As reported in the October 1977 issue of *Reciprocity*, I am now in the process of preparing the first volume of a revised edition of the book in which I introduced the Reciprocal System of theory, *The Structure of the Physical Universe*, a book which has been out of print for several years. As the successive chapters of the manuscript are completed, I have been circulating them for review and comment by a number of those members of the New Science Advocates with whom I have corresponded on the subject matter. One point that is already evident from the first comments that have Been received is that it will be necessary to go into more detail in the discussion of the way in which our apprehension of the basic physical motions is affected our choice of a reference system. I had already recognized this to the extent to including a chapter entitled “Reference Systems” in the draft of the revision that is now being circulated, but it seems clear from the comments that some aspects of the situation will require further clarification. I therefore intend to make some additions to the manuscript, but in the meantime a review of the principal points at issue may be of interest to the readers of *Reciprocity*.

The first point to be noted is that whether or not an object is in motion, and the amount of that motion, if any, depends on the reference system. An object which is stationary in one reference system is moving in any reference system that is in motion relative to the first system. Whether we see the motion of the object as a complex motion, a simple motion, or no motion at all depends on the reference system to which we relate it. One of the important findings of modern physics, confirmed by the Reciprocal System, is that there is no *absolute* reference system. No stationary reference system that we may select has any valid claim to superiority over another.

Another significant finding is that a reference system for motion necessarily includes a time datum as well as a space datum. For most ordinary purposes we refer changes in spatial position to the surface of the earth, but we realize that these motions would have some very different aspects if we adopted a different reference system, one based on the sun, for example. The development of the Reciprocal System of theory now shows that for a complete definition of a motion we must also specify position in time relative to some selected reference system, This is the fundamental fact that has heretofore gone unrecognized because it has been assumed (”without examination,” as one prominent physicist puts it) that time always progresses uniformly at the rate indicated by a clock. On the basis of this assumption, the time registered by a standard clock is the same at all points in space. This makes it possible to represent motion in a coordinate system which provides only for variability in the three dimensions of space; that is, a *spatial* coordinate system. When we are dealing only with relatively low velocities this is satisfactory, as the deviations from clock time at these velocities are negligible. At high velocities, on the other hand, the true rate of change of position in time is different from the rate indicated on a standard clock. In this case the conventional assumption that the standard clock registration is a correct measure of the change in time position is wrong, and it introduces an error.

The point that we now need to realize is that when we select some physical object, such a, the earth, to define a spatial reference system, we are, by the same act, utilizing the position of the earth in time to define a temporal reference system. If an object A is ejected from the earth with a speed x this means that the change in the position of that object in space relative to the earth‘s location in space divided by the elapsed clock time plus or minus the change of position of that object in time relative to the earth‘s location in time is x. If a similar object B is ejected from Mars at speed x, the same statements apply to the motion of that object relative to the reference system defined by Mars. But if it is now desired to express the velocity of B in terms of the reference system defined by the earth, everyone realizes that the change in the relative spatial position of Mars and the earth must be taken into account. What was not realized before the development of the Reciprocal System is that there is also a change in the relative position of these two planets in time, and whenever the magnitude of this change is significant it too, must be taken into consideration. The true measure of the speed is the amount of change of position in space divided by the total time including the amount of change of relative position in time. Clock time is a correct measure of the total time only at low relative speeds.

Much of the difficulty that some students of the theory are having in understanding the motion of photons of radiation could be avoided if it is recognized that although the photon motion is inherently scalar once a direction has been imputed to it in the context of the spatial reference system, the photon moves in the same manner as any other object. The object A in the preceding paragraph could just as well be a photon as anything else. A photon emitted from the earth moves away *from the earth *just as any ejected material object will do, not from any kind of an absolute position that the earth was occupying at the time of emission. There is no absolute reference system by means of which such a position could be defined. When one unit of clock time has elapsed, the photon will be one unit of space distant from the earth, and since, in this case, clock time is the total time, the speed is 1/1 = 1.

