Throughout history one of mans most persistent ambitions has been to know and understand the physical world in which he lives and of which he is, to some degree at least, a part. To a certain extent this has been a cold-blooded materialistic objective. The better one understands the physical realities with which his life is intimately tied up the better he is able to manipulate them for the advancement of his own purposes. But over and above this practical urge to acquire knowledge for the gains which it will bring is the spirit of intense curiosity which is a part of the birthright of the race. Man seeks knowledge not only because of the use he can make of it; he seeks knowledge also for its own sake, for the pure satisfaction of knowing.
At the start of the great quest back in that prehistoric era when the human intellect first began to emerge from its prehuman origins, the boundaries of knowledge were close at hand. Wherever man turned he was face to face with the unknown. In such a situation it is little wonder that this imaginations were peopled with demons, ogres and countless other supernatural beings, generally of a malevolent nature, for life was harsh and relentless in those days. Through the long centuries that have elapsed in the meantime one after another of those phenomena that primitive man was forced to ascribe to supernatural causes has been traced back to some prosaic origin within the boundaries of the normal physical universe. No one who studies the record can deny that the human race has come a long way in the search for understanding.
Yet in spite of this steady progress which has pushed back the frontiers of knowledge farther and farther year by year, decade by decade, and century by century, there is still no indication that any kind of a limit is being approached. On the contrary, every advance in knowledge merely multiplies the unsolved problems. We are in the position of one who starts out from a given point to explore his surroundings. Every new section of territory covered adds that much to the total known area but at the same time it extends the frontiers of the unknown. The more terrain one maps the more lies just beyond the range of his coverage.
The process of increasing knowledge is essentially a three-sided one. First comes the accumulation of factual data through observation and measurement. Before we can know why we must know what. Preferably we should also know how much. Then through systematic analysis and inductive reasoning general principles governing the interrelationship of these facts are derived. Finally the general principles are applied singly and in combination to the solution of specific problems through mathematical treatment and deductive reasoning.
In the advance of knowledge the normal course of events is that the broad general principles underlying the major relations are the first to be established on a sound footing. These then lead to subsidiary principles and the latter continue branching into more and more specialized fields, just as a growing tree branches out in all directions. Naturally the great bulk of the effort applied to study and research is devoted to the multiplication and extension of these branches. After the tree has grown steadily for years the solidity of the main stem tends to be taken for granted.
But this confidence may not be warranted. Human knowledge is never absolutely certain. We cannot guarantee that our most careful observations and measurements are free from error; we cannot be sure that even the most firmly established products of our reasoning will stand the test of time or will necessarily be valid in the regions beyond the range of our present powers of observation. At best, therefore, what we term knowledge is merely an approximation and the advancement of knowledge is essentially a process of arriving at ever closer approximations to the ultimate truth.
Fundamental laws and principles are no exception. Even though they may have served us well and faithfully in those fields wherein we have utilized them thus far, yet they may be and probably are only first approximations to the truth and when the time comes that greater accuracy is needed we must replace them with closer approximations in order that progress may continue unimpeded. The carpenters rule serves its own limited purpose very satisfactorily but the marvels of modern machinery would be impossible without micrometer calipers or their equivalent. From time to time, therefore, it is well that we should undertake a critical examination of our fundamental theory in order to determine whether it is still adequate to carry the additional burdens that our more advanced facilities for observation and measurement have placed upon it. Perhaps the branches of the tree may have become too numerous and heavy for the trunk to support.
This present work is the result of such an undertaking. As originally conceived it was intended to cover only one single field: the relation of physical properties to chemical composition. The specific objective was to develop a mathematical correlation whereby the physical properties of the elements and their compounds could be calculated directly from the atomic numbers of the elements involved without the use of empirical relations or arbitrary factors. After a long period of intensive study and analysis of those physical properties which appeared to offer the greatest possibility of responding to such an attack, reasonably satisfactory mathematical expressions were finally developed for two important properties: specific heat and interatomic distance in the crystalline form. However the most strenuous efforts to account for the terms occurring in these expressions in the light of currently accepted physical theory were fruitless and it therefore became necessary to look for some alternative explanation of the physical universe which would be in harmony with the mathematical relationships that had been developed.
The obstacles in the way of attaining this objective can readily be appreciated and this second phase of the investigation developed into as great a task as the first. Eventually, however, after examining and discarding a host of possibilities, it was found that the observed relationships in both heat capacity and interatomic distance could be accounted for if certain simple assumptions were made as to the nature of space and time. When these new ideas were definitely formulated and examined it became apparent that they were applicable to a much wider field than that which was covered by the original inquiry; no less a field, in fact, than the whole underlying structure of the physical universe. The fundamental theory that has emerged as a result of these studies and the application of this theory to an explanation of basic physical phenomena constitute the subject matter of the following pages.
