Presenting the Reciprocal System

Dewey B. Larson
755 N.E. Royal Court
Portland, Oregon 97232

Dec. 28. 1988

Dear Frank,

I am working on an answer to your letter of Dec. 12, but I do not know how long it will take me to finish the job, as I am not doing very well at present, and can only work a short time each day.

In the meantime, I want to give you some of my thoughts as to how we should present our case when we enter into a dialog with supporters of conventional physics. The work that we have done in the field of physical science falls into two categories:

  1. The studies of fundamental relations that have led to the conclusion that the physical universe is a universe of scalar motion.
  2. Development of the consequences of the postulates that express this conclusion, to show that they agree, item by item, with the observations of the actual physical universe.

Since the early days of the investigation, when I was working mainly with the fundamentals, 99 percent of our attention has been centered on the items that make up Category 2. This has fostered a tendency to argue our case on the basis of the merits of some one or more of the items of this class.

This may have some advantages in discussions with students or with non-scientists, but it does not accomplish anything in discussions with physicists. As long as a physicist is convinced that the accepted concepts and laws of his profession are valid, he will not give any credence to a theory that contradicts one of those accepted ideas. In our dealings with the physicists we therefore need to concentrate on our findings with respect to the items included in Category 1.

I am enclosing a statement of these findings, as I seem them at the present time. In my opinion, this is the case that should be presented to the physicists. If we can get them to see that the physical universe is a universe of scalar motion, the desirability of a full development of the consequences of this finding should be obvious without further argument.


In 1964 Dr. Richard Feinman gave a series of lectures at Cornell University in which he discussed the nature and extent of our knowledge of physical fundamentals. These lectures were later published in book form with the title The Character of Physical Law. In the book we fin this assertion:

Every one of our laws is a purely mathematical statement,

and also this:

Today our theories of physics, the laws of physics, are a multiple of different parts and pieces.

The fragmented nature of this basic knowledge is due to the fact that these physical laws have not been derived from any central source. As Feynman puts it, “We do not have one structure from which all is deduced.” Instead, the laws applicable to different physical areas have been derived independently, each from the empirical information available with respect to that particular field. To those who have not had occasion to make any critical study of this situation it may seem natural and logical to handle the derivation in this piecemeal manner, in view of the lack of the kind of a general theoretical framework that could serve as a base from which to deduce the laws. In fact, however, it has been possible to use this kind of an approach only because of a peculiarity of mathematical knowledge.

None of the mathematical formulations of these laws is known to be unique. In many, perhaps most, cases there are known alternatives that lead to the same answers (within the accuracy to which they can currently be tested), and in all cases it is obviously possible that there are alternatives as yet unknown. But in mathematics, different formulations that lead to the same answers are not different mathematical expressions; they are merely different ways of stating the same expression, and they are interconvertible. It follows that just as soon as we obtain a mathematical formulation that yields the correct answers, we have the valid mathematical relation or law. Working on this basis, the cumulative efforts of a host of investigators over long years of research have given us a body of mathematical laws and relations that, we can feel confident, correctly represent, within current limits of accuracy, the physical entities and relations with which we deal.

There is, however, another side to the physical picture. We are not satisfied to know only the mathematical aspects of the physical world.. We also want a physical interpretation of these mathematics, an explanation of what the mathematical terms and relations mean. So, in addition to mathematical knowledge that has accumulated, we are also attempting to build up a corresponding knowledge of what we may call the conceptual aspects of the physical universe. Here, again, the lack of any general theoretical foundation has forced the scientific community to resort to the piecemeal, area by area, method of deriving its results, and here, too, those results take the form of “a multitude of parts and pieces.”

As in the mathematical situation, the current formulations that fit the known facts within the current limits of accuracy are not unique. Indeed, far more conceptual than mathematical alternatives are known, and here again it is always possible that there are other alternatives as yet unknown. In the realm of conceptual knowledge, alternative formulations that arrive at the same results are not different forms of the same theory; they are different theories. Only one of them can be correct, even though all of them are in agreement with the observations. We have no way of identifying this correct alternative. It follows that a conceptual theory or conclusion cannot be verified by agreement with observation.

Obviously, the statement of a mathematical relation tells us nothing about the physical meaning of that relation. In fact, this mathematical statement gives us no indication that it has any connection with physical existence. The names that may be attached to the mathematical statement are part of the conceptual structure, and have no mathematical significance, hence they do not participate in the verification of the validity of the mathematical relation. Thus, a conceptual theory or conclusion cannot be verified mathematically.

No other method of verification has been available. It is true that there is another method that is theoretically possible. The number of alternative explanations of an interconnected set of physical phenomena decreases as the number of different phenomena included in that set increases, because each extension of the diversity imposes new constraints on the possible explanations. It follows that if a fully integrated conceptual theory of a large and highly diversified set of physical entities and phenomena could be constructed, a positive correlation with observation would establish its validity on a probability basis. But long-continued efforts have failed to produce any such far-reaching theory. As matters now stand, therefore, conventional science has no way of validating conceptual conclusions that it has reached in the physical field.

