The thought of Dewey B. Larson in his Reciprocal System diverges significantly from some patterns prevalent in current physical science* Therefore, it seems advisable to set forth his criteria for physical theory, his understanding of the intellectual environment into which the Reciprocal System has been introduced, and his philosophy of physical theory. Rigorous scrutiny is applied by Larson to both physical assumptions and hypotheses and to the manner in which mathematics has been utilized in their construction and validation. Study of the intellectual environment includes awareness that objective physical theories are constructed by and for subjective human beings in whom psychological factors cannot be ignored. Finally, the Reciprocal System presupposes a certain general and specific philosophical perspective of physical reality and theories constructed to describe it.
D.B. Larson advocates closer scrutiny and sharper refinement of fundamental physical concepts, particularly of space and time, and of their interrelationships. In accord with this philosophy, the fundamental concepts of the Reciprocal System will be later defined in connection with the basic assumptions and postulates of the theory. He feels that physicists have a tendency to use an undefined concept in a mathematically rigorous manner. This point of view seems to be reflected by Lindsay and Margenau in commenting upon the interpretation of time in modern physics. “Abstract time, as it appears in the equations of physics, is merely a parameter which serves as a useful independent variable ... From the point of view taken here, the use of the time parameter in physics may be looked upon as a matter of convenience and nothing more." Quantification has loomed larger than delineation: “As in the matter of position, it is the measurement of time rather than any speculation as to its nature that is of principal concern.“ Customarily, little more than passing note is made of conceptual vagueness in defining space and time pragmatically in terms of spectral wavelengths and clocks. “Although not elegant from the philosophical point of view, these are the definitions of length and time we use in gathering experimental results which we shall express in theoretical terms."
In contrast to such vagueness, Larson is in favor of rigidly defined fundamental concepts. But they should be derived from experiment and not arbitrarily set forth as free inventions of the human mind. Some physicists, although inclined to grant the need for a more precise definition of time, would construct their definition on the basis of theory instead of observation, Mario Bunge writes:
“A reasonable theory of physical time should satisfy the following desiderata: (a) it should refine and work out our intuitions about physical time; (b) it should purge those intuitions of subjective elements; (c) it should tally with important physical theories; (d) it should be quantitative; (e) it should be well organized; and (f) it should include the proper semantics, in the sense that it should deal with a certain relation among objective happenings rather than with ghostly absolute time.”
Such a definition would make time a pliable tool of theoreticians rather than a foundation upon which physical theory could be constructed. Rigorous observation-based definitions of fundamental concepts may still be incorrect insofar as one’s interpretations of data are in error. Larson considers Newton’s separation of space and time and Einstein’s treatment of time as a component of a four-dimensional structure to result in fundamental errors regarding motion. He regards both positions as arbitrary human assumptions without foundation in fact, even contrary to observation. One theoretical physicist comments on the transition from the Newtonian to the Einsteinian notion of space and time thus:
“Disregarding hypotheses which are contrived ad hoc, and which are therefore unsatisfactory, the result of the Michelson-Morley experiment leads compulsorily to a revision of our concepts concerning space and time. The negative result of this experiment makes it very evident that absolute space is a fiction. But absolute time must also be abandoned. The definitions occurring in the treatment of time by the old mechanics are imperfect.“
From Larson’s point of view, this stance reflects the exchange of one set of ad hoc assumptions concerning space and time for an equally ad hoc set. Although it is not imperative to begin construction of physical theory with the fundamental concepts of space and time, Larson holds that they form a most useful initial set. The Reciprocal System, as will be seen, is so constructed.
In addition to a rigorously defined set of fundamental concepts, D.B. Larson urges what he considers to be appropriate application of the extrapolation principle. He is not suggesting extrapolation as a substitute for experimental research. Extrapolation is not intended as a means of generating untestable hypotheses. Rather, there are legitimate concerns of physical science, particularly astrophysics, which are currently beyond available means of observation. Proper extrapolation may represent a means of formulating hypotheses which are amenable to experimental test. Larson proposes to exercise as an operational hypothesis the notion that relations applicable in regions accessible to observation also apply to inaccessible regions. Until substantial contrary evidence is collected, this notion is to be regarded as the best initial hypothesis. It is improper to assume a priori that the unobservable world, either at the atomic or intergalactic level, is unlike the known world. This idea is a fundamental philosophical tenet of the Reciprocal System.
