As indicated in the preceding chapter, the concept of a universe of motion has to be elaborated to some extent before it is possible to develop a theoretical structure that will describe that universe in detail. The additions to the basic concept must take the form of assumptionsor postulates, a term more commonly applied to the fundamental assumptions of a theorybecause even though the additional specifications (the physical specifications, at least) obviously do apply to the particular universe of motion in which we live, there does not appear to be adequate justification for contending that they necessarily apply to an possible universe of motion.
It has already been mentioned that we are postulating a universe composed of discrete units of motion. But this does not mean that the motion proceeds in a series of jumps. This basic motion is progression in which the familiar progression of time is accompanied by a similar progression of space. Completion of one unit of the progression is followed immediately by initiation of another, without interruption. As an analogy, we may consider a chain. Although the chain exists only in discrete units, or links, it is a continuous structure, not a mere juxtaposition of separate units.
Whether or not the continuity is a matter of logical necessity is a philosophical question that does not need to concern us at this time. There are reasons to believe that it is, in fact, a necessity, but if not, we will introduce it into our definition of motion. In any event, it is part of the system. The extensive use of the term progression in application to the basic motions with which we are dealing in the initial portions of this work is intended to emphasize this characteristic.
Another assumption that will be made is that the universe is three-dimensional. In this connection, it should be realized that all of the supplementary assumptions that were added to the basic concept of a universe of motion in order to define the essential properties of that universe were no more than tentative at the start of the investigation that ultimately led to the development of the Reciprocal System of theory. Some such supplementary assumptions were clearly required, but neither the number of assumptions that would have to be made, nor the nature of the individual assumptions, was clearly indicated by existing knowledge of the physical universe. The only feasible course of action was to initiate the investigation on the basis of those assumptions, which seemed to have the greatest probability of being correct. If any wrong assumptions were made, or if some further assumptions were required, the theoretical development would, of course, encounter insurmountable difficulties very quickly, and it would then be necessary to go back and modify the postulates, and try again. Fortunately, the original postulates passed this test, and the only change that has been made was to drop some of the original assumptions that were found to be deducible from the others and therefore superfluous.
No further physical postulates are required, but it is necessary to make some assumptions as to the mathematical behavior of the universe. Here our observations of the existing universe do not give us guidance of as definite a character as was available in the case of the physical properties, but there is a set of mathematical principles which, until very recent times, was generally regarded as almost self-evident. The main body of scientific opinion is now committed to the belief that the true mathematical structure of the universe is much more complex, but the assumption that it conforms to the older set of principles is the simplest assumption that can be made. Following the rule laid down by William of Occam; this assumption was therefore made for the purpose of the initial investigation. No modifications have since been found necessary. The complete set of assumptions that constitutes the fundamental postulates of the theory of a universe of motion can be expressed as follows:
Postulates are justified by their consequences, not by their antecedents, and as long as they are rational and mutually consistent, there is not much that can be said about them, either favorably or adversely. It should be of interest, however, to note that the concept of a universe composed entirely of motion is the only new idea that is involved in the postulates that define the Reciprocal System. There are other ideas, which, on the basis of current thinking, could be considered unorthodox, but these are by no means new. For example, the postulates include the assumption that the geometry of the universe is Euclidean. This is in direct conflict with present-day physical theory, which assumes a non-Euclidean geometry, but it certainly cannot be regarded as an innovation. On the contrary, the physical validity of Euclidean geometry was accepted without question for thousands of years, and there is little doubt but that non-Euclidean geometry would still be nothing but a mathematical curiosity had it not been for the fact that the development of physical theory encountered some serious difficulties which the theorists were unable to surmount within the limitations established by Euclidean geometry, absolute magnitudes, etc.
Motion is measured as speed (or velocity, in a context that we will consider later). Inasmuch as the quantity of space involved in one unit of motion is the minimum quantity that takes part in any physical activity, because less than one unit of motion does not exist, this is the unit of space. Similarly, the quantity of time involved in the one unit of motion is the unit of time. Each unit of motion, then, consists of one unit of space in association with one unit of time; that is, the basic motion of the universe is motion at unit speed.
