It is not necessary to be a member of the kind of a super-race envisioned in the preceding chapter in order to arrive at the postulates that were there formulated. But it took the author of this book almost twenty years to reach these conclusions by the slow and painful processes that man normally employs when he attempts to change the direction of his thinking, whereas the preceding discussion shows that they could be reached in less than twenty minutes by following the cold-blooded, logical and systematic course of procedure that we could expect homo super-sapiens to utilize.
Because of the inherently strong probability that the results of extrapolation are valid, we know in advance that the two Fundamental Postulates which express the conclusions of the investigation are almost certainly a correct representation of the basic relations of the actual physical universe but, of course, we will want to eliminate the qualification “almost” from the foregoing statement, and the second major objective of the present project has therefore been to prove that these postulates formulated in the first phase of the project are, in fact, correct. As indicated in the introductory chapter, the method that has been utilized to accomplish this proof is that of reducing the probability that the postulates are incorrect to the point where this probability is negligible.
In carrying out this program the necessary consequences of the postulates have been developed in much detail and the validity of the conclusions reached as a result of this development has been established by comparing these theoretical conclusions with the results of observation and measurement. The feature of the theoretical development which makes these comparisons so significant is that even though the conclusions reached by this means are so numerous and so all-embracing that they constitute a complete theoretical universe, yet the entire system has been derived solely from the two Fundamental Postulates without introducing anything from the observed physical universe or from any other outside source. The mere existence of space and time with the postulated properties gives rise to certain primary consequences. Interaction of these consequences with each other and with the postulates then results in a large number and variety of secondary consequences, which, in turn, involve further consequences, and so on until a whole theoretical universe has been defined.
In view of a rather general reluctance to believe that such a thing is possible, because previous efforts to unify physical theory have been wholly unsuccessful, it seems advisable at this point to emphasize the fact that the statements in the preceding paragraph mean just exactly what they say. The development of the consequences of the Fundamental Postulates leads not only to a definition of the relations between physical entities, all that is normally expected of a theory, but also requires the existence of these entities, and where numerical values are involved, indicates the magnitudes, or at least the possible magnitudes, of such values. Matter, for example, is not brought into the system because we find it in the observed physical universe. An entity with the properties that we observe in matter must exist if the Fundamental Postulates are valid. It must exist in the form of a series of elements, these elements must combine in certain ways and no others, the elements and their compounds must have certain properties such as volume, specific heat, etc., these properties must conform to certain sets of numerical values, and so on. All of these are necessary and unavoidable consequences of the two postulates: purely theoretical conclusions that are, so far as their origin is concerned, completely independent of what we observe in the actual physical universe.
The entire Reciprocal System, consisting of the two Fundamental Postulates together with their necessary consequences, is thus a single integral unit. If the postulates are valid, then each and every one of the necessary consequences is likewise valid. Conversely, if even a single one of the thousands of these necessary consequences conflicts with a fact that has been definitely established, the postulates are thereby invalidated and the entire structure falls. This unitary character of the system is the feature that makes proof by the probability method possible.
An analogy that was discussed in considerable detail in Beyond Newton compares the construction of a physical theory to the preparation of a map, the usual process of theory construction being compared to the traditional method of map making, and the development of the theoretical structure of the Reciprocal System being compared to the production of a map by aerial photography. Whatever the production process may be, either a map or a theory must be checked for accuracy before we can put any confidence in it, but the nature of the process of construction makes a big difference in the kind of a test that we apply. In testing a product of the traditional map making or theory construction processes it is necessary to verify each and every feature of the map or theory individually, as there is little or no connection between the individual features and, with relatively few exceptions, verification of any one feature does not guarantee the accuracy of any other. But in testing an aerial map or an analogous theoretical product such as the Reciprocal System, where the entire map or theory is produced in one operation by a single process, every test that is made by comparing the product with the observed facts is a test of the process itself, verification of the individual features selected for test being merely incidental. If anything that can definitely be seen on the map conflicts with anything that we positively know from direct observations of the terrain, then the process is not accurate and the map as a whole can be discarded.
