Chapter IV

Laying the Foundation

One of the most interesting questions that has arisen out of the activities of modern science is that of the ultimate future of the human race. There is no doubt but that homo sapiens is a very adaptable species—he manages to thrive anywhere within a surprisingly wide range of environments, climatic and otherwise—but it is still an open question whether he has attained a degree of adaptability comparable to that of the cockroach, for example, which will enable him to survive for millions of years, or whether sapiens will sooner or later give way to some new and more advanced species, just as he superseded homo erectus and erectus replaced his pre-human ancestors. This intriguing question is not likely to receive an authoritative answer anytime in the near future, but for the purposes of the present chapter let us indulge in a little flight of fancy and assume that these evolutionary processes have actually taken place and that homo sapiens has been supplanted by a super-race. Then let us further assume that we who are now concerned with the subject matter of this volume as author and readers are a group of individuals of that super-race—homo super-sapiens, let us say—to whom has been assigned the task of ascertaining the nature of the basic structure of the physical universe.

Before we can don the robes of the super-scientist and proceed with our project it will first be necessary to give some consideration to the question as to just what advantage super-sapiens has over his predecessor. Those who speculate about the possible emergence of a super-race usually envision a great increase in intelligence: a rise in the average I.Q. to perhaps 300 or 400. If we adopt this viewpoint we will have to abandon our undertaking before we get started, as reproducing the mental processes of a vastly more intelligent race is clearly an impossible task. But an increase in the intelligence level is not the only way in which a super-race might develop.

One of our prominent science fiction writers has just recently published a story in which a superior race develops simply by suppressing the emotional reactions that govern so much of the activity of homo sapiens, and basing all decisions and actions on logical analysis and reasoning. This we should be able to duplicate, at least on a particular assignment and for a short period of time, if we put forth the necessary effort.

Of course, science already accepts such a code of procedure in principle, but there is a wide gap between that which scientists subscribe to as a matter of principle and that which they do in actual practice. In principle valid criticism of accepted ideas should be hospitably received as a worth-while contribution to scientific knowledge; in practice such criticism is strongly resented by the “experts” in the particular field involved, and in line with the old adage that “it is the truth that hurts,” the more pertinent the criticism the stronger the resentment. In principle a new idea of merit should be welcomed with open arms; in practice even a relatively modest proposal for modification of existing viewpoints is looked upon with distaste and suspicion, while a major new development has to fight every inch of the way. The most important and most valuable discoveries are not exempt from this treatment; on the contrary they often meet the most hostile reception. Some, like Mendel’s basic findings in the field of genetics, or Waterston’s pioneering formulation of the kinetic theory, never did succeed in penetrating the wall of prejudice and disinterest, and these important discoveries simply remained dormant until they were rediscovered by someone else many years later. Other important scientific advances prevailed only by overcoming strong opposition, based more on emotional than on logical grounds. For example, Planck’s theory of the quantum, now recognized as one of the most important of modern scientific developments, was accepted only after a long and difficult struggle, during which, Planck complains bitterly, his “sound arguments fell on deaf ears.”⁷⁴

In order to assume our roles as members of the super-sapiens race for purposes of the present inquiry it will be necessary not only to lay aside the emotional preferences and prejudices which lead homo sapiens to violate his own code of scientific procedure, but also to overcome the characteristically human distaste for leaving the comfortable groove of established thought. These are difficult, but not impossible, requirements. Let us therefore adjust our thinking to the super-sapiens pattern and proceed with a cold-blooded, logical and systematic study of the problem at hand.

With the benefit of the logical approach to all questions that characterizes our super-race, it is obvious, to begin with, that the proper way of analyzing a complex subject of this kind is to explore its simpler and more basic aspects first, and then gradually work toward the more complicated details. As our first step, then, we will want to study the nature and properties of some of the fundamental entities of the universe. It is not absolutely essential that we start with the most fundamental, but there are some definite advantages in so doing, and the first item in our program should therefore be to identify the most fundamental entities that we can find in the physical universe. Although the various physical entities do not carry labels which brand them as fundamental or not fundamental, there is little doubt but that the leading candidates for the distinction of being most fundamental are space and time.

There are other points of view, of course. Some would give matter the preference over space and time or, at least, assign it a coordinate position. Supporters of the relational hypothesis of space and time are also likely to raise the contention that “events” are logically prior to space and time and hence the latter cannot be fundamental. But it should be remembered that this conclusion is purely hypothetical and even though it happens to be the hypothesis that has been most favored by homo sapiens, the opposing concept of space and time existing prior to events cannot be ruled out. Furthermore, it is clear that both matter and events are very complex entities, whereas space and time appear to be simpler. The choice of space and time as the initial subjects for investigation therefore seems well founded, particularly when we bear in mind that it is not essential that we start with the most basic entities. If we have made the wrong choice here we do not put any insurmountable obstacle in the way of success in our undertaking; we merely make our task somewhat more difficult.