As in the preceding illustration which referred to the motion of material objects, if we want to express the nation of a photon emitted from Mars in terms of a reference system defined by the earth, the spatial distance traveled by the Mars photon in the reference system during~ one unit of clock time will be 1+a, where a is the effect of the relative motion of Mars and the earth. However the distance component a is traversed during a time a, which is separate and distinct from the one unit of time registered on the clock. The total time involved in the motion is there 1+a and the speed is 1+a/(1+a) = 1. Thus the speed of the photon motion is independent of the reference system, but the *spatial location* is not.

No doubt some of the misunderstanding that I am now trying to correct is due to my use of the term “natural reference system.” Even though I have continually emphasized that space and time do not constitute a setting or background for physical action, and that there is no absolute reference system, it has been widely assumed that this “natural reference system” is such a setting. As one correspondent puts it, “Whenever you talked about the progression of space...we instinctively assumed you were talking about the expansion of some background space...Objects not participating in such an expansion would emit photons by simply ‘cutting them adrift in the expansion.” The term “natural reference system,” as I am using it, has no such implications. A spatial reference system can be stationary, in which case the distances between its various parts remain the same as time progresses. Or it can he a moving system, in which case the distances between its various parts increase as time progresses. Inasmuch as each of the primitive undifferentiated nations that are the fundamental units of the physical universe involves one unit of space in association with one unit of time the datum for physical activity — the *natural* reference system — is a system in which the various parts are moving outward (that is. distances are increasing) at a uniform unit speed. This is the natural system because it is the system in which any object., such as a photon, that has no capability of independent motion is stationary. It is essential to use the concept of such a reference system in the development of theory, and a name must be assigned to it. The word “natural” is intended to express the fact that this system moving at unit speed is the system to which the universe actually conforms; that is, the only system with respect to which an object that *cannot* move is not represented as moving. While I realize that the term “natural reference system” is frequently misinterpreted, I do not believe that there is any alternate wording less open to misinterpretation that will express the true meaning.

The concept of an expanding system of reference is applicable only to scalar motion. It is unfamiliar because the existence of inherently scalar motion was not recognized prior to the development of the Reciprocal System, notwithstanding the fact that motions such as those of spots on an expanding balloon are obviously different *in kind* from ordinary vectorial motions. A reference system for scalar motion in a three-dimensional universe necessarily takes the form of a sphere. As the imputed direction of a scalar motion in such a universe is determined by chance, an object which has moved a scalar distance d from its point of origin during a certain interval will be found somewhere on the surface of a sphere of radius d.

For the purpose of explaining the relation of such a reference system to the more familiar types, let us assume an object A to be motionless. A sphere centered at A then constitutes a stationary system of reference (magnitudes in which can, of course, be expressed either in polar or rectangular coordinates). A sphere centered at object B which is not moving relative to A is part of the same reference system. A sphere centered at object C, which is in motion relative to A is *another* reference system of the same kind. However, if the sphere centered at A is assured to be expanding at rate x, this constitutes a reference system of a different kind: a moving system. In the special case where the rate of expansion x is unity, one unit of space per unit of time, we have the *natural* moving system, the reference system to which the basic units of the universe actually conform. If an expanding sphere of this kind is centered at object B instead of object A, it is another part of the natural system. However, both A and B can occupy positions in the same stationary reference system only if they are moving inward gravitationally. For all practical purposes, therefore, it can be considered that a separate system of reference is centered at B. It is true that all points in reference system B are moving outward from A but this_ outward motion is counterbalanced by the inward gravitational motion of equal magnitude, so that the only *effective* ration of photons emitted from B is the nation outward from B.

