The Fundamental Postulates
It is generally recognized that present-day physical theory is no longer adequate to meet the growing demands upon it. Those theoretical concepts which only a few years ago were hailed as the keys to the innermost mysteries of nature are now totally unable to cope with the flood of new discoveries emanating from our laboratories and it has become obvious that some very different approach to the problem is essential. As one observer, Ernest Hutten, sums up the situation in a recently published book, “Most physicists feel that the time is ripe, again, for a radical change in our ideas, and for a new theory.”
In retrospect it is clear that this is not a new development but a recurring crisis; each time a major advance is made in the observational field existing physical theory finds itself unable to account for the newly discovered facts and a drastic revision of the theory is necessary. But each successive revision no more than takes shape before a new crisis is upon us; a new set of facts is discovered which the revised theory does not anticipate and cannot explain. A certain amount of modification and revision is no doubt inevitable in the early stages of any theory but the same pattern of helplessness in the face of new experimental advances has been repeated so often that it becomes pertinent to inquire whether modern theory is actually proceeding in the right direction. The continually renewed demand for a “radical change in our ideas” strongly suggests that something more than a minor reconstruction is required and that we should back up and take a fresh start along a different path.
When we review the evolution of modern physical theory to appraise the direction in which we are now moving as a preliminary to charting a different course, it is apparent that the outstanding general trend in the theoretical development has been the gradual loosening of the ties between fundamental theory and the facts of everyday life. Beginning with Einstein’s introduction of the concept of physical quantities whose actual magnitude varies with the position of the observer, the divergence has increased at an ever accelerating rate until the latest theoretical developments have passed completely beyond the bounds of objective reality and have placed the basic processes of nature in what Bridgman calls “a shadowy domain which he (the physicist) cannot even mention without logical inconsistency.”
In the scientific field we are inclined to think that we have come a long way since the days when all unexplained phenomena were attributed to demons and ogres, but the current tendency to meet all difficult problems by assuming the existence in the unobservable region of the universe of phenomena and relationships totally unlike those which are found in the known world is essentially the same pattern that was followed by primitive man: a resort to the supernatural when ever explanation becomes difficult. Aside from the personification of forces, which is no longer in vogue, it is hard to detect any material difference between the mysterious unobservable forces of modern science and the demons of old.
Of course we must admit that when we are dealing with the unknown any assumption may be valid, no matter how fantastic it may seem when judged by the standards of our everyday experience, and if the bizarre theories of modern physics were adequate to meet the demands upon them they would certainly be acceptable regardless of the doubts with which their basic assumptions might have been regarded initially. But when these theories are not adequate and when insistent demands for revision are heard from all directions, it is in order to suggest the possibility that an undue readiness to part company with reality and to build the foundations of theory on unsupported assumptions may be the root of the present difficulty. In this connection it should be recognized that although we cannot arbitrarily reject any fundamental assumption that is proposed, since we must concede that the true relationships in the areas beyond the frontiers of knowledge are unknown, there is in each case one possible assumption which is initially so far superior to all others, so much more likely to represent the true situation, that we are never justified in turning to anything else unless and until we have established beyond a reasonable doubt that the consequences of this assumption are not in accord with the facts. This greatly superior hypothesis is, of course, the assumption that the relationships which are found to apply in the regions accessible to observation also apply in the unknown regions.
It will no doubt be contended that in physical science the extrapolated relationships have always been examined and their inapplicability has in each case been demonstrated before any other assumptions were made. Someone is sure to point out that relativity theory was formulated only alter Newton’s Laws failed at high velocities; that non-Euclidean geometry was developed only when Euclidean geometry came to a dead end; that the concept of atomic events as happenings which do not take place in space or time was devised as a last resort only after all attempts to explain these phenomena by means of the laws of the world of objective reality had proved fruitless, and so on. But this present investigation has disclosed that the applicability of a theory based wholly on extrapolated relations was never tested in any of these instances, and that the supposed failures were not actually due to deficiencies in the laws being examined but to the fact that in their application these laws were always coupled with arbitrary and erroneous assumptions as to the relation between space and time: a fatal handicap for any theoretical structure.
Newton looked upon space and time as two independent entities. Modern theory recognizes that they are not independent, and regards them as components of a four-dimensional structure in which there are three dimensions of space and one dimension of time. But if we examine the bases of these two hypotheses it is apparent that they are both purely arbitrary assumptions, and in view of the points brought out in the preceding paragraphs neither of them should ever have been given any consideration until after the consequences of extrapolating the relation applicable in the known region had been thoroughly explored. In this known region the relation between space and time is recognized as motion. Motion is measured as velocity, and in velocity time and space have a reciprocal relationship; that is, more space is the equivalent of less time and vice versa. The most conservative assumption that we can possibly make concerning the general relation of space and time, the hypothesis that is by far the most probable representation of the underlying truth, is that this relationship which holds good in the known phenomenon also holds good in general. This hypothesis of a general reciprocal relation between space and time has therefore been adopted as the first of the assumptions of the new theory that will be developed in this work and it may be regarded as the cornerstone of the entire theoretical structure.