This does not mean that all of the currently accepted laws and relations are conceptually wrong. On the contrary, the majority of them are probably correct, as there are indications of various kinds that serve to identify some alternatives as more probable than others. However, it does mean that there is no proof of the validity of any of these laws and relations, and it indicates that there is sufficient possibility of error in each case to make it evident that many of the formulations are not valid, particularly where a long sequence of successive conclusions is involved.

Although the scientific community has closed its eyes to this situation and refuses to recognize that the so-called “proofs” of validity that it offers—such as the contention that mathematical agreement establishes conceptual validity—are untenable, there is a widespread recognition of the fact that the status of theoretical physics would be greatly improved if a physical theory of wide applicability could be constructed. This point was recognized quite early in the history of scientific investigation. It was also realized that such a far-reaching theoretical structure would almost certainly have to be based on an understanding of physical fundamentals. For almost three thousand years, therefore, one of the primary goals of science has been to derive a general physical theory, one by means of which the answers to all physical questions can be derived from a single set of basic premises.

In spite of all of effort that has been applied to the search over this long period of time, there has been no appreciable progress toward the goal. Physical knowledge remains as characterized by Feynman: a multitude of separate pieces. Attempts have been made to connect some of the pieces by means of assumption, but the need for an assumption identifies a discontinuity. It does not establish a connection. The question then arises, Why has this long and determined effort failed to reach its objective?

Although practically nothing is said about this subject in the current scientific literature, there is really very little doubt as to where the difficulty lies. A theory is no better than its foundations, and the foundation upon which the investigators are attempting to build a general physical theory is faulty because the true nature of the basic physical entities is almost entirely unknown. The electric charge, for instance, is basic to a wide range of phenomena, but the physicists cannot answer the question: What is an electric charge? The textbook tell us merely that we should not ask the question. The nature of time is even more mysterious, and the same uncertainty is present in some degree in our knowledge of all of the entities that are treated as fundamental in the development of theory.

These basic entities are the ultimate physical units, the foundation stones on which theory must be erected. Even though we do not have actual knowledge as to their nature and properties, we must nevertheless use them in the theoretical development. We must therefore make assumptions, and substitute them for the knowledge that we do not have, in order to have something whit which to work. Most of these basic entities enter into almost every physical process in one way or another. As a consequence, each of the "multitude of different parts and pieces" than in total constitute the conceptual structure of physical theory rests, in part, on some or all of 30 or 40 assumptions about unknown or poorly known basic physical constituents.

No doubt many of these assumptions are correct expressions of the physical facts. Perhaps most of them are. But it is totally unrealistic to expect that all of these many assumptions about the elusive basic entities are valid, and any error in the foundations of the structure of theory invalidates, in whole or in part, all of the theoretical conclusions that rest on these foundations. It is thus evident that the "parts and pieces" of modern physical theory must contain many errors.

Ordinarily it can be expected that the imperfections in observational knowledge will be gradually eliminated, or at least minimized, as further observations and measurements are accumulated. But observation of the basic entities is severely limited, and scientific investigation has not been able to gather much more direct information about them than is available to the casual observer. Many changes in the assumptions about these entities have been suggested during the course of the various investigations that have been undertaken, and some of them have gained general acceptance. There is a widespread tendency to regard this general acceptance as the equivalent of proof, but in fact, an assumption is never more than guesswork, regardless of the extent of its support. Substituting one assumption for another may or may not bring us closer to the truth. In any event it adds nothing to our actual knowledge of the phenomena to which the assumptions apply. the changes in the accepted assumptions have not added anything to our actual knowledge of the conceptual aspects of physical phenomena.

As a result of the long continued inability to increase factual knowledge of the basic entities it has been generally conceded that the prospect for any advance of this kind are very dim. Most scientific opinion now appears to accept Einstein's dictum that the true nature and properties of the fundamental physical entities are not only unknown, but unknowable. He specifically condemned the idea that"the basic concepts and laws of physics could be derived from experience," and asserted that they could only be grasped "by speculative means." The issue has thus receded into the background, and at present remains dormant.

As it happened, however, after the observers had given up hope and had discontinued active search for more factual information about fundamentals, some new developments have taken place. A number of the new discoveries in the far-out regions of physical science that have been made in recent years have given us the king of direct observational information about basic entities that science has so long sought. But because the scientific community is no longer looking in this direction, it has not recognized what has now been revealed.

One of these significant new developments is the discovery of the interconvertibility of some of the basic entities. We now know that, under appropriate conditions, mass can be converted into kinetic energy, this energy can be converted into electric charge, and so on. In order to be completely interchangeable--that is, convertible from one to the other without adding or removing anything, as these entities are--such entities must necessarily be nothing more than different forms of the same thing. They are different forms of some common denominator, we may say. The observations thus show that electric charge, kinetic energy, and matter(of which mass is a property) are not separate and distinct phenomena, but are different forms of something basic. Either two of them are forms of the third, or all are forms of some still more fundamental entity.