Aside from the obvious possibility of logical error, this extrapolation principle may yet fail to yield a correct hypothesis. No means may be available - or yet devised - for testing the hypothesis. More frequently, he feels, error occurs as a consequence of coupling the extrapolation principle with erroneous assumptions. There may exist critical points in the extrapolated region which are not clearly predictable from data in the observable region. Extrapolation may cause a correct empirical mathematical relationship to yield significant error, e.g.-, through slight deviation in assumed values of numerical constants from their true values.
Extrapolation of the negative may also be implemented cautiously as an initial legitimate assumption. The fact that certain events do not happen in the known region tentatively suggests that they may not happen in the unknown region. But such events may occur unobserved in the known region of the universe. Furthermore, non-occurrence does not eliminate the possibility of future occurrences either in the known or unknown regions.
Strongly discouraged, however, is the use of ad hoc assumptions. Larson claims instances in which they have been proposed to avoid confrontation of a 19 cherished theory by an embarrassing fact. Postulation of phenomena for which there is no evidence, even contrary evidence, is unacceptable. An ad hoc assumption should not be generated even though it seems to be the only logical alternative to another ad hoc assumption. For example, physicists have been unwilling to assume action-at-a-distance, but several have postulated finite speed of propagation of gravitational effects as a forced alternative to action-at-a-distance on the basis of dubious evidence as justification. If proposed at all, ad hoc assumptions should not be lightly made. Such a case was postulation of the existence of the neutrino where affirmation of its existence historically seemed more in harmony with established fact than its denial. The Reciprocal System is claimed to be free of any such assumptions.
The relationship between theory and data are critical and delicate issues in the philosophy of science underlying the Reciprocal System. The issue is obviously critical to the status of a theory. But it is also delicate in that one discovers some discrepancies between belief and action in scientific usage of facts.
Fact occupies a key position in the theory of conventional science and in the Reciprocal System. Dr. William George of the Royal Society expressed it thus:
"In its passionate and challenging devotion to facts, science seems to be distinguished from all other human activities. Science neither has, nor desires, any protection whatever against statements of fact. A passionate devotion to statement of fact outside of science may alienate a man from his friends, if not put him in a law court, prison, concentration camp, or before a firing squad. ... In science it is never impolite, immoral, disloyal, unpatriotic or ’’not done" to state facts."
Larson holds that facts should be the only criterion in evaluating a theory, other theories to the contrary notwithstanding. The likelihood of a proposed theory being in conflict with accepted theories may well increase with the extent of the new theory and with the divergence of its fundamental postulates from those of accepted theory, but a sine qua non of any theory must be strict harmony with scientific fact.
However, Larson does question the manner in which the criterion of fact is used in assessing a physical theory. A theory should not be hastily accepted on the basis of agreement of prediction and fact in a limited number of instances. Rather, proof of the validity of a theory requires comprehensive correlation of theory and observation. Consistency of observation with a theory does not constitute proof of a theory. For example, he would argue that failure to detect absolute motion does not imply its non-existence. He would further insist that the mere possibility of the correctness of a theory should not be equated with proof of the theory. Experimental support for some, but not all, of the postulates of a theory should be construed as supporting only those postulates, but not theory based on all the postulates. He observes that there is a tendency to judge a new theory on the basis of accepted theory treated as fact. Scientists must carefully differentiate between theory and data. For facts are being confused with 29 attempts to explain the facts. Larson expresses concern that fundamental assumptions are being regarded as if they were facts. One should remember that evidence that can be adduced in support of several hypotheses supports none of them. Rigorous application of these principles involving the use of fact are encouraged in examination of the Reciprocal System.