On the other hand, since each check against the observed facts is a test of the accuracy of the process, every additional test that is made without finding any discrepancy reduces the mathematical probability that any such discrepancy exists anywhere on the map. Hence by making a sufficiently large number of correlations distributed over a substantial portion of the map the probability of the existence of any error can be reduced to a negligible level. The same is true of the Reciprocal System. When we check the theoretical conclusions of this system against the results of observation and measurement in thousands of different applications throughout an extremely wide range of physical phenomena and find no contradiction or inconsistency, then we have reduced the mathematical probability of any error in the basic structure of the system to the point where it is negligible.
In aerial photography we first complete the map and then, after the completed product is available, we verify its accuracy by making whatever checks against the results of observation may seem appropriate. From a purely logical standpoint there would be much in favor of following the same procedure in the physical area; that is, developing the theoretical universe of the Reciprocal System, the RS universe, as we will hereafter call it for convenient reference, in complete detail, without any reference at all to the observed physical universe and then, after the theoretical product is complete, comparing the individual features of the RS universe with the corresponding features of the observed universe. As a practical matter, however, this procedure is not feasible, particularly in the initial presentation of the system, because of the enormous amount of detail involved. What we will have to do is to proceed with a step by step development of the consequences of the Fundamental Postulates of the system and, as each step is taken, compare the features of the RS universe defined by those consequences with the corresponding features of the observed physical universe.
It is essential to bear in mind, however, that all of the conclusions that are reached in the theoretical development refer to the theoretical RS universe, not to the physical universe. This would be obvious if we were able to complete our theoretical map of the universe in its entirety before we began the operation of checking it against experience, but the situation is not altered by the piecemeal procedure, which we find it necessary to follow. For example, when we arrive at the conclusion that sub-atomic particles are incomplete atoms, not constituents of atoms, this is not a conclusion about the actual physical universe, nor has it been reached by a consideration of the available knowledge concerning physical particles of this kind. It is purely a theoretical conclusion: something that necessarily and unavoidably follows if the Fundamental Postulates of the Reciprocal System are valid. The assertion that is here being made is that in the theoretical RS universe developed from these postulates by logical and mathematical processes, the theoretical entities corresponding to sub-atomic particles are incomplete atoms. This assertion is not subject to challenge unless it can be contended that there is a flaw in the logical development whereby it was derived from the postulates.
A similar theoretical development, which determines the features of the theoretical RS universe applicable to the particular field under consideration, is carried out in each section of the presentation in this and the other volumes of the series. In the discussion of these matters, frequent reference will be made to the fact that the Theoretical conclusions apply specifically to the RS universe, but this presentation would be much too awkward and unwieldy if we attempted to qualify all theoretical statements in this manner. It should therefore be emphasized in advance that every theoretical statement in the subsequent pages-every statement about what entities are theoretically present in the universe, how they are related, and what properties they possess-is a statement about the RS universe, whether or not it is specifically labeled as such.
In the second phase of the presentation, carried out in conjunction with the theoretical development, it will be shown that each and every one of the theoretical conclusions is consistent with all positively established facts. Here, again, it is important to keep in mind the exact nature of the undertaking. No attempt is being made to prove the validity of each of the theoretical conclusions individually. For instance, the presentation will offer no proof that sub-atomic particles are incomplete atoms rather than constituents of atoms; what it will do is to show that there are no positively established facts that are inconsistent with the hypothesis that this is the true status of the sub-atomic particles in the physical universe, just as it necessarily is in the theoretical RS universe.
