature. Some of the less common observed units have been identified as members of this antimatter class, and the existence of aggregates of antimatter is asserted by most theories, although there is no observational evidence of such aggregates. Since matter is one of the principal features of the known physical universe, the general agreement as to the existence of antimatter goes a long way toward acceptance of an anti-universe, such as the inverse sector that we find exists.

The reciprocal relation between space and time in scalar motion, from which the conclusions outlined in the foregoing paragraphs are derived, is simply the relation between the numerator and denominator of a fraction, and it is incontestable, but it is worthwhile mentioning that the reciprocity clearly does hold good in the only relation between space and time that is actually known observationally: the relation in motion itself. In motion, more space is the equivalent of less time. It makes no difference whether we travel twice as far in the same time, or take half as much time to travel the same distance. The effect on the speed, the measure of the motion, is the same in both cases. The significance of this point has been obscured to some extent by the fact that direction, in our ordinary experience, is a property of space only, and this seems to distinguish the space aspect of motion from the time aspect. Recognition of the existence of scalar motion changes this situation, as it shows that vectorial direction is not an essential property of motion. When it is realized that there are some motions without an inherent direction, and some that have direction in space, the conclusion that there are still others that have direction in time follows suite naturally.

Although the concept of three-dimensional time, and the many important consequences that result from its existence, may seem to involve a major departure from previous scientific thought, a review of the progress in this field in the past hundred years shows that the thinking of the scientific profession has been gradually moving in this direction. As in some of the problems discussed earlier, the first step was taken by Einstein. Before his day, it was generally agreed that the time applicable in one location is applicable everywhere, and under all conditions. Einstein found that this led to inconsistencies under some conditions, particularly at high speeds. He therefore rejected the idea of universal simultaneity, and introduced the assumption that two events simultaneous in one system of coordinates are not simultaneous in a relatively moving system. On the basis of this hypothesis, the rate of progression of time, instead of being constant, varies with the speed of movement.

Many of those who have accepted Einstein’s view of the relativity of simultaneity, and have tried to explain it in textbooks or otherwise, have (perhaps unknowingly) improved upon the original ideas, and have come very close to seeing the situation in the light in which it now appears as a result of the findings of the scalar motion investigation. For instance, Marshall Walker puts the case in this manner:

It had been assumed that an absolute time existed such that any timers anywhere could be synchronized with it. Nature was pointing out most emphatically that such absolute time does not exist. We will see later that it is as nonsensical to expect in general to find the same “time” at two different places as it is to expect to find the same “point” at two different places.

^{71}

Here Walker draws an analogy between the “point” (that is, location in space) at a “place,” and the “time” (that is, location in time) at a “place.” The analogy thus recognizes that there are locations in time, just as there are locations in space. It follows that there is a difference in time between any two such time locations. All this is in accord with the findings described in the preceding pages. But Walker stopped here and did not take the next logical step, recognition of the fact that the differences in time between the various locations are independent of the time registered on a clock.

Identification of the properties of scalar motion now reveals that the true explanation of the difference in time between stationary and moving systems is not that simultaneity is relative, but that two different time components are involved. Clock time is a measure of the *time **progression*, and since this is simply the outward movement of the natural frame of reference, all locations in the universe are at the same stage of the progression. Thus the pre-Einstein view of time is correct to this extent. The time component of the progression of the natural reference system conforms to Newton’s view of the nature of time in general. The problems that have arisen in applying clock time to high speed processes are not due to any variability in clock time itself, but to the fact that the total time entering into these processes includes an additional component of an independent nature: the difference in time between the locations that are involved. The requirement in Einstein’s theory that the clock must indicate the * total* time amounts to a demand that this device, which performs one operation (measuring the relative motion of the two reference systems) when stationary, must take on an additional task of a different kind (measuring the difference in time between locations) when it is moving.

The possibility of motion in time has been a subject of speculation for centuries, and is a favorite in the science fiction field. It is generally rejected by scientists, not because there is any actual evidence that rules it out, but because this idea conflicts with the subjective impression of time as a continual flow. The option of rejection is no longer open. The existence of motion in time is now seen to be a necessary consequence of observed physical facts, and it is therefore itself factual. The status of scalar motion as a reciprocal relation between integers requires the existence of a system of scalar motions in time symmetrical with the scalar motions in space. Motion in time is now one of the known features of the universe with which all theories and all individual viewpoints must come to terms.

It should be noted, however, that the kind of motion in time, or “time travel,” that the science fiction writers envision, and that most individuals think of when the subject is mentioned, is movement along the line of the scalar progression; that is, travel to an earlier or later era. In the light of the findings of this work, time travel of that nature is impossible. The time progression is a result of the motion of the natural reference system relative to the fixed reference system, and it is therefore not subject to any kind of modification. The motion in time that is being discussed here involves a change of position in three-dimensional time independent of, and coincident with, the change of time position due to the progression of the natural reference system. It is analogous to the change of position within one of the distant galaxies due to motion in space, while the time registered on a clock is analogous to the space traversed in the recession of the galaxy.

The possibility of returning to the time and place of a past event, one of the favorite goals of the “time travel” enthusiasts, is definitely excluded. We are already aware that this objective cannot be accomplished by travel in space. It is possible, in principle, to return to any specified point in space, but we cannot return to the same place at the same time. We can only reach it at some later time. Travel in time is subject to exactly the same kind of a limitation (another result of the reciprocal relation). It is possible, in principle, for an object capable of existing at the speeds of the cosmic sector to return to any specified point in time by means of time travel, but this point cannot be reached at the same place. It can only be reached at some more distant location.

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