This is a presentation of the results obtained thus far in an investigation on which I have been engaged for the past twenty-five or thirty years. Originally begun as a leisure time activity with very limited objectives, the study was confined to quite orthodox channels in the early stages, but as tangible results began to appear the task of reconciling these findings with the basic tenets of currently accepted physical theory became more and more obviously hopeless. I was finally faced with the choice of abandoning the project, or of discarding the fundamental ideas of accepted theory and laying some new theoretical foundations upon which I could erect a superstructure that would be in harmony with my initial findings. Naturally I was reluctant to abandon the promising beginning that had been made and I therefore chose the alternative course, in spite of the heavy odds against success.
As could be expected, a good many years of stumbling around in dark corners and blind alleys followed, but by virtue of a little more than a fair share of good fortune together with what I consider a sound plan of procedure, based upon a rigid policy of separating fact from fancy and building only upon firmly established relationships and conservative extrapolations thereof, I was finally able to arrive at two fundamental postulates from which it is possible to derive a theoretical universe that is identical both qualitatively and quantitatively with the physical universe upon which we make our observations.
In the first few pages of this presentation the seven separate assumptions included in these postulates, three as to the physical nature of space-time, three as to its mathematical behavior, and the further assumption that space-time as thus defined is the sole constituent of the physical universe, are stated and explained. The remainder of the work consists of a demonstration that a mathematical and logical development of the consequences of these assumptions requires the existence of a universe which coincides exactly with the observed universe, within the limits of accuracy of our measurements.
Since the new fundamental assumption and the theoretical structure based thereon are in direct conflict with current scientific thought in many respects, the problem now arises as to how the relative merits of the conflicting ideas are to be judged; in common parlance, which explanation is true. Unfortunately, the concept of absolute truth is involved in so many philosophical and metaphysical controversies that it is practically impossible to reduce it to scientific terms, and the objective of this work is not to demonstrate that the new theoretical structure represents the absolute truth, whatever that may be, but that it represents the scientific truth, which is taken to be synonymous with agreement with observation and measurement. On this basis anything that is in full agreement with the observed facts is true, within the limits to which this correction has been carried, anything that approaches full agreement is a close approximation of the truth, anything that conflicts with the results of authentic observation is not true, and anything that cannot be adequately tested by means of such a comparison is merely hypothesis. It should be understood that the term results of observation as used in this connection refers only to actual measurements or qualitative observations and does not include inferences drawn therefrom or theories formulated to explain the findings.
Scientific truth as thus defined is not necessarily unique, there may be two or more explanations which produce the same result within a particular area and by definition are equally true within these limits. This is, indeed, the normal situation, since a theory is not ordinarily advanced unless it is consistent with the observed facts in some area of application. The choice between any two conflicting theories is therefore not a matter of deciding which is true and which is untrue, but of determining which is the more general statement of the truth. The primary criterion is, of course, sheer volume. Other things being equal, the theory which explains the greater number and variety of the observed facts is obviously the better theory. Application of this principle is complicated, however, because we are not usually dealing with a single theory but a group of theories; that is, each separate assumption is itself a theory and in evaluating the merits of any theoretical structure we must take into consideration not only the extent of coverage but also the number of separate theories (assumptions) that have been required to cover this field. In general we can express the relative merit of any such theoretical structure somewhat roughly by the ration c/a, where c is the field of coverage and a is the number of separate assumptions involved in the theory.
Ordinarily there is considerable latitude for differences of opinion in the appraisal of the field of coverage and as to the relative weight to be give to these factors of simplicity (a) and general applicability (c), particularly since the choice usually lies between a complex theory which applies to a wide field and a simpler theory with a narrower field of application, but there questions of opinion and judgment do not enter into the evaluation of the theory presented in this work, since the new theory covers a much wider field while it is based on a much smaller number of assumptions. In this presentation the theoretical universe which necessarily results from the postulates that have been formulated is developed and compared with the observed universe to the extent that such comparisons are possible and physical limitations permit. Aside from a few instances where references to other theories assist in clarifying the new theoretical picture, no comparisons have been made with the results obtained by other methods. The theoretical universe herein developed is shown to be in agreement with observation and measurement of the actual physical universe, within the scope and accuracy of the observations, and this establishes the validity of the new theoretical structure and of the postulates from which it was derived. Whether or not other conflicting theories also meet the definition of scientific truth within their own limited fields has no bearing on this situation. The new theory has no competitors, no previous theory even remotely approaches the point of being generally applicable.