The Reciprocal System is even more rigorous with respect to fact than conventional theories in one unique respect. Currently accepted physical theories are limited in scope and are based on observations. A new fact consequently requires that the theory be supplemented by ad hoc assumptions to “explain" that fact which was not in the initial set of observations upon which the theory was based. But the Reciprocal System claims to be a universal system of theory based on postulates. A fact, therefore, must be a logically predictable outgrowth of the Reciprocal System; if not, the theory falls.
An example of this uniquely rigorous condition one may impose on the Reciprocal System is the quasar. It will later be seen that Larson in his publications predicted the quasar and its properties several years prior to its discovery. While the quasar has represented a somewhat uncomfortable fact for astrophysics, it was merely a logical consequence of the Reciprocal System. If the Reciprocal System was correct, quasars had to exist.
This illustration also serves to suggest that one criterion of a valid theory is its predictive power of as yet unknown phenomena. A theory may lie fallow with few researchers determining and testing its predictions. A theory is not disproven by failure to generate testable hypotheses, but it thereby becomes rather suspect.
Emphasis on rigorous scrutiny of physical theories in terms of logic is a significant aspect of the scientific philosophy underlying the Reciprocal System. Although this is certainly a goal of reputable scientists, as a human activity it is subject to error. Vigilance is required to avoid the logical non sequitur. D.B. Larson feels that logical inconsistencies have subtly permeated the fabric of modern physical theory.
Obvious when called to one’s attention, some of the more glaring logical inconsistencies, Larson maintains, are as follows. One logical faux paux is analogy: although a useful mental aid to understanding, analogy does not prove an argument. He is particularly concerned about the analogies drawn between radiation and gravitation in support of the theory of finite propagation of gravitational waves.
Another issue is internal logical consistency. For example, relative to Einstein’s famous E = mc2 equation, to claim mass-energy equivalence and increase of mass with kinetic energy, he argues, is to be logically inconsistent.
Obviously, likelihood of logical or mathematical error increases with the length of a chain of logic. Furthermore, research effort increases because each step requires factual corroboration. Hence, the closest possible relationship between postulates and theory is advised. Larson advocates application of Occam's Principle as a pragmatic guideline: formulate no unnecessary hypotheses and keep the required ones as simple as possible.
Particularly in connection with atomic theory, D.B. Larson encourages re-examination of the logical relationship between "parts" and the whole. For example, the fact that particle A emanates from atom B does not imply that particle A exists as an entity within atom B. He further objects to logical inconsistency in application of this illogical premise, rejecting it on one occasion and invoking it in a different situation.
Three other logical concerns may be cited. Ignorance of a theoretical explanation for a given phenomenon, even though sought assiduously, does not justify postulation of no reason for the phenomenon. Radioactive decay, although observing a well-established exponential law, has defied all efforts to explain why one atom and not another atom experiences decay at a given instant. But that failure should not be interpreted to imply that no reason exists. Larson also objects to "eliminating" a problem by postulating that the problem does not exist. One target of this criticism is the group who insist that a mathematical formulation of a theory is an end in itself which requires no physical conceptualization. Finally, agreement between observations and a mathematical expression of a theory does not thereby prove the conceptual validity of the theory. Restricted to their legitimate domain, the equations of special relativity are correct as indicated by a mass of experi - mental evidence, but this mathematical compatibility, Larson, holds, does not thereby imply conceptual validity of Einstein's ideas. The relationship of mathematics to theory will be discussed later in more detail.
The approximate!y forty years' effort in constructing and testing the Reciprocal System of theory suggests a well-defined philosophy of the functions of a theory. A theory should promote scientific knowledge. If it is notably deficient in this respect, like general relativity, it should be regarded as questionable. Specifically, a physical theory should have the potential for generating testable hypotheses as, for example, the Reciprocal System predicted the quasar and its properties.