Thus our first problem is to determine the general nature of space and time and the relationship between them. Since only a relatively small portion of the universe is accessible to direct and accurate observation, we cannot make such determinations directly, and what we have to do is to assume some properties and relations, develop the consequences of these assumptions, select those of the consequences which fall within the accessible area, and then compare these theoretical consequences with the observed facts. If they disagree, then one or more of our assumptions is incorrect, and we must go back and start all over again with new assumptions. If there is full agreement, then the validity of the assumptions is substantiated to a degree, which depends on the number and variety of the correlations that were made. The immediate question, therefore, is, What assumptions shall we make?

Here, again, the clear and unprejudiced vision of a super-race makes the proper course evident; showing us that such a question can best be approached by first examining the general situation in which we are considering the relation of any quantity x to any other quantity y. In this general situation there will be a region accessible to direct observation and another region which is not accessible. The relation in the accessible region can, of course, be determined by direct means, and what we need to ascertain in order to complete our knowledge is the relation in the inaccessible region. Since this relation is, by definition, unknown, it could be almost anything, and the range of possible assumptions is almost unlimited. But when we consider this general situation, without the distracting influences, which always accompany consideration of any specific physical situation, it is apparent that there is one possible assumption, which is far superior to all others. This greatly superior assumption is the assumption that the relation, which we find in the region accessible to observation also, holds well in the inaccessible region.

As has been pointed out, our original hypothesis, whatever it may be, will ultimately have to be tested by developing its consequences in all of the physical fields to which it is applicable and determining whether or not these consequences agree with the facts of observation and measurement. But the extrapolation assumption—the assumption that the situation which we observe in our local sector of the universe prevails throughout the universe as a whole—is initially by far the best hypothesis that we can make: one that not only has a far greater a priori probability of being correct than any other possible assumption, but a much greater probability than all other possible assumptions combined. For example, the fact that space is three-dimensional where we are in direct contact with it does not guarantee that it is three-dimensional everywhere and that this is a general property of space, but it means that there is an extremely strong probability that this is true and that the existence of an n dimensional space in which n has a value other than three is very unlikely.

If we were looking at this issue through the eyes of homo sapiens there would no doubt be some tendency to question whether the a priori probability of the validity of an extrapolation of a physical relationship is as great as indicated in the preceding paragraph, because sapiens is very much over impressed by certain highly publicized 20th Century developments in physics which are currently interpreted as proof that some of the basic relations which govern the world of everyday experience—Newton’s Laws of Motion, for example—cannot be extrapolated to the realms of the very small and the very large. But a race which looks at everything from a logical and factual standpoint, without being influenced by emotional arguments or propaganda in favor of the popular ideas of the moment, will realize that even if this were true, the number of items involved is extremely small compared to the enormous number of instances in which science has made extrapolations into regions beyond the then current range of observation, and subsequently, through the invention of improved methods or instruments, has verified the accuracy of the extrapolations.

Furthermore, the clear-thinking super-scientist will realize that the so-called “failures” of the extrapolated relations in the cases mentioned are only hypothetical. On first consideration homo sapiens would probably regard this statement as absurd. The Laws of Motion are accurate and dependable in application to macroscopic events, but they admittedly do not give the correct results when they are applied to events at the atomic level. It seems, therefore, that extrapolation of these laws to the microscopic realm has been a failure. But those who look at the situation in this light are overlooking the fact that this is not simply an extrapolation; it is an extrapolation plus an assumption. Newton’s Laws of Motion are applicable at the level of our ordinary experience to the kind of motion which is there encountered, and a pure extrapolation would lead to the conclusion that the Laws are applicable to this kind of motion wherever it exists. But in order to apply these laws to events at the atomic level it is necessary not only to extrapolate the application of the laws but also to assume that the atomic motion is the same kind of motion as that encountered in the macroscopic world. If this assumption is erroneous (and the subsequent development in this volume will show that it is, in fact, erroneous) then the so-called “extrapolation” is not an extrapolation at all.

Careful examination will disclose that most of the “failures” of extrapolated relations are of this nature. The so-called extrapolations are, in reality, extrapolations plus one or more assumptions, and the fault lies in the erroneous nature of the assumptions, not in the inapplicability of the relations that are being extrapolated. Such “failures” are, of course, completely irrelevant to the question as to the reliability of the extrapolation process, and when we exclude them from consideration, the number of cases where extrapolated physical relations have been found inapplicable is insignificant compared with the vast number of successful applications. Since it is the mathematical expression of experience that determines the probability, the previous statement as to the strong a priori probability of the validity of the extrapolated relations is amply supported.