The object of comparing the theoretical conclusion regarding the sub-atomic particles with the experimental and observational data is not to test the validity of this conclusion itself, an undertaking which is not feasible at present because of the lack of sufficient data of a specific and unequivocal character, but to test the validity of the hypothesis that the theoretical RS universe is identical with the actual physical universe. If there were any definitely known facts about the observed sub-atomic particles that could be shown to be inconsistent with the nature and properties of the corresponding particles in the RS universe, as deduced from the Fundamental Postulates, then the postulated identity of the theoretical and observed universes would be disproved. But since there is no such inconsistency, a certain degree of probability has been established for the identity hypothesis, regardless of whether or not any definite agreement can actually be demonstrated in this instance. Each additional comparison of the same nature is another test of the validity of the same hypothesis. If any contradiction or inconsistency is found in any of these tests, the identity is disproved. If no such discrepancy is found, then every additional test of this kind decreases the mathematical probability that any discrepancy exists anywhere. Hence by making a sufficiently large number and variety of similar tests, the probability that the theoretical RS universe is not identical with the observed physical universe can be reduced to the point where it is negligible, which is one way of proving that the two are identical.
This proof that the observed physical universe is identical with the theoretical RS universe means that each and every feature of the physical universe exists exactly as portrayed by the theoretical development. Thus, while we do not submit any individual proof that sub-atomic particles are incomplete atoms, we prove collectively the validity of all of the theoretical conclusions derived from the postulates of the Reciprocal System, including the one that we have been using for purposes of illustration: the conclusion that sub-atomic particles are incomplete atoms.
The plan of presentation of the Reciprocal System in the several volumes of this series can thus be summarized as follows:
It is evident from this that the status of previously existing theories has no bearing at all on the points at issue. The two numbered statements can be refuted only if (1) it can be shown that there is a logical flaw in the chain of deductions from the postulates, or (2) it can be shown that there is an inconsistency between the consequences of the theory and the established facts. Conflicts with previous theories have no relevance to either of these issues.
Under the circumstances it would be quite appropriate to present the new theoretical structure, and establish its validity in the manner indicated, without any reference at all to previous theories. This policy was followed, with only a few exceptions, in the initial volume of the series, The Structure of the Physical Universe. Experience has indicated, however, that comparisons with previous ideas have considerable value as an aid in gaining an understanding of the new concepts and theories, and for that reason the more recent books have devoted a substantial amount of space to discussing existing theory. It is important to recognize that such discussion is merely for purposes of clarification, and has no place in the actual development of the primary thesis of this work. In particular, it should be understood that no issues are being decided on the preponderance of evidence.
Ordinarily, when a question such as that of the status of the sub-atomic particles arises, the relative weight of the evidence on each side is the basis on which a decision is made. The evidence for and against the theory that the sub-atomic particles are atomic constituents is gathered and evaluated, the same is done for the theory that these particles are incomplete atoms, and a decision is then reached in the manner of a verdict in a case in court. Such a decision is a judgment—an opinion as to which case is the—and it is subject to all of the weaknesses of human mental processes as well as to the uncertainty that is inherent in conclusions based on interpretations of incomplete and often contradictory evidence. The program of this work, on the other hand, leads to a purely objective conclusion, in which opinion and judgment play no part. Definite and specific theoretical conclusions are compared with positively established facts and in each case the answer can be an unequivocal yes or no.
This obviously means that a great deal of care must be exercised in making certain of the authenticity of the supposed facts that are utilized for the comparisons. There is no justification for basing conclusions on anything that falls short of positive knowledge. In testing the accuracy of an aerial map we realize that we can not justify rejecting the map because the location of a lake as indicated on the map conflicts with the location which we think that the lake occupies. In this case it is clear that unless we actually know exactly where the lake is, we have no legitimate basis on which to dispute the location shown on the map. We also realize that there is no necessity for paying any attention at all to items of this kind: those, which are uncertain. There are hundreds, perhaps thousands, of features about which we do have positive knowledge, more than enough for purposes of comparison, so we do not need to give any consideration to features about which there is any degree of uncertainty.
The same is true in testing the validity of the Reciprocal System. There are thousands of places in all of the major fields of physical science where the pertinent facts are positively and definitely known; as in the case of the aerial map, more than enough for purposes of comparison. Here again there is no justification for giving any consideration at all to features about which there is any degree of uncertainty. The reason for stressing this point so strongly is that so many of the items included in the current store of “knowledge” in physical science is not established facts at all but merely interpretations of the actual observations. The conclusions of the Reciprocal System conflict with a great many of these interpretations, but conflicts with “knowledge” of this kind are meaningless. There is no good reason why a new theoretical structure should be expected to agree with existing theories or with interpretations of experimental results based on those theories. Indeed, a correct theory must disagree with at least some of them; otherwise it could not succeed where they failed. The Reciprocal System is prepared to meet the test of conformity with all positively established physical facts. A correct theory can do no less, but neither can it do more; it cannot agree with both fact and error.
