Larson’s Reciprocal System Theory


It’s important to understand that Larson’s Reciprocal System theory (RSt) is a general physical theory developed under his new scalar system of physical theory, the Reciprocal System of Physical Theory (RST); that is, using the RST, Larson developed the world’s first theory of that system, the RSt. In this way, we can more fully appreciate that while his RSt is necessarily incomplete and subject to revision, correction, and expansion, the RST, which made it possible to construct such a theory is not incomplete or subject to revision, correction, or expansion, lest in doing so, we inadvertantly destroy this new basis for a renewed round of inductive science, by converting it into just another instance of inventive science, so prevalent in the modern practice of physics.

Larson’s RSt is the world’s first general theory of the structure of the physical universe. He explains why this is so in the essay, Just What Do We Claim?:

I. The reciprocal system is a general physical theory, one that derives all of its conclusions in all physical fields from a single set of basic premises—the only such general physical theory that has ever been formulated.
II. Within the range of phenomena thus far covered in the development of the consequences of the fundamental postulates of the system, an area which includes the basic features of all of the major branches of physical science and a wide variety of subsidiary phenomena, all of the conclusions that are reached from the theory are consistent with the physical facts that have been definitely established by observation and measurement (although they do not necessarily agree with inferences from or extrapolations of those facts, nor with theories previously devised to explain the facts).
III. Because all conclusions are derived from the same basic premises, the entire structure of theory is a single integral unit that is not subject to modification or adjustment. Every comparison of theory with observation is therefore a test of the validity of the theoretical system as a whole. Thus each of the thousands of such tests that have already been made without finding a discrepancy has reduced the probability that a discrepancy will ever be found, and as matters now, stand it is practically certain that the theoretical universe of the reciprocal system is a true and accurate representation of the actual physical universe.

Of course, the “single set of basic premises” he refers to in Claim I, is the set of assumptions known as the fundamental postulates of the system:

First Fundamental Postulate: The physical universe is composed entirely of one component, motion, existing in three dimensions, in discrete units, and with two reciprocal aspects, space and time.
Second Fundamental Postulate: The physical universe conforms to the relations of ordinary commutative mathematics, its magnitudes are absolute and its geometry is Euclidean.

It is the assumptions in these two postulates that constitute the RST. The necessary consequences that follow from these assumptions constitute the RSt; that is, the set of conclusions deduced from the fundamental assumptions of the system constitute a general physical theory of radiation, matter, and energy that form a general theory of the structure of the physical universe. Therefore, the success of this theory, as measured by comparison with the results of experiment and observation, is an indication of the validity of the premises upon which it is based. As Larson indicates, a very good agreement has been obtained to this point, but the process has barely commenced.

Nevertheless, the rate at which new experiments and observations are being made is simply astounding. As a consequence, the task of comparing the theoretical results with these new data is overwhelming, especially since the new results are reported in terms of the established theoretical concepts in a given field and in the mathematical language of legacy physics, which is based on the Newtonian system of physical theory; that is, current physics is based on the concept of vectorial motion and the concepts of force and acceleration derived as a function of the vectorial motion of objects and fields, while the new system is based on a different concept of motion, the concept of scalar motion.

Moreover, the expectation that every conclusion in the RSt is a necessary conclusion that correctly follows from the postulates, and is therefore not subject to challenge, is obviously a naive and unrealistic position to take. Larson was anything but naive and unrealistic, yet the text of Claim III that states that the “entire structure of theory is a single integral unit that is not subject to modification or adjustment,” seems to clearly state this position. However, upon reflection, it’s not difficult to see that what Larson is saying is that any conclusion that is correctly deduced from the postulates is not subject to modification or adjustment. This is not to say that all current conclusions are firmly established as necessary consequences of the postulates.

Certainly, Larson didn’t believe that his own thinking was infallible. He knew that incorrect conclusions are bound to be found in the RSt, especially as knowledge of the physical structure grows by leaps and bounds. However, his insistence on the importance of recognizing that the test of the postulates rests in the valid comparison of the theoretical conclusions to observation was motivated by the realization that any change in the set of fundamental assumptions, by adding additional assumptions, or support from empirical observation, to establish a given theoretical conclusion, would destroy the validity of the test of the system that has been accomplished to this point.