The most satisfactory theory provides an explanation of the first order; that is, it relates a phenomenon directly to simple inherent properties of the universe. In this sense, then, Newton's law of universal gravitation is a third order explanation in that it leaves two questions unanswered. It does not explain how the gravitational force originates nor how it operates. Einstein's general theory of relativity is likewise of third order. The general theory does not provide the property of mass which deforms space-time nor does it yield the mechanism of such deformation. A satisfactory theory should be internally consistent and in agreement with a!1 observed facts or at least not inconsistent with observed facts. Such a theory should be complete in its ability to account for both the qualitative and quantitative characteristics of observed phenomena. Finally, it should yield enlarged fields of application or more extensive relationships with other physical phenomena.
Open-mindedness to the possibility of alternatives, perhaps inconceivable at present, is a key aspect of the philosophical stance maintained in the Reciprocal System. Failure to consider alternatives has both hindered the growth of physical theory and has diverted it into unprofitable directions. Apparent lack of a reasonable alternative does not eo ipso validate a given hypothesis although such lack may provide motivation for testing a given hypothesis. For one can never be sure that one has examined all conceivable alternatives. This principle suggests a viable modus operand! in theory construction. Suppose a seemingly logical chain of reasoning leads to a prediction contrary to observation and in conflict with other theories well established on the basis of observation. Rather than expend fruitless effort in "patching41 the theory, Larson advises assuming the existence of at least one other alternative and searching for it as a more profitable exercise. Suppose now that an alternative hypothesis has been proposed. In that event, facts in accord with two or more hypotheses do not support one hypothesis over against another. Finally, it is illogical to refuse to consider an alternative as if the initial hypothesis were a proven fact. D.B. Larson maintains that the Reciprocal System is such an alternative which requires an open mind to alternatives in order that it might be subjected to impartial examination.
Although scholars such as Mario Bunge have made admirable progress in systematizing semantic problems in physical theory, names and labels are still sources of confusion hampering advancement. Larson cautions awareness of this problem. Space, time, mass, force, energy, etc., have different shades of meaning in classical, relativistic, and Reciprocal System physics. One should differentiate between a physical reality and the label attached to it. For the label is attached by theorists on the basis of a hypothesis which may or may not be correct. Conversely, failure to assign a name does not mean that a given entity does not exist. It may reflect failure to assign a place to a phenomenon in a theoretical structure. Such nameless phenomena, possessing possible potential challenge to a theory, have a tendency to be ignored and forgotten by virtue of the very fact that they are nameless.
The problem of labels is reflected in the issue of scientific pictures and models. Pictures are envisioned as descriptions of reality while models are regarded as helpful tools of thought. Models and pictures, therefore, are not equivalent. In part because the picture and the model often bear the same label, they are often confused. One should carefully distinguish by more than a mere label between one's statements regarding a model and one’s observations pertaining to the physical reality. But scientific writers and/or their readers on occasion fail to make the necessary differentiation. For example, quantum theory provides a model, not a picture of the atom. Uncertainty and anomaly are properties of the Copenhagen atom-model, not of the physical atom or electron. Larson maintains that abandonment of causality by the Copenhagen school of thought is a consequence of confusing a model and a picture of the atom. In the extreme case, a model may sever all ties with reality and explain nothing whatsoever of the physical reality.
The Reciprocal System reflects a philosophy of mathematics in the construction and application of physical theory which diverges from the thought of the current majority of scientists. D.B. Larson vehemently objects to equating a mathematical expression with a satisfactory physical explanation. Mathematical expressions may offer a clue to physical reality, but they are in no sense to be regarded as a blueprint of that reality. A useful tool, mathematics is not essential for thought, nor is it a substitute for thought. Some conceptual ideas can be cast in mathematical form, but not all mathematical expressions represent conceptual knowledge. Heavy emphasis is placed on the idea that the physical interpretation of a correct or nearly correct mathematical formulation may be quite incorrect. Today, relatively more ingenuity should be exercised in conceptual clarification of the mathematical expressions of physical theory than in invention of even more powerful mathematical tools.