The remarkable progress that has been made in scientific knowledge in recent times has had a tendency to obscure the rather haphazard state in which physical theory now exists, and in support of the statements in the preceding paragraph it may be advisable to comment briefly on the existing situation. At the present time there is one basic theory, relativity, which deals with large scale phenomena, and another, the system variously style wave mechanics, quantum mechanics, etc., which deals with small-scale phenomena. While these theories are fundamental in that they describe basic processes, they are directly applicable only to a limited range of activity and their applicability cannot be extended to any wider field without invoking the aid of additional theories, each of which carries its own set of assumptions, independent of and not necessarily consistent with the assumptions of the fundamental theories.
For example, the theory of relativity tells us nothing about the liquid state of matter. Neither does quantum mechanics. In order to arrive at a theory of the liquid state within the framework of accepted scientific thought we must therefore set up some new assumptions, beginning with the assumption that such a thing as a liquid actually exists, and including enough additional assumptions to account for the liquid properties which we observe. Furthermore, these theories and their underlying assumptions do not usually lead directly to the numerical values of the physical magnitudes involved. In order to calculate these values, if they can be calculated at all, by any method now available, still further assumptions must be made on a wholesale scale and we find our handbooks full of tables of empirical or semi-empirical constants, each of which actually represents an additional hypothesis over and above the general assumptions of the applicable theory or theories.
Obviously this loosely knit fabric of theory resting upon thousands of individual assumptions is something of a totally different order from the fully integrated structure which is presented in this work; a structure in which every component part is derived from the Fundamental Postulates without the aid of additional assumptions or subsidiary theories. It will not be necessary, for instance, to assume either the existence of the liquid state or the properties of that state. Although the postulates specify only the properties of space-time, development of the consequences of these space-time properties requires the existence of matter and requires matter to have different properties under different conditions. One of the required sets of properties is identical with the properties of the liquid state, not only the the general relationships but in the specific numerical magnitudes as well.
It is true that in the present incomplete stage of the project the theoretical development often leads to a set of several possible numerical values rather than a unique answer, and selection of the appropriate value from these possibilities is a semi-empirical process as yet, but the variable factor is always a structural constant, a small whole number with a definite physical meaning, and it seems evident that extension of the mathematics of the theory to the specific determination of this factor is merely a matter of sufficient time and effort.
Both the nature of the work itself and the fact that force of circumstances has made it a single-handed effort, have necessitated certain limitations on the scope of the project which should have some comment. It was obviously desirable to confine the investigation as far as possible to the main line of the theoretical development, leaving collateral matters for later treatment, in order that the items covered could be given sufficient attention to insure continuity in the logical and mathematical development all the way from the Fundamental Postulates to each o the derived relationships. This has had the effect of excluding from the initial presentation many subjects such as viscosity, vapor pressure, solutions, x-rays, etc., which branch off from the main line, even though these subjects are of considerable interest and many of them have been given a great deal of study during the course of the project.
Another policy adopted for the same purpose limited the calculated values of the various properties, in most instances. To one or two less significant figures than given in the reports of the experimental work. Intensive coverage of such an extensive field as that defined by the general objective of the project was clearly impossible with the available time and facilities, and since the general area of coverage could not be reduced beyond a certain point without defeating the purpose of the work, the required reduction in scope was attained by limiting the extent to which the fine structure was studied. Any refinements in the calculations which had a negligible effect on the results within these established limitations were omitted.
This same limitation policy was applied to other than mathematical items whenever the effect was the same; that is, when any resulting inaccuracy was less than the accepted tolerance. For instance, no attempt has been made to establish the exact probability relations in each case where probability functions enter into the computations, as this item alone could easily require more time than was available for the entire project. In any case where the theoretical development indicated that the magnitude of a particular property was determined by probability it was considered sufficient to demonstrate that the experimental values could be reproduced within the accepted limits of accuracy by the application of some standard probability function, without attempting any theoretical justification for the use of this particular function. The validity of the results is no affected since the true function, whatever it may be, must produce these same results, within the accepted limits of variation, and substitution of one function for the other has no significant effect.