Although the long search for the ultimate constituent of the physical universe has been unsuccessful in its primary objective, it has added to our knowledge of the situation by including a thorough examination of the suitability of the various known basic physical entities as candidates for the status of the ultimate constituent. The net result of this intensive scrutiny has been to eliminate all but three of the possibilities. these are (1) motion, (2) energy, and (3) some currently unknown entity. Alternatives (2) and (3) no longer have any significant support, and for many years the general conclusion has been that if there is a single basic constituent of the physical universe it must be motion.

The advantages of motion for this fundamental role are so obvious that even on the basis of the limited amount of evidence now available, many prominent scientists and philosophers have been fully convinced that the physical universe is a universe of motion. Thomas Hobbes, for instance, stated categorically that " all things have but one universal cause. which is motion." But these supporters of the motion hypothesis have not been able to translate their belief into a general physical theory, or even to make a reasonably good start toward such a theory. The search for a unifying constituent has therefore come to a halt, and has as little attention in recent years. Current research is directed toward a search for the ultimate constituent of matter, rather than for the ultimate constituent of the universe.

Here , again, one of the recent observational discoveries has thrown an entirely new light, not yet recognized in conventional physical thought, on the situation. It has been found that the distant galaxies are all moving radially outward from each other at high speeds.Unless we assume that our Milky Way galaxy is the only stationary object in the universe, a hypothesis that is rejected by modern science, it must be receding from all of the others. If these were ordinary vectorial motions, oppositely directed motions would cancel each other, and the net result would be little or no actual change in position. But the galactic separations are increasing rapidly, and if our galaxy is not unique we must be participating in the changes of position that cause the increase in separation. Thus we are actually moving outward in all directions from any initial position. This means that the recession motions of the galaxies have no specific direction. They are simply outward (that is, positive) and each can be completely described by a positive magnitude. They are scalar motions.

The galactic motions are currently attributed to an "expansion" of the universe, but whatever they are called, and however they may originated, observations shows that they are a scalar motions. Once the existence of scalar motion anywhere in the universe is established, it follows that this type of motion is one of the constituents of the physical universe. Inasmuch as it is obviously simpler than vectorial motion (which is scalar motion plus a direction) it is more fundamental. If the physical universe is a universe of motion, as the results of long years of investigation seem to indicate, the ultimate constituent of that universe must therefore be scalar motion.

Vectorial motion, the motion of our ordinary experience, is motion with a direction relative to the spatial reference system being used, usually either the absolute Newtonian system or Einstein's system, in which space is distorted by the presence of mass. Scalar motion has no inherent direction, and therefore cannot be represented in its true character in a three-dimensional system of reference;that is, the successive points in the line of travel cannot be specifically identified in that system. To make a representation of some kind possible, it is necessary to introduce a one-dimensional datum, a reference point, thus converting the spatial reference frame to a combination one and three-dimensional system. But even with this expedient, the motion is not shown in its true character. The positions that are identified are correct only for the motion relative to the reference point. In the case of the galaxies, for example, if we observe distant galaxy X from our galaxy A, we find that it is moving in the direction AX in the spatial reference system. But if we observe it from galaxy B we find that it is moving in the very different direction BX. When galaxy C is the reference point, it is moving in the direction CX. And so on.

This inability of the reference system to represent one of the basic constituents of the physical universe--scalar motion--in its true character demonstrates that the "space" of that system is not a physical entity, the kind of thing that can be "curved", or otherwise distorted, or can interact with physical matter. It is an arbitrary construction for reference purposes--nothing more. The true physical "space" is the spatial aspect of motion.

The need to call upon an expedient such as the reference point in order to make any kind of a representation of scalar motion possible in the reference system also explains why conventional science has not discovered the existence of scalar motion. Motions of this nature have not been recognized as motions. For instance, it is evident, as soon as the factors governing the representation in the reference system are clarified, that the inverse square forces--electrostatic, electromagnetic,and gravitational--are the force aspects of scalar motions, but they have not been recognized as such, because their observed characteristics are so different from those of vectorial motions. Here is the explanation of the physicists' inability to answer the question, What is an electric charge?

This identification of the basic physical constituent as scalar motion opens the door to construction of the long-sought general physical theory. When the possible ways in which units of this scalar motion can be disposed relative to the reference system are determined, these are found to agree, item by item, with the fundamental physical entities. Thus, in a universe of scalar motion, the true nature and properties of radiation, matter, electric and magnetic charge, and the other basic entities, are specifically and accurately defined. In this way, a solid foundation is laid on which a comprehensive general theory can be erected.


International Society of  Unified Science
Reciprocal System Research Society

Salt Lake City, UT 84106

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