Indeed, mathematics can be an obstruction to the development of physical theory among those for whom simplicity is suspect. Such scientists have a tendency to equate complexity with rigor. Modern mathematics provides powerful assistance in modifying theories to fit facts. Mathematical apparatus may so obscure the inadequacy of a theory that would otherwise be properly rejected. Application of more complex mathematical tools can lead to “in principle" solutions which pragmatically cannot be executed even with the aid of an electronic computer. To such "in principle” solutions Larson is opposed as a form of self-deception.
Before turning to the critical function of the scientist in theory construction and testing, a few final points of Larson’s philosophy of scientific theory may serve as summary. First, all theories remain perpetually tentative. Hence, no theory is an acceptable basis for verifying or disproving another theory. Successful postulates of a theory will accept other laws as valid. It happens that most classical theory is in accord with the Reciprocal System together with the Planck hypothesis, the photoelectric effect, the Lorentz transformation, and the mathematical aspects of special relativity.
A theory is to be assumed incorrect if it lacks experimental support or if it is contrary to fact. This is not to deny that incorrect theories may yield correct experimental predictions in a restricted domain. However, a theory is to be judged, not on the basis of past successes, but rather on the basis of present failures. Furthermore, a theory constructed on the principle of impotence and thereby incapable of proof is to be rejected a priori as incorrect. Application of the principle of impotence is opposed because it tends to undermine the intrinsic reasonableness of the universe. Rather than assume the universe to be absurd, as many do, one should regard assumptions leading to an apparent absurdity as ridiculous. Finally, rejection of an incorrect theory on valid scientific grounds entails no obligation to provide a new theory.
If and when a new physical theory is proposed, projection of its prospects for objective investigation should not ignore the triad of physical reality - physical scientist - physical theory. Physical reality per se does not require man’s aye or nay, not even his existence, but the human factor is obviously a key ingredient of theory. Subjective investment in currently accepted theory, a most impressive edifice, does not tend to predispose the intellect to open-minded objectivity toward other possibilities. Rigorous training and seasoned experience, which have shown certain thought patterns to be productive, may generate a certain mental and emotional inertia inhospitable to alternatives. The scientist, as a human being, emotionally enjoys a certain identity with the community, past and present, which has contributed so heavily to modern physical theory. Although the mind of a reputable scientist functioning analytically would reject the notion as illogical, there may remain the feeling at the emotional level that the scientific community already has considered the viable alternatives. A scientist is also exposed to the risk of eventually accepting as true a theory which he initially regarded merely as the best explanation pro tempore. More blatantly, a theory may rise to a position of acceptance because it seemed to be the only logical candidate. Larson believes that special relativity filled such an intellectual vacuum.
A number of psychological factors magnify the scientist’s hesitancy to objectively consider radically different ideas. One may indeed experience an antagonistic reaction to a theory which challenges the very foundations of one's physical perspectives. Rather than admit ignorance, a scientist may unwittingly tender an irrational explanation for a physical phenomenon. Interpretation of data may be colored by one’s theoretical views. Specialization may cause confusion of fact and interpretation. That is, one specialist may properly conditionally circumscribe his interpretation, but another specialist in a different field may absorb the interpretation as fact. A scientist may find himself dwelling on the past accomplishments of a theory instead of confronting its present failures. He may falsely assume that other competent scientists have previously critically examined the concepts of a theory. He is troubled with the insidious temptation to equate general acceptance by the scientific community with scientific proof. Particularly in the United States of America he is subtly propelled by a negative social pressure to conform.
The scientist conscious of such subjective influences deriving from his humanity is better equipped for objective scrutiny of alternate theories. But he is obliged to recognize that objectivity is a goal to be sought, not a quality ingrained. Contrarily, current physical theory has been virtually elevated to the status of articles of faith which may not be questioned. Astronomer E.J. Opik laments from bitter experience:
“While religious - or antireligious - abstract dogma stands beyond the reach of science, in science itself the dogmatic approach has played, and i still playing, a conspicuous role, but with a difference: the preconceived ideas in science are subject to verification or rejection through further research. They remain “dogma” only as their adherents refuse to consider alternatives to their doctrines, rejecting criticism beforehand.”