Cosmologists often begin their analyses of large-scale physical processes with a consideration of a hypothetical empty universe, one in which no matter exists in the postulated space-time setting. But an empty universe of motion is an impossibility. Without motion there would be no universe. The most primitive condition, the situation which prevails when the universe of motion exists, but nothing at all is happening in that universe, is a condition in which units of motion exist independently, with no interaction. In this condition all speed is unity, one unit of space per unit of time, and since all units of motion are alikethey have no property but speed, and that is unity for allthe entire universe is a featureless uniformity. In order that there may be physical phenomena that can be observed or measured there must be some deviation from this one-to-one relation, and since it is the deviation that is observable, the amount of the deviation is a measure of the magnitude of the phenomenon. Thus all physical activity, all change that occurs in the system of motions that constitutes the universe, extends from unity, not from zero.
The units of space, time, and motion (speed) that form the background for physical activity are simply scalar magnitudes. As matters now stand, we have no geometric means of representation that will express all three magnitudes coincidentally. But if we assume that the time progression continues at a uniform rate, and we measure this progression by some independent device (a clock), then we can represent the corresponding spatial magnitude by a one-dimensional geometric figure: a line. The length of this line represents the amount of space corresponding to a given time magnitude. Where this time magnitude is unity, the length of the line also represents the speed, the space per unit time.
In present-day scientific practice, the datum from which all speed measurements are made, the point identified with the mathematical zero, is some stationary point in the reference system. But, as has been explained, the reference datum for physical magnitudes in a universe of motion is not zero speed but unit speed. The natural datum is therefore continually moving outward (in the direction of greater magnitudes) from the conventional zero datum, and the true speeds that are effective in the basic physical interactions can be correctly measured only in terms of deviation upward or downward from unity. From the natural standpoint a motion at unit speed is no effective motion at all.
Expressing this in another way, we may say that the natural system of reference, the reference system to which the physical universe actually conforms, is moving outward at unit speed with respect to any stationary spatial reference system. Any identifiable portion of such a stationary reference system is called a location in that system. While less-than-unit quantities of space do not exist, points within the units can be identified. A spatial location may therefore be of any size, from a point to the amount of space occupied by a galaxy, depending on the context in which the term is used. To distinguish locations in the natural moving system of reference from locations in the stationary reference systems, we will use the term absolute location in application to the natural system. In the context of a fixed reference system an absolute location appears as a point (or some finite spatial magnitude) moving along a straight line.
We are so accustomed to referring motion to a stationary reference system that it seems almost self-evident that an object that has no independent motion, and is not subject to any external force, must remain stationary with respect to some spatial coordinate system. Of course, it is recognized that what seems to be motionless in the context of our ordinary experience is actually moving in terms of the solar system as a reference; what seems to be stationary in the solar system is moving if we use the Galaxy as a reference datum, and so on. Current scientific theory also contends that motion cannot be specified in any absolute manner, and can only be stated in relative terms. However, all previous thought on the subject, irrespective of how it views the details, has made the assumption that the initial point of a motion is some fixed spatial location that can be identified as the spatial zero.
But nature is not required to conform to human opinions and beliefs, and in this case does not do so. As indicated in the preceding paragraphs, the natural system of reference in a universe of motion is not a stationary system but a moving system. Inasmuch as each unit of the basic motion involves one unit of space and one unit of time, it follows that continuation of the motion through an interval during which time is progressing involves a continued increase, or progression, of both space and time. If an absolute spatial location X is in coincidence with spatial location x at time t, then at time t + n this absolute location X will be found at spatial location x + n. As seen in the context of a stationary spatial system of reference, each absolute location is moving outward from its point of reference at a constant unit speed.
Because of this motion of the natural reference system with respect to the stationary systems, an object that has no independent motion, and is not subject to any external force, does not remain stationary in any system of fixed spatial coordinates. It remains at the same absolute location, and therefore moves outward at unit speed from its initial location, and from any object that occupies such a location.
Thus far we have been considering the progression of the natural moving reference system in the context of a one-dimensional stationary reference system. Since we have postulated that the universe is three-dimensional, we may also represent the progression in a three-dimensional stationary reference system. Because the progression is scalar, what this accomplishes is merely to place the one-dimensional system that has been discussed in the preceding paragraphs into a certain position in the three dimensional coordinate system. The outward movement of the natural system with respect to the fixed point continues in the same one-dimensional manner.
