## CHAPTER 3## Reference SystemsAs 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 assumptions–or postulates, a term more commonly applied
to the fundamental assumptions of a theory–because 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 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 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 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 alike–they have no property but speed, and that is unity for all–the
entire universe is a featureless uniformity. In order that there may 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 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
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 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 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 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 BA–that is, X is moving away from B–the 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 In order to place the one-dimensional
progression of an absolute location in a three-dimensional coordinate
system it is necessary to define a 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 reference–emitters 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 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 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 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. 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.”
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.” |