Many of the erroneous conclusions of present-day science have been generally accepted for so long a time that they are widely believed to be factual, and where items of this kind have been encountered in the development they have been given some attention in order to demonstrate their true status. It should be understood, however, that for present purposes it is not necessary to prove that these conclusions are wrong; all that is needed is to show that there is a reasonable doubt as to their validity. Where there is any substantial doubt as to the correctness of currently accepted ideas, any conflicts with the new system are meaningless; they have the same standing as the conflict between the position of the lake shown on the aerial map and the position which we think that the lake occupies.
This is an important point, as it is easy to demonstrate that many accepted ideas are mere assumptions, which have no factual basis, whereas it may be extremely difficult to disprove them. For example, there is a great deal of indirect evidence indicating that the commonly accepted explanation of the source of energy of the stars, the conversion of hydrogen to helium, is not correct, but to prove this point conclusively is not possible at present, because of the lack of direct information as to the conditions that exist in the stellar interiors. The subject of the stellar interiors, says Bonnor, “is an extremely difficult one because all that is really observed of stars is their exteriors, and from this the whole structure of the interior has to be inferred. As Fred Hoyle once said, it is like trying to deduce the composition of a chimney sweep from the color of his skin.”75 But this same lack of information is equally effective in reverse; it precludes proof of the affirmative position as well as the negative. Hence even the staunchest supporters of the hydrogen conversion theory have to admit that it is only a hypothesis. This means that if the Reciprocal System conflicts with the current theory of stellar energy generation—which it does—it is not in conflict with an established fact, which would be fatal; it is merely in conflict with a currently popular hypothesis, and this conflict has no actual significance one way or the other.
In view of the extraordinary importance attached to any one possible inconsistency between theory and fact in testing the Reciprocal System, it is essential to use an extraordinary degree of care in making certain that the alleged facts utilized for comparison are actually facts, not assumptions or interpretations masquerading as facts. When every test is a crucial test-one which can destroy the entire development if a definite inconsistency is found-then it is imperative that every test be a thorough and honest test. In principle every new theory is entitled to be evaluated in the most careful and painstaking manner, since new ideas are the most important raw material of scientific investigation, and if the human race habitually followed the logical and systematic procedures that we attributed to homo super-sapiens this policy would no doubt be carried out, but human science does not operate in this manner. The scientist who undertakes to evaluate a new theory of the usual kind knows from the start that the odds are overwhelmingly against it. The great majority of all new theories that are proposed are wrong in some essential respect, hence the evaluator does not expect that the particular new theory which he is examining will meet his tests, and he would be greatly surprised if it did. He therefore views his task more as a matter of locating and exposing the error which he feels certain exists in the new theory than as a matter of ascertaining whether or not there is any such error, and he is psychologically prepared to render a negative verdict as soon as some seemingly unfavorable bit of evidence appears, without taking the time and trouble to examine that evidence carefully and critically.
In the present instance, this kind of an examination is simply not adequate. Here the probabilities are completely reversed, and it would be very surprising if the theory does not meet the particular test that is being applied. The postulates of the Reciprocal System are not mere assumptions on the order of the basic hypotheses of the usual physical theory, but have been derived by the reliable process of extrapolation of observed facts and hence have a strong probability of being correct. It is quite unlikely, the probability principles assure us, that any discrepancy will be found between the results obtained from this system and the true facts. Consequently there are, in this case, strong grounds for doubting the validity of anything that seems to contradict the validity of the theoretical conclusions. When we take this into consideration along with the extraordinary effect that any one inconsistency would have if it did exist, it is clear that any seeming conflict should be examined with the utmost care and thoroughness. The Reciprocal System admittedly conflicts with many tenets of present-day scientific doctrine, but it can be shown that these are not conflicts with established facts, and hence they have no bearing on the points at issue.