The scalar nature of the progression of the natural reference system is very significant. A unit of the basic motion has no inherent direction; it is simply a unit of space in association with a unit of time. In quantitative terms it is a unit scalar magnitude: a unit of speed. Scalar motion plays only a very minor role in everyday life, and little attention is ordinarily paid to it. But our finding that the basic motion of the physical universe is inherently scalar changes this picture drastically. The properties of scalar motion now become extremely important.
To illustrate the primary difference between scalar motion and the vectorial motion of our ordinary experience let us consider two cases which involve a moving object X between two points A and B on the surface of a balloon. In the first case, let us assume that the size of the balloon is maintained constant, and that the object X is something capable of independent motion, a crawling insect, perhaps. The motion of X is then vectorial. It has a specific direction in the context of a stationary spatial reference system, and if that direction is BAthat is, X is moving away from Bthe distance XA decreases and the distance XB increases. In the second case, we will assume that X is a fixed spot on the balloon surface, and that its motion is due to expansion of the balloon. Here the motion of X is scalar. It is simply outward away from all other points on the balloon surface, and has no specific direction. In this case the motion away from B does not decrease the distance XA. Both XB and XA increase. The motion of the natural reference system relative to any fixed spatial system of reference is motion of this character. It has a positive scalar magnitude, but no inherent direction.
In order to place the one-dimensional progression of an absolute location in a three-dimensional coordinate system it is necessary to define a reference point and a direction. In the subsequent discussion we will be dealing largely with scalar motions that originate at specific points in the fixed coordinate system. The reference point for each of these motions is the point of origin. It follows that the motions can be represented in the conventional fixed system of reference only by the use of multiple reference points. This was brought out in the first edition of this work in the form of a statement that photons (which, as will be shown later, are objects without independent motion, and therefore remain in their absolute locations of origin) travel outward in all directions from various points of emission. However, experience has indicated that further elaboration of this point is necessary in order to avoid misunderstandings. The principal stumbling block seems to be a widespread impression that there must be some kind of a conceptually identifiable universal reference system to which the motions of photons and other objects that remain in the same absolute locations can be related. The expression natural reference system probably contributes to this impression, but the fact that a natural reference system exists does not necessarily imply that it must be related in any direct way to the conventional three-dimensional stationary frame of reference.
It is true that the expanding balloon analogy suggests something of this kind, but an examination of this analogy will show that it is strictly applicable only to a situation in which all existing objects are stationary in the natural system of reference, and are therefore moving outward at unit speed. In this situation, any location can be taken as the reference point, and all other locations move outward from that point; that is, all locations move outward away from all other locations. But just as soon as moving objects (entities that are stationary, or moving with low speeds, in the fixed reference system, and are therefore moving with high speeds relative to the natural system of referenceemitters of photons, for example) are introduced into the situation, this simple representation is no longer possible, and multiple reference points become necessary.
In order to apply the balloon analogy to a gravitationally bound physical system it is necessary to visualize a large number of expanding balloons, centered on the various reference points and interpenetrating each other. Absolute locations are defined only in a scalar sense (represented one-dimensionally). They move outward, each from its own reference point, regardless of where those reference points may be located in the three-dimensional spatial coordinate system. In the case of the photons, each emitting object becomes a point of reference, and since the motions are scalar and have no inherent direction, the direction of motion of each photon, as seen in the reference system, is determined entirely by chance. Each of the emitting objects, wherever it may be in the stationary reference system, and whatever its motions may be relative to that system, becomes the reference point for the scalar photon motion; that is, it is the center of an expanding sphere of radiation.
The finding that the natural system of reference in a universe of motion is a moving system rather than a stationary system, our first deduction from the postulates that define such a universe, is a very significant discovery. Heretofore only one so-called universal force, the force of gravitation, has been known. Later in the discussion it will be seen that the customary term universal is somewhat too broad in application to gravitation but this phenomenon (the nature of which will be examined later) affects all units and aggregates of matter within the observational range under all circumstances. While not actually universal, it can appropriately be called a general force. In a universe of motion a force is necessarily a motion, or an aspect of motion. Since we will be working mainly in terms of motion for the present, it will be desirable at this point to establish the relation between the force and motion concepts.