Generalizing the principle brought out in the foregoing paragraphs, we may say that scalar motion can be represented in a stationary three-dimensional system of reference only if *reference points* are defined. This limitation on our ability to represent motion in a fixed coordinate system may be annoying, but if we want to understand the physical universe we will have to take it as it is; we cannot force it to conform to what we think it ought to be, or to what we find convenient. The discovery that the physical universe transcends the limitations of our usual reference systems is one of the most significant of the results that have been obtained from the development of the Reciprocal System of theory. It is now clear that this universal cannot be forced into the mold that previous physical theories have prepared for it. There is no valid reason why physical action *must* be limited to those events and those phenomena that can be represented in the reference systems that the human race is capable of constructing, and the finding of the Reciprocal System is that it is *not* so limited. The inability to deal with scalar motion on the same basis as vectorial motion is only one of a number of instances where the universe refuses to stay within~the boundaries of what is convenient for the human investigator.

Inability to represent change of position in tin,e in a spatial reference system is another case of the same kind. I am continually receiving letters from individuals who :ay that they need help because they are having difficulty in “drawing a diagram” to represent some motion in which change of position in time is involved, according to the theoretical findings. I cannot give any help in these cases, because motion in* time cannot* be represented in a *spatial* diagram. We are able to represent low-speed motion in such a diagram because no significant change of relative position in time is involved, but as soon as the speed is great enough to introduce such a change, the spatial diagram can no longer represent the motion accurately.

This is not something that is peculiar to the Reciprocal System. The *reason* for the difficulty at high speeds was unknown prior to the development of this new theoretical system, but its *existence* has long been recognized. It is a matter of fact that has to be faced regardless of what physical theory is accepted. In order to understand just what is involved, it should be realized that a diagram, or graphical representation, of a motion does not give us a true picture of that motion unless the spatial positions of the moving objects as shown in the reference system are consistent with the speeds. For J instance, if the distance between A and B increases by x in time t, then the speed must be x/t; otherwise the motion is not correctly represented. But no spatial reference system can maintain this kind of consistency in representing high-speed motion.

The two-photon case that I have frequently discussed in my publications demonstrates this point. In this illustration, we assume two photons, A and B, emitted simultaneously from an object 0 in opposite directions. At the end of one unit of clock time, A and B are separated by two units of distance, and x/t = 2/1 = 2. But experiments show that the speed of A relative to B is only 1. Clearly, either the distance entering into the determination of the speed differs from that measured in the reference system, or the time differs from the uniform rate of progression that has to be assumed in order to make it possible to represent motion in a spatial coordinate system. In either case, the spatial reference system is not capable of representing the motion accurately. Current physical theory, based on Einstein assumptions, simply says that the coordinate positions have no meaning at high speeds. As expressed by Moller, “In accelerated systems of reference the spatial and temporal coordinates thus lose every physical significance; they simply represent a certain arbitrary, but unambiguous, numbering of the physical events.”

Those who insist ihat we should be able to represent every motion by a spatial diagram are demanding something that has long been known to be impossible. Perhaps some day a device may be invented whereby change of position in three dimensions of space and change of position in three dimensions of time can be accurately represented in a diagram that can be comprehended by the human mind. In the meantime, we will sin,ply have to recognize that some natural phenomena are not amenable to our cherished diagramatic modes of representation, regardless of what kind of a theory we may use in our attempt to understand them. The only difference between the Reciprocal System and other theories, so far as this point is concerned, is ihat this new theoretical system has clearly identified the phenomena that the conventional systems of reference are unable to handle, including sonre phenomena such as scalar motion that have heretofore been overlooked, largely *because* of the tendency to insist that nature must conform to what the hunan theorists find convenient.

There is no good reason, however, why we should be disconcerted because nature refuses to make things easy for us. If we start with the basic units of motion and build the possible combinations of these units step by step in accordance with the rules specified in the fundamental postulates of the Reciprocal System, we define the physical universe, the universe of motion, in alt of its detail. The universe as thus defined is rational, logical, and *understandable*. The fact that some of its magnitudes cannot be represented graphically in the manner to which scientists have been accustomed merely indicates that previous ideas as to the basic nature of these magnitudes are erroneous.