When we thus begin with a solid foundation based on extrapolation of an observed relationship rather than starting with a purely arbitrary hypothesis, we will find that the necessity for postulating that “things are different” in other parts of the universe disappears, and we will be able to take the position that the portion of the universe which is accessible to our observation is a reasonably representative sample of the whole and that the physical behavior of all other sectors of the universe can be deduced from the relationships which we find in the observable regions. This means, of course, that a large part of the existing structure of physical theory must be discarded, regardless of the great skill and ingenuity that have gone into its construction, as even the highest degree of competence cannot derive the right answers from the wrong basic assumptions. Starting with an untruth in physical theory is no different from making a false statement in everyday life; in either case an ever widening structure of fabrication is required in order to evade the contradictions which develop as a consequence of the original deviation from the truth.
Having arrived at a logical hypothesis as to the general relationship between space and time, let us now apply the same extrapolation process to the formation of the additional assumptions that will be necessary for a complete description of space-time. It is clear that when the reciprocal assumption is made it must immediately be followed by another. If space and time are reciprocally related they must have the same dimensions. We have very little specific knowledge of time, either as to dimensions or otherwise, but we do know from observation that there are at least three dimensions of space, and the simplest assumption which is consistent with the reciprocal hypothesis and the observed properties of space is that both space and time are three-dimensional. Here again the assumption is merely an extrapolation from the known to the unknown. We observe space to be three-dimensional where we are in direct contact with it, and by extension we assume that this is a general characteristic valid throughout the universe. The reciprocal hypothesis then requires the further extension of this assumption to time, a step which may also be regarded as simply a generalization of the geometrical properties of the more readily observed component of space-time.
The third assumption of the new theory is that space and time exist in discrete units. This, too, is an extrapolation from known facts into the region that is unknown. In the early days of science it was generally believed that all of the primary physical phenomena were continuous and infinitely divisible, but as knowledge has grown during the succeeding centuries one after another of these phenomena has been found to exist only in units. The atomic structure of matter was the first to be demonstrated. Later the unit of electricity was isolated and still more recently the work of Planck made it clear that radiant energy follows the same pattern. There is also strong evidence for the existence of basic units in other phenomena, such as magnetism for instance. Since experience shows that as our knowledge widens more and more physical phenomena are proved to exist only in discrete units, it is merely a reasonable extrapolation to assume that if all of the facts were known this would also be found to be true with respect to the basic entities, space and time.
These three assumptions constitute the definition of space-time which will be used in this work. For maximum economy of hypotheses it will be further postulated that space-time as thus defined is the sole constituent of the physical universe. We may then express the assumptions as to the physical nature of the universe as follows:
FIRST FUNDAMENTAL POSTULATE
The physical universe is composed entirely of one component, space-time, existing in three dimensions, in discrete units, and in two reciprocal forms, space and time.
In developing the consequences of this First Postulate it will be necessary to use some mathematical processes and we must therefore make some assumptions as to the mathematical behavior of the universe. Until comparatively recently the validity of the relationships which will be assumed in this work was generally considered axiomatic, but other systems have been devised in the meantime and although we are unable to discover any physical reality corresponding to these unorthodox systems they do put us in the position where we must postulate the validity of the processes which we propose to utilize.
The first of this second group of assumptions will be that the physical universe conforms to the relationships of what may be called ordinary mathematics, for want of a better term. This means that two plus two equal four, the product ab equals the product ba, multiplication is the inverse of division, and so on. It is to be understood that probability mathematics are specifically included. Next the validity of Euclidean geometry will be assumed and finally it will be postulated that all primary physical magnitudes are absolute.
Here again the assumptions are merely generalizations of the relationships that are found to be valid in the regions which are accessible to observation. It is true that there are some experimental data which are currently accepted as being in conflict with the third assumption but these are not direct observations; they are merely inferences based on certain interpretations of the observed facts. It will be shown later in the discussion that these interpretations are not necessarily valid and that there are other equally acceptable interpretations of the same observations which are entirely consistent with the assumption of absolute magnitudes.
Combining these assumptions we have the
SECOND FUNDAMENTAL POSTULATE
The physical universe conforms to the relations of ordinary mathematics, its magnitudes are absolute and its geometry is Euclidean.
If these two Fundamental Postulates are valid then a great many consequences necessarily follow. The objective of this presentation is to develop these consequences and to show that they describe a universe which is identical both qualitatively and quantitatively with the observed physical universe wherever comparisons can be made. It will be demonstrated that just because of the validity of these Postulates and without the intervention of any other factor, radiation, matter, electrical and magnetic phenomena, and the other major features of the observed physical universe must exist, matter 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 specific sets of numerical values, and so on.