For this purpose, let us consider a situation in which an object is moving in one direction with a certain velocity, and is simultaneously moving in the opposite direction with an equal velocity. The net change of position of the object is zero. Instead of looking at the situation in terms of two opposing motions we may find it convenient to say that the object is motionless, and that this condition has resulted from a conflict of two forces tending to produce motion in opposite directions. On this basis we define force as that which will produce motion if not prevented from so doing by other forces. The quantitative aspects of this relation will be considered later. The limitations to which a derived concept of this kind are subject will also have consideration in connection with subjects to be covered in the pages that follow. The essential point to be noted here is that force is merely a special way of looking at motion.
It has long been realized that while gravitation has been the only known general force, there are many physical phenomena that are not capable of satisfactory explanation on the basis of only one such force.
For example, Gold and Hoyle make this comment:
Karl K. Darrow made the same point in a different connection, emphasizing that gravitation alone is not sufficient in many applications. There must also be what he called an antagonist, an essential and powerful force, as he described it.
The globular star clusters provide an example illustrating Darrow's point. Like the formation of galaxies, the problem of accounting for the existence of these clusters is customarily passed over with little comment, by the astronomers, but a discussion of the subject occasionally creeps into the astronomical literature. A rather candid article by E. Finlay-Freundlich which appeared in a publication of the Royal Astronomical Society some years ago admitted that the main problem presented by the globular clusters is their very existence as finite systems. Many efforts have been made to explain these clusters on the basis of motions acting in opposition to gravitation, but as this author concedes, there is no evidence of the existence of motions that would be adequate to establish an equilibrium, and he asserts that their structure must be determined solely by the gravitational field set up by the stars which constitute such a cluster. This being the case, the only answer he was able to visualize was that the clusters have not yet reached the final state of equilibrium, a conclusion that is clearly in conflict with the many observational indications that these clusters are relatively stable long-lived objects. The following judgment that Finlay-Freundlich expressed with respect to the results obtained by his predecessors is equally applicable to the situation as it stands today:
But now we find that there is a second general force that has not hitherto been recognized, just the kind of an antagonist to gravitation that is necessary to explain all of these otherwise inexplicable phenomena. Just as gravitation moves all units and aggregates of matter inward toward each other, so the progression of the natural reference system with respect to the stationary reference systems in common use moves material units and aggregates, as we see them in the context of a stationary reference system, outward away from each other. The net movement of each object, as observed, is determined by the relative magnitudes of the opposing general motions (forces), together with whatever additional motions may be present.
In each of the three illustrative cases cited, the outward progression of the natural reference system provides the missing piece in the physical puzzle. But these cases are not unique; they are only especially dramatic highlights of a clarification of the entire physical picture that is accomplished by the introduction of this new concept of a moving natural reference system. We will find it in the forefront of almost every subject that is discussed in the pages that follow.
It should be recognized, however, that the outward motions that are imparted to physical objects by reason of the progression of the natural reference system are, in a sense, fictitious. They appear to exist only because the physical objects are referred to a spatial reference system that is assumed to be stationary, whereas it is, in fact, moving. But in another sense, these motions are not entirely fictitious, inasmuch as the attribution of motion to entities that are not actually moving takes place only at the expense of denying motion to other entities that are, in fact, moving. These other entities that are stationary relative to the fixed spatial coordinate system are participating in the motion of that coordinate system relative to the natural system. The motion therefore exists, but it is attributed to the wrong entities. One of the first essentials for an understanding of the system of motions that constitutes the physical universe is to relate the basic motions to the natural reference system, and thereby eliminate the confusion that has been introduced by the use of a fixed reference system.