Such regard for physical theories of the moment suggests an emotional attachment to them which makes logical analysis difficult if not suppressed. Larson pessimistically observes with Max Planck that new ideas must wait for another generation of scientists.
Several mental stances may engender sluggishness in consideration of alternatives. Scientists tend to be predisposed against any new theory because admittedly there is a strong likelihood that it is wrong. A new theory may become trapped in a whirlpool of obscurity. A theory of significance is likely to diverge significantly from accepted theory. It may, therefore, receive little consideration because the greater effort required to assimilate and test it could generate proportionately more opposition. Scientists, furthermore, are conditioned to expect only small theoretical advances. They tend to expect a new theory to contain existing theories or, at least, to be consistent with them. Accustomed to pro tern theories of limited scope, a scientist tends to weigh which theory is better rather than which theory is true. Perhaps the ultimate negative predisposition is toward an irrationally absurd universe. Such physicists assume the a priori impossibility of a comprehensive, clearly understandable, general physical theory.
By contrast, Larson’s development of the Reciprocal System of theory reflects an explicitly optimistic attitude toward the universe. Granting the possibility of a temporary unfamiliarity, Larson is opposed to the doctrine of incomprehensibility. One should labor under the assumption that a complete and understandable physical theory is possible. Such theory should portray the universe as simple, understandable and rational.
A desirable physical theory should display certain key characteristics. A unified theory will provide for deduction of all physical principles in all areas of physical science from one set of postulates. No internal contradictions shall be permissible in a self-consistent theory. Accuracy requires all deductions to be in fu11.agreement with the result of observation or not inconsistent with any observation. Such theory shall be unequivocal: consequences of the postulates must be specific; no postulate of impotence will be permitted in order to avoid admitting a discrepancy. Rationality requires a definite explanation of all phenomena with express exclusion of ad hoc assumptions. The ideal theory will be complete, qualitatively and quantitatively describing a complete theoretical universe, providing for the existence of all phenomena and of their interrelations. Completeness precludes introduction of the results of observation as foundation for the theoretical structure. These criteria lend themselves to an eminently testable theory, a theory which can be tested in a wide variety of situations against available facts.
Although the fundamental physical assumptions and postulates receive detailed consideration in the next chapter, perhaps the philosophical preliminaries should include a brief resume of Larson's key perspectives on the universe. First, he envisions a Euclidean universe. Its space is three-dimensional, homogeneous, and isotropic. He sees no experimental evidence for curvature of space by matter or by gravitational fields. Space shows no experimental evidence of possessing the properties required for propagation of gravitational effects. No such ad hoc assumptions will be permitted by metaphysical premise. This universe conforms to ordinary commutative mathematics and its magnitudes are absolute.
Larson's view of time contrasts strikingly with conventional notions. Time is subject to a uniform progression, but it is not necessarily unidirectional. It is scalar insofar as it has no direction in space. But time is three-dimensional, not one-dimensional, being an assumption with far-reaching implications. A reciprocal relationship exists between space and time. Time is neither an isolated property as in the Newtonian scheme nor is it a component of a four-dimensional space-time continuum as in special and general relativity. Since so many aspects of nature are discontinuous, Larson proposes that space and time should also be considered discrete.
Space and time are no longer a mere background or ‘'stage” in which matter and energy occupy prominent positions. The interchangeability of basic physical entities suggests to Larson that one should reject the notions of “building blocks” and "parts” as being fundamental. The interconvertibility of matter and radiation prompts him to consider neither as basic in the universe. He postulates that motion is the fundamental entity in terms of which all physical phenomena can be adequately described. Such motion will also be quantized.
In terms of this metaphysical context, the Reciprocal System of theory attempts nothing less than an explanation of all physical phenomena of the entire universe! Since no other unified general theory has ever been proposed, it is a unique theory rather than a new theory replacing or modifying others» The above discussion indicates the criteria according to which Larson believes the theory should be constructed, tested and evaluated. Since the present research is restricted to the Reciprocal System relative to astrophysical phenomena, it should be borne in mind that this is only a small portion of the scope of the theory.