In undertaking to report the results of investigations of this kind one of the first problems that makes its appearance is the selection of a method of presentation. The historical approach is widely used and has many advantages, particularly where the historical development has been a step by step process of advancement along the same general line. Here the reader can proceed gradually from the simple to the complex by retracing the steps through which the existing body of knowledge was accumulated. Where a sharply contrasting idea is being advanced the method of exposition by comparison has a great deal of merit. By emphasizing the points wherein the propositions currently presented differ from accepted doctrines attention is concentrated on these relevant issues rather than being dispersed over a variety of matters on which nothing new is being offered.
In the present instance, however, where the divergence from accepted theory is of major proportions and reaches back to the basic assumptions as to the nature of the building stones of which the universe is constructed, it has seemed advisable from the standpoint of clarity of presentation to develop the new theoretical structure on its own foundations without stressing either the historical background or the divergence from current scientific thought, except insofar as reference to conflicting ideas may aid in the exposition. The basic theory of the universe to which this research has led will be expressed in the form of certain fundamental postulates. It will then be demonstrated that the mere existence of a universe such as has been postulated necessarily leads to the appearance of a vast and complicated system of subsidiary phenomena. The general principles and mathematical relations governing these phenomena will be developed from the fundamental postulates and finally it will be shown by comparisons with observational data that these theoretical phenomena are identical both qualitatively and quantitatively with the actual physical phenomena that we observe in the universe in which we live.
It should be definitively understood that no attempt will be made in this presentation to use observed facts and measured quantities as a basis from which to derive the various principles and relations that will be set forth in the subsequent pages. The structure of theory will rest entirely upon the fundamental postulates and the aim of the mathematical and logical treatment will simply be to demonstrate that these principles and relations are necessary consequences of the postulates and form a complete and self-contained system, all parts of which are consistent with each other and with the postulates on which they are based.
Up to this point we will be dealing not with the actual universe but with a purely hypothetical universe. We will determine the nature and characteristics of the varied phenomena which would exist in a universe of the kind that would result from the basic relations that we have postulated. Of course, if it then appears that the phenomena appertaining to this hypothetical universe have no counterparts in the actual universe which we observe about us the work will be valueless. On the other hand if we find, as we will, that the properties and magnitudes of our hypothetical universe coincide within the limits of accuracy of our methods of measurement with the properties and magnitudes of the real universe wherever and whenever the latter are accessible to our observation we are justified in concluding that they also coincide where observation is not possible or inconclusive and that the real universe is identical with the universe that we have built up from purely hypothetical foundations.
Many of the principles and relations that will be set forth herein, particularly those of the most general nature, belong in the class which cannot be definitely proved or disproved by any of the means of observation or measurement now available. To avoid misunderstanding it is desirable to emphasize in advance that this has no bearing on the validity of the conclusion. The entire theoretical structure is based on the fundamental postulates and as long as it can be shown that the end results of a chain of reasoning agree with observational data it is not material whether or not all of the intermediate links in the chain can be individually verified.
As so often happens in scientific work the actual approach through which the basic principles underlying this work were developed was purely a matter of mathematical necessity, not one of logic. It was found that observed magnitudes of the physical phenomena which were being given critical and intensive study could be accounted for by postulating the existence of a universe with certain specific mathematical properties. After arriving at a definition of these properties, however, it became apparent that the same conclusions could have been reached through a logical consideration of the pertinent facts had there been equal freedom of thought in the mathematical and logical fields.
Actually, of course, there is no such equality. Those ideas which we express in words acquire an authority that increases progressively as time goes on until a stage is reached where it seems almost impossible to think along any other line. Many a path of inquiry that might prove fruitful is inhibited by an inability to get our thoughts out of the conventional groove. But mathematical investigation is largely free from such inhibitions. If a direct proportion fails there is no hesitation about trying a reciprocal, although the upside down thinking in doing the same thing in speculative reasoning about physical processes is often extremely difficult. If a trigonometric function does not quite serve our purpose we are ready to try a logarithmic function without further ado, yet this is a deviation of such magnitude that it probably would seem rank heresy if the corresponding principle were explained in words.
But once having arrived at the mathematical result by reason of the greater freedom of exploration in this medium it is often possible to revert back to words and attach meaning to the steps that have been taken so freely in the abstract realm of mathematics. The obstacles that have blocked the path are then revealed and it becomes possible to reconstruct the entire chain of thought in verbal rather than mathematical language. This has been true in the present instance and in order to take advantage of the greater clarity of presentation the verbal approach will be utilized in the next chapter even though the results were originally obtained by purely mathematical means.