It is worth noting, however, that the conflicts with the current thought of the scientific profession are not nearly as numerous as might be expected from the basic nature of the new concepts that are being introduced. Surprising, as it may seem, in view of the drastic nature of these conceptual changes, the new system is in full agreement with the great bulk of existing physical theory. There are some rather spectacular conflicts with the so-called “modern” developments, to be sure, but in spite of the prominence that “modern physics” has acquired in recent years, these subjects in themselves represent only a relatively small part of the total field. Almost all of the theoretical relations applicable to our immediate environment which have been firmly enough established to enable the applied scientists-the engineers-to utilize them on a practical basis can be derived from the postulates of the Reciprocal System in essentially the same form in which they are now known. These relations-Newton’s Laws of Motion, the gas laws, the laws of thermodynamics, the laws of optics, the kinetic theory, Newton’s Law of Gravitation, Kirchhoff’s Laws, Ohm’s Law, Hess’s Law, Faraday’s Law, Avogadro’s Law, Pascal’s Law, and so on-are incorporated into the Reciprocal System practically intact. Where some change has been necessary, as in the laws of motion, this change has usually been in the definition of the concepts entering into the particular relation, rather than in the physical or mathematical expression of the relation itself. Newton’s Laws of Motion, for instance, are retained in his original form, but the concept of time has been altered.
The new system is likewise in harmony with at least some of the original concepts and ideas of the so-called “modern” physics: those portions of modern theory, which are based directly on empirical findings. Planck’s original theory of the quantum of radiant energy is fully compatible with the consequences of the postulates of the system, as is Einstein’s extension of Planck’s hypothesis to the photoelectric effect. The Lorentz transformations are likewise acceptable to the Reciprocal System and, as has been brought out in the preceding pages, this system and the Special Theory of Relativity are therefore in agreement mathematically, although the new information developed from this present investigation shows that the Special Theory is conceptually wrong.
Within the realm of everyday experience-the fields of the engineer, the chemist, the geologist, etc.,-the role of the Reciprocal System has been primarily a matter of filling in the gaps in existing knowledge. In such fields as that of chemical combination, for example, where existing theory is painfully inadequate, it has been possible to establish complete and correct theoretical structures. Furthermore, the new system has made a major contribution by extending the scope of theory to the magnitudes of physical quantities. Of course, previously existing theory covers the mathematical relations between physical quantities-indeed, the quantitative treatment is often regarded as the essence of science-but in general, these previous theories have not been able to account for the individual magnitudes. They have not been able, for example, to specify the magnitude of the gravitational constant, or the molar gas volume, or Planck’s constant h, or the Faraday constant, and so on; it has been necessary to measure these quantities and to use the values thus determined.
Likewise, the theorists have not heretofore been able to devise any means whereby we can calculate from purely theoretical foundations (except in rare and very special cases) the numerical values of the properties of physical entities-such properties as density, specific heat, viscosity, refractive index, etc.-even though these properties do have definite magnitudes which clearly must be subject to some kind of physical laws. The development of the postulates of the Reciprocal System yields not only qualitative relations but also quantitative relations, and the absolute magnitudes, or at least the possible magnitudes, of such items as the foregoing can be derived from theory alone.
In the far-out regions the task of the new system has been to build a completely new theory. Here, where empirical knowledge has been too scanty and too confused to constitute any effective restraint on the imaginations of the theorists, previous theory constructors have attempted to explain the observed phenomena by pure speculation and ad hoc modification of the principles applicable to the more familiar regions, and as a result it is here that theoretical science is finding itself unable to keep up with the progress of experimental discovery. The Reciprocal System is not subject to the handicaps that conventional theory encounters in these less accessible regions, as this system derives its entire theoretical structure from a logical and mathematical development of the consequences of the Fundamental Postulates, and does not depend on guidance or assistance from observational or experimental information. By reason of this purely theoretical derivation, the new system has been able to arrive at complete and consistent theories covering the phenomena not only of those regions where observational data are meager, but also some other regions, which are still completely unknown observationally.