When this is done it can be seen that the units of motion involved in the progression of the natural reference system have no actual physical significance. They are merely units of a reference system in which the fictitious motion of the absolute locations can be represented. Obviously, the spatial aspect of these fictitious units of motion is equally fictitious, and this leads to an answer to the question as to the relation of the space represented by a stationary three-dimensional reference system, extension space, as we may call it, to the space of the universe of motion. On the basis of the explanation given in the preceding pages, if a number of objects without independent motion (such as photons) originate simultaneously from a source that is stationary with respect to a fixed reference system, they are carried outward from the location of origin at unit speed by the motion of the natural reference system relative to the stationary system. The direction of motion of each of these objects, as seen in the context of the stationary system of reference, is determined entirely by chance, and the motions are therefore distributed over all directions. The location of origin is then the center of an expanding sphere, the surface of which contains the locations that the moving objects occupy after a period of time corresponding to the spatial progression represented by the radius of the sphere.
Any point within this sphere can be defined by the direction of motion and the duration of the progression; that is, by polar coordinates. The sphere generated by the motion of the natural reference system relative to the point of origin has no actual physical significance. It is a fictitious result of relating the natural reference system to an arbitrary fixed system of reference. It does, however, define a reference frame that is well adapted to representing the motions of ordinary human experience. Any such sphere can be expanded indefinitely, and the reference system thus defined is therefore coextensive with all other stationary spatial reference systems. Position in any one such system can be expressed in terms of any other merely by a change of coordinates.
The volume generated in this manner is identical with the entity that is called space in previous physical theories. It is the spatial constituent of a universe of matter. As brought out in the foregoing explanation, this entity, extension space, as we have called it, is neither a void, as contended by one of the earlier schools of thought, or an actual physical entity, as seen by an opposing school. In terms of a universe of motion it is simply a reference system.
An appropriate analogy is the coordinate system on a sheet of graph paper. The original lines on this paper, generally lightly printed in color, have no significance so far as the subject matter of the graph is concerned. But if we draw some lines on this sheet that are relevant to the subject matter, then the printed coordinate system facilitates our assessment of the interrelations between the quantities represented by those lines. Similarly, extension space, per se, has no physical significance. It is merely a reference system, like the colored lines on the graph paper, that facilitates cognition of the relations between the significant entities and phenomena: the motions and their various aspects.
The true space that enters into physical phenomena is the spatial aspect of motion. As brought out earlier, it has no independent existence. Nor does time. Each exists only in association with the other as motion.
We can, however, isolate the spatial aspect of a particular motion, or type of motion, and deal with it on a theoretical basis as if it were independent, providing that the rate of change of time remains constant, or the appropriate correction is applied for whatever deviation from a constant rate actually does take place. This ability to abstract the spatial aspect and treat it independently is the factor that enables us to relate the spatial aspect of translational motion to the reference system that we recognize as extension space.
It may be of interest to note that this clarification of the nature of extension space gives us a partial answer to the long-standing question as to whether this space, which in the context of a universe of matter is space in general, is finite or infinite. As a reference system it is potentially infinite, just as number is potentially infinite. But it does not necessarily follow that the number of units of space participating in motions that actually have physical significance is infinite. A complete answer to the question is therefore not available at this stage of the development. The remaining issue will have further consideration later.
The finding that extension space is merely a reference system also disposes of the issue with respect to curvature, or other kinds of distortion, of space, and it rules out any participation of extension space in physical action. Such concepts as those involved in Einstein's assertion that space has the physical property of transmitting electromagnetic waves, are wholly incorrect. No reference system can have any physical effects, nor can any physical action affect a reference system. Such a system is merely a construct: a device whereby physical actions and their results can be represented in usable form.
Extension space, the container visualized by most individuals when they think of space, is capable of representing only translational motion, and its spatial aspect, not physical space in general. But the spatial aspect of any motion has the same relation to the physical phenomena in which it is involved as the spatial aspect of translational motion that we can follow by means of its representation in the coordinate system. For example, the space involved in rotation is physical space, but it can be defined in the conventional reference system only with the aid of an auxiliary scalar quantity: the number of revolutions. By itself, that reference system cannot distinguish between one revolution and n revolutions. Nor is it able to represent vibrational motion. As will be found later in the development, even its capability of representing translational motion is subject to some significant limitations.