The inherent superiority of the extrapolation process is all the more important because it is not usually possible to test the consequences of a single physical hypothesis in isolation. Most of the phenomena, which we must use for test purposes, are complex events that are not the result of a single property of space or of time but are results of a number of properties of both space and time. Even the most casual consideration of the probability principles is sufficient to emphasize the tremendous advantage to be gained by the extrapolation of the results of observation under such circumstances. Where the probability of any one hypothesis being correct is very low, as is true when pure assumptions are made concerning physical processes or properties, the probability that all of several such hypotheses are correct is almost negligible. Furthermore, the probability that all but one of these hypotheses is correct is likewise extremely small. On the other hand, if each individual hypothesis has a high probability of being correct, as is true when these hypotheses are extrapolations, the probability that more than one of them is incorrect is close to zero. In this case, if the original set of assumptions fails to produce the correct results, the search for the correct answer can be a matter of substituting other assumptions one at a time for each of the original assumptions in turn. A search of this kind is a tremendous undertaking, to be sure, but it has some chance of success, whereas if two or more of the original hypotheses are incorrect, so that the one at a time technique of substitution is precluded, the odds against success are almost prohibitive.

Our consideration of the general situation thus leads directly to the conclusion that the procedure in carrying out the assignment of determining the basic structure of the physical universe should be to ascertain the properties of space and time and the relations between these two entities as they are manifested in the region accessible to direct observation, extrapolate these properties and relations to the universe as a whole, develop the consequences of the hypotheses thus derived, and then determine whether these consequences are in agreement with the observed facts. There is a very strong a priori probability that we will find full agreement, and if so, the set of assumptions derived in this manner is correct; if there is any discrepancy, one of the assumptions, but almost certainly no more than one, is in error. What we will then have to do is to locate the error, make the necessary change in our postulates, and repeat the original procedure.

The positively established conceptual knowledge concerning the properties of space and time in the region accessible to direct observation and the nature of the relation between these two entities in the accessible region were summarized at the end of Chapter II. In accordance with the conclusions stated in the preceding paragraph, we will now proceed to generalize these findings (omitting the one uncertain item) and express them as hypotheses applicable to the entire universe. In this manner we arrive at the following hypotheses:

• Space is three-dimensional, homogeneous and isotropic throughout the universe.
• Time progresses uniformly throughout the universe.
• Throughout the universe the scalar relation between space and time is reciprocal, and this relation constitutes motion.

One conspicuous feature of these hypotheses is the absence of the usual assumption as to the one-dimensionality of time, an assumption which, in view of the points brought out in Chapter II, can no longer be regarded as having any observational support. At this stage, however, no postulate of multi-dimensionality is being advanced. All that we are doing at the moment is to determine what hypotheses as to the properties and relations of space and time in the universe as a whole can be legitimately derived by extrapolation of our direct observations, and these direct observations tell us nothing at all about the dimensions of time.

Since we are viewing this situation with the clear insight of a super-race, rather than through the veil of prejudices and pre-conceived ideas that hampers homo sapiens in his reasoning, it will be apparent to us that the logical status of all of the assumptions in the foregoing list is identical. In each case the situation in the known region is clear and unequivocal; we have eliminated those items that are in any way questionable. Hence the inherently strong probability of validity that attaches to any extrapolation from the known to the unknown applies with equal force to all these assumptions. This does not mean that all must necessarily be true if one is true, but it means that there is no justification for any advance judgment that one is more likely to be correct than another.

This point is particularly important because some of these assumptions are thoroughly familiar to homo sapiens and are accepted by him as practically axiomatic, whereas others are not only entirely unfamiliar, but also wholly foreign to established human habits of thought on these matters, and hence subject to the antagonism with which the human race tends to greet heresy in any form. Scientist and layman alike are strongly inclined to classify some ideas as “reasonable” and hence believable, while others are regarded as “unreasonable” and consequently unworthy of serious consideration. But what this really amounts to is prejudging the case on emotional grounds before the evidence is presented. It is quite true that many of the ideas or assumptions that are proposed are self-contradictory or in direct conflict with firmly established facts, and such items certainly cannot be accepted, but neither these nor any other ideas should be condemned on the basis of any advance emotional judgment. If they must be rejected, this should be done only after the evidence is at hand. Where conclusive evidence can easily be obtained, the verdict can be reached quickly, but there is never any justification for reaching positive conclusions without adequate evidence.

When we look at the situation now under consideration from the standpoint of pure logic, without the emotional overtones that are so characteristic of human reaction to innovations, it is evident that, as long as our observations in the accessible regions are definite and positive, we are just as much entitled to extrapolate one as another, and our general knowledge of the extrapolation process justifies the assertion that each and every one of the assumptions derived by extrapolation is very probably true. Before we can take the next step and assert that they are, in fact, true, it will be necessary to demonstrate their validity in the standard manner by showing that they meet the test of comparison with experience, but it should be recognized at the outset that there is but little chance that they will fail to meet the test.