The most drastic changes made by the new system, as distinguished from additions to or clarifications of previous theories, come in these areas where scientists have, without being aware of the fact, made contact with regions of the universe other than the one in which we happen to be located and to which our familiar physical relations apply. It is here that the theorists have attempted the impossible; they have attempted to fit the relations appertaining to one region of the universe to the phenomena of other regions that are actually governed by totally different, and in some cases diametrically opposite, relations. And it is here that they have, as a direct consequence, found themselves in a state of confusion and uncertainty: a situation that is responsible for what Hanson calls “the agonies which now confound quantum theory and cosmology,”76 and for the recurring “crises” in other physical fields.
In the light of the information developed in this present investigation it is clear that the existing confusion was inevitable. The theorists who have attacked these problems have lavished an immense amount of intelligence, ingenuity and perseverance upon them, but a problem cannot be solved, no matter how great the ability of those who undertake its solution, or how much effort they apply to the task, if the basic nature of the problem is misunderstood. “The most interesting fact about laws of nature,” says Michael Scriven, “is that they are virtually all known to be in error.”77 But this conclusion is not at all representative of the true situation; it is merely one of the results of the physicists’ misconception of the nature of the phenomena with which they are dealing. Most of the so-called “classical” laws are correct in their proper sphere, and the “errors” that are commonly charged against them are simply consequences of attempting to apply them in areas which are governed by totally different relations.
As Freeman J. Dyson points out, some major innovation is required in order to “put an end to the present confusions”14 an “epoch-making” innovation, he says. The Fundamental Postulates of the Reciprocal System as developed by extrapolation of the observed properties of space and time in the preceding chapter now provide us with the kind of a conceptual innovation that is needed, and the remainder of this volume will be devoted to showing how the development of the consequences of these postulates brings order out of confusion in the unsettled areas of physical science.
This is an appropriate point at which to reiterate that the entire theoretical development rests upon these two postulates, without the introduction of any additional assumptions or any data from observation. In the next chapter it will be demonstrated that the existence of matter and of radiation are direct consequences of the postulates, and that the primary properties of these entities are specifically defined by the further development of these consequences. Chapter VII will then show that matter, which originates in this manner, must exist in the form of individual atoms, and that the possible structures of such atoms constitute a series which we can identify as a series of chemical elements. Further development of the consequences of the postulates, without reference to anything outside of the system defined by these consequences, then leads to a complete theoretical universe which, on comparison, we find to be identical with the observed physical universe.
The program that will be followed in the subsequent pages of this present volume will not involve complete development of any sector of the theoretical RS universe, but will merely trace the development far enough in each major physical field to indicate the general nature of the modifications which will be necessary in each of these areas by reason of the new concepts of space and time which the theory introduces. As the theoretical structure is gradually erected, the way in which it clarifies hitherto obscure points and brings seemingly discordant observational data into harmony will be illustrated by a brief consideration of the appropriate phenomena. Details will, however, be held to a minimum, as the aim of this presentation is to give a bird’s eye view of the new theoretical structure as a whole: one which will emphasize the unitary character of the system, the simple and logical nature of the explanations which it offers, and the complete agreement with the facts, including many that previous theories have been unable to cope with.
There is nothing surprising or unexpected about the fact that a theoretical system which is able to prove that it is correct in its entirety should be capable of providing simple and logical solutions for extremely difficult problems of long standing, as well as meeting the many less exacting demands that are made upon it. Such achievements are, however, very dramatic and conclusive demonstrations of the power and versatility of the new system, and for that reason they warrant some special attention over and above whatever comment may be made as to their contribution toward the general proof of the identity of the theoretical RS universe and the observed physical universe. In the ensuing discussion, therefore, we will specifically point out a number of the Outstanding Achievements of the Reciprocal System and will explain the significant contribution that each has made toward overcoming previously existing difficulties.