Regardless of whether motion is translatory, vibratory, or rotational, its spatial aspect is space, from the physical standpoint. And whenever a physical process involves space in general, rather than merely the spatial aspect of translational motion, all components of the total space must be taken into account. The full implications of this statement will not become apparent until we are ready to begin consideration of electrical phenomena, but it obviously rules out the possibility of a universal reference system to which all spatial magnitudes can be related. Furthermore, every motion, and therefore every physical object (a manifestation of motion) has a location in three-dimensional time as well as in three-dimensional space, and no spatial reference system is capable of representing both locations.
It may be somewhat disconcerting to many readers to be told that we are dealing with a universe that transcends the stationary three-dimensional spatial reference system in which popular opinion places it: a universe that involves three-dimensional time, scalar motion, a moving reference system, and so on. But it should be realized that this complexity is not peculiar to the Reciprocal System. No physical theory that enjoys any substantial degree of acceptance today portrays the universe as capable of being accurately represented in its entirety within any kind of a spatial reference system. Indeed, the present-day official school of physical theory says that the basic entities of the universe are not objectively real at all; they are phantoms which can only be symbolized by partial differential equations in an abstract multidimensional space. 32 (Werner Heisenberg)
Prior to the latter part of the nineteenth century there was no problem in this area. It was assumed, without question, that space and time were clearly recognizable entities, that all spatial locations could be defined in terms of an absolute spatial reference system, and that time could be defined in terms of a universal uniform flow. But the experimental demonstration of the constant speed of light by Michelson and Morley threw this situation into confusion, from which it has never fully emerged.
The prevailing scientific opinion at the moment is that time is not an independent entity, but is a sort of quasi-space, existing in one dimension that is joined in some manner to the three dimensions of space to form a four-dimensional continuum. Inasmuch as this creates as many problems as it solves, it has been further assumed that this continuum is distorted by the presence of matter. These assumptions, which are basic to, in relativity theory, the currently accepted doctrine, leave the conventional spatial reference system in a very curious position. Einstein says that his theory requires us to free ourselves from the idea that co-ordinates must have an immediate metrical meaning.33 He defines this expression a metrical meaning as the existence of a specific relationship between differences of coordinates and measurable lengths and times. Just what kind of a meaning the coordinates can have if they do not represent measurable magnitudes is rather difficult to understand. The truth is that the differences in coordinates, which, according to Einstein, have no metrical meaning, are the spatial magnitudes that enter into almost all of our physical calculations. Even in astronomy, where it might be presumed that any inaccuracy would be very serious, in view of the great magnitudes involved, we get this report from Hannes Alfven:
Our theoretical development now demonstrates that the differences in coordinates do have metrical meaning , and that wherever we are dealing with vectorial motions, or with scalar motions that can be referred to identifiable reference points, these coordinate positions accurately represent the spatial aspects of the translational motions that are involved. This explains why the hypothesis of an absolute spatial reference system for the universe as a whole was so successful for such a long time. The exceptions are exceptional in ordinary practice. The existence of multiple reference points has had no significant impact except in the case of gravitation, and the use of the force concept has sidestepped the gravitational issue. Only in recent years have the observations penetrated into regions outside the boundaries of the conventional reference systems.
But we now have to deal with the consequences of this enlargement of the scope of our observations. In the course of this present work it has been found that the problems introduced into physical science by the extension of experimental and observational knowledge are directly due to the fact that some of the newly discovered phenomena transcend the reference systems into which current science is trying to place them. As we will see later, this is particularly true where variations in time magnitudes are involved, inasmuch as conventional spatial reference systems assume a fixed and unchanging progression of time. In order to get the true picture it is necessary to realize that no single reference system is capable of representing the whole of physical reality.
The universe, as seen in the context of the Reciprocal System of theory, is much more complex than is generally realized, but the simple Newtonian universe was abandoned by science long ago, and the modifications of the Newtonian view that we now find necessary are actually less drastic than those required by the currently popular physical theories. Of course, in the final analysis this makes no difference. Scientific thought will have to conform to the way in which the universe actually behaves, irrespective of personal preferences, but it is significant that all of the phenomena of a universe of motion, as they emerge from the development of the Reciprocal System, are rational, clearly defined, and objectively real.