Similarly where theory indicates, for example that quantity A is a function of quantity B and the measured values are found to be consistent with the relation A = 3B, no attempt has been made to develop a rigorous proof of the validity of the explanation given for the existence of a coefficient of this particular magnitude. Here again the general situation is not affected. If the explanation given is incorrect, the true explanation must still be its exact equivalent, so far as this particular property is concerned, and as long as there is no conflict at any other point in the theoretical structure, the substitution of one for the other does not affect the general situation.
This cheerful acceptance of the possibility of error in minor details may be regarded in some quarters as unscientific, but it is one of the many limitations on the scope of the project that has been required in order to reduce the task to finite dimensions and bring it within the bounds of practicability. The objective has been to develop a sound basic theoretical structure and the subsidiary relations have been followed out only to the extent, mathematically or logically, that has appeared essential to the attainment of the primary objective.
It should not be assumed from this, however, that the particular subject matter included in this initial presentation and the extent of coverage of each subject necessarily reflect a judgment as to the relative importance of the various physical properties and processes. In working toward the established objective it has been necessary to look for soft spots and to exploit any breakthrough at one of these spots to the utmost as a means of paving the way to a further advance at some other location. The extent of coverage of any particular subject is therefore determined to a large degree by the channels which the investigation has followed in the long and involved process through which the results now being published here have been obtained. Aside from the fact that the choice of subject matter in this initial presentation is dictated to some extent by the necessity of maintaining the continuity by which the whose structure has been developed from the fundamental postulates, the attention devoted to any one subject is primarily a matter of the amount of new information available rather than an indication of relative importance. The coverage is generally more complete in the earlier sections than in the later ones, as might be expected from the fact that the order of presentation is essentially the same as the original order of development of the theory.
The experimental values of physical properties used for purposes of comparison with the calculated values have been taken principally from handbooks and other compilations, with recourse to original sources in the literature only where necessary for more complete coverage. Identification of the particular sources has been omitted since reference to a collection of values from different sources serves no useful purpose and, furthermore, any attempt to appraise the accuracy of any individual experimental values merely confuses the issue, since these subjective judgments are merely estimates of probabilities and cannot be accepted as authoritative so far as any individual value is concerned. In order to meet this situation in which the degree of accuracy of the individual results is unknown, I have adopted a sort of mass action policy in which I am relying on the cumulative weight of reasonably close agreement in a very large number of separate comparisons with experimental results, rather than attaching any great significance to any individual case.
Normally the findings of an investigation of this kind would be reported item by item as fast as significant discoveries are made, and some explanation as to why the customary procedure was not followed in this case is probably in order. The answer is simply that this was not a matter of choice but of necessity. Efforts were made from time to time to obtain publication of some of the results or to enlist assistance in bringing these findings to the attention of the scientific profession, but without success. I have found in the course of this and other similar work, which I have undertaken, that new ideas that are essentially extensions or minor modifications of current theory are welcome, but that no hospitality is extended to anything in the nature of a challenge to accepted fundamental doctrine, and a chilly reception is all the more certain if this challenge comes from one who is placed in the category of an outsider even though he may be a worker in an allied field. One prominent American scientist expressed the general attitude very succinctly in a letter of comment on a portion of my work, which I had submitted for his consideration during one of my periodic attempts to release portions of my findings in some manner. He enumerated the currently accepted principles with which my results were in conflict and the laid down the dictum, There is no chance that they are wrong.
This reaction is readily understandable as it is typically human, but it does present an almost insurmountable obstacle to any new ideas on basic subjects (a fact which has been widely recognized has has been the subject of comment by many writers on scientific methods)., and it has therefore been necessary to carry this work to the point where it could be published as a single package in which statement of the basic assumptions of the new theory is immediately followed by sufficient development of the consequences to demonstrate the validity of the assumptions. The resulting long delay in making the findings available for general use is unfortunate but apparently unavoidable.