In essence, unless we hold inviolate the set of assumptions that constitutes the RST, the results of comparing the RSt to the results of experiment and observation, in order to establish the validity of the premises upon which the theory is based, will be invalidated. Once the set of fundamental assumptions is permitted to be modified or adjusted, to accommodate a new conclusion, the RST is no longer the RST, but some other system.

If one carefully distinguishes between the system of theory and the theory developed using the system, it is very clear that Larson didn’t mean that the RSt is not to be modified or adjusted, but that its inflexibility is a highly desirable characteristic of the system of theory, by which the set of conclusions constituting the general theory was developed. He discusses this in an article published in the Journal Reciprocity,:

The first fact that should be noted is that the theory is derived in its entirety from the fundamental postulates; that is, it consists entirely of the postulates and their necessary consequences, without any content from other sources. This is very important, because it provides the basis for verifying the validity of the theory by application of the probability principles.
…It needs to be recognized, however, that the fixed character of the theory that enables establishing its validity also imposes some severe constraints on its further development. In particular, it prohibits introducing any additional assumptions, or anything from observation, in developing the details of application of the theory to specific areas. In order to preserve the status of the theory as a single, integral entity that can be tested as a whole these details must be derived in the same manner as the major conclusions; that is, as necessary consequences of the basic postulates.
…the chief merit of the theory, the characteristic that enables us to verify its validity, is its status as a fixed structure, one that we cannot modify to suit our preferences or prejudices.

Nevertheless, having established that the chief merit of the theory is its inflexibility, he then explains that in spite of such restrictions:

It does not follow that those of us who have undertaken to develop the details of the theory have necessarily arrived at the correct conclusions in every case. None of us makes any claim to infallibility. Thus it is entirely in order for anyone to take exception to a previous conclusion, providing that he can show that a different conclusion can be derived from a development of the consequences of the fundamental postulates. But if the dissenting opinion is based, either totally or partially, on considerations other than those derived from the postulates of the Reciprocal System it is an expression of a different theory, and it has no claim to a favorable reception by those of us who are working to extend and amplify the Reciprocal System.

Clearly, in the above paragraph, Larson distinguishes between the “details of the theory” and the postulates of the system upon which these details are developed. What he is stating is that the inflexibility of the theory, which is the “chief merit” of the system, does not apply to the details of the theory in the same manner that it applies to the postulates of the system upon which these details depend; that is, it is certainly possible that incorrect conclusions may exist in the details of the theory, but, if so, alternate conclusions must be consistent with the system of theory.

This distinction is crucial and for this reason we have formalized it by referring to the “system” aspect of the theory, as the RST and the “details” of the theory as the RSt. Thus, any conclusion of the RSt can be challenged, providing that the challenger “can show that a different conclusion can be derived from a development of the consequences of the fundamental postulates,” the RST. In so doing the inflexibility, or inevitability, of the RSt is maintained, which is its most beautiful and compelling feature. It is this logical completeness that makes the theory beautiful: As Steven Weinberg, in his Dreams of a Final Theory, writes:

Completeness is the “beauty of everything fitting together, of nothing being changeable, of logical rigidity.” A sense of the inevitable surrounds the theory and one must feel like the conclusion reached is complete, with nothing lacking and nothing extraneous. As Einstein said of general relativity, “to modify it without destroying the whole structure seems to be impossible.” If any part of the theory can be changed, the entire theory is not logically complete.

Obviously, a general theory of the universe, that has the power to explain the entire structure of the physical universe in one sentence, or one equation, would be the ideal. Indeed, in the end such a theory might boil down to nothing more than the famous final answer, the calculation “42.” However, understanding comes from knowing how a given physical entity, in the observed physical structure, came to have the properties and behavior that it has, based on the existence of a prior fundamental principle, or set of fundamental principles. To discover this knowledge is to discover the truth and for that reason we pursue the study of physics.

In short, the RSt, consistently developed from the RST, to the extent that it is logically rigid and inevitable, yet consistent with observation in all respects, demonstrates that the structure of the physical universe actually is nothing but motion, combinations of motions, or relations between motions, existing in three dimensions, with two reciprocal aspects, space and time.