It is particularly essential to keep this fact in mind when the first deductions as to the direct consequences of these basic assumptions are made, because the conclusions thus derived will seem very strange—perhaps altogether incredible—to those who are imbued with previous ideas and concepts, and even a super-race may find the necessary adjustment of thinking rather difficult. The first conclusion of this kind that we draw from the extrapolated assumptions is that inasmuch as these specify the existence of a general reciprocal relation between space and time, there must be complete scalar symmetry between these two entities. All properties, which are possessed by either space or time individually, are therefore properties of both space and time. We thus arrive at the conclusion that both space and time are three-dimensional, homogeneous and isotropic, and both progress at a uniform rate.

Every conclusion that we derive from the original hypotheses offers us an opportunity to test the validity of the entire system of hypotheses plus derivatives. Such a test cannot give us a positive result; that is, even if the conclusion is found to agree with the observed and measured facts in all respects, this does not assure us that the system is valid, since there is still a possibility of conflict with other facts at present unknown, a possibility that can be eliminated only by complying with some much more stringent requirements. But any test can give us a negative result. If the conclusion conflicts with any positively established fact, this is sufficient for disproof. The conclusion that all properties of either space or time are properties of both space and time would be immediately demolished if any of the properties extrapolated from one to the other turned out to be inconsistent with established facts, and in view of the great differences which appear to exist between space and time as we ordinarily envision them it would seem offhand that discrepancies of this kind should be easy to locate. But we will find on close examination that this is not the case; there is no conflict or inconsistency anywhere.

It is true that the concept of three-dimensional time is in direct conflict with the ideas of homo sapiens, but it is only conflicts with facts that are fatal, and human ideas as to the dimensions of time are not factual. As brought out previously, the long-standing concept of time as one-dimensional is based on a misunderstanding of the nature of time dimensions. A dimension of time is not a dimension in space, nor is it anything space-like; it is a property of time itself. The scalar nature of the time term in the equations of motion is not a result of time being one-dimensional; it results from the fact that time has no direction in space, regardless of how many dimensions or directions of its own it may have. Thus there is nothing at all in our observations that precludes time from being three-dimensional, as required by the conclusion that time has all of the properties which we observe in space.

To those who are accustomed to thinking along different lines, the idea of a progression of space similar to the observed progression of time may seem even more outrageous than the concept of three-dimensional time, but the fact is that we have actual observational evidence of such a progression. Of course, we cannot see locations in space, but we can see objects which occupy locations in space, and by means of the giant telescopes now in service we can see objects—galaxies—which are so far away that any random motions which they may possess are unobservable, and the effect of gravitation is attenuated to the point where it is no longer a controlling factor. Under these circumstances, if there is a progression of space, as our theoretical development requires, the spatial locations occupied by these distant galaxies should be moving steadily outward away from us, carrying the galaxies with them. This is just exactly what our observations indicate is actually happening.

We normally visualize the progression of time as a unidirectional flow rather than an outward movement, but this is pure assumption. As brought out in Chapter II, the presumed one-dimensional flow of time is actually scalar rather than one-dimensional, and when we analyze the motion of the distant galaxies, this also turns out to be scalar. The recession of any galaxy A has a definite direction MA when viewed from M, our own Milky Way galaxy, but the direction of the recession is BA when viewed from galaxy B. CA when viewed from galaxy C, and so on, which means that the motion actually has no specific direction. It is simply a scalar motion, outward from all other galaxies.

The significance of a positive and unequivocal confirmation of this kind can hardly be overestimated, as there is a tremendous difference between the standing of a purely ad hoc hypothesis and that of a hypothesis which is derived from one source and confirmed by independent evidence from another physical source. Such hypotheses as those of a “nuclear force” that holds the hypothetical constituents of the atom together, the “propagation” of gravitation that is presumed to transmit the gravitational effect from one mass to another, or the mysterious unnamed “force” that is supposed to induce atoms to acquire or lose electrons to attain the inert gas configuration, are nothing more than euphemisms for ignorance. What meaningful difference is there between saying that no one knows what holds the constituents of the atom together and saying that they are held together by a “force” dreamed up for this specific purpose and totally unknown in any other connection?

But a hypothesis such as that of the progression of space, which is derived by theoretical reasoning based on extrapolation of our observations of space and time in our everyday experience, and is then corroborated by an entirely different physical phenomenon altogether remote from our daily experience, the recession of the distant galaxies, is something of a much different character. With the benefit of this information, we are in a position to assert that we have here increased our actual knowledge of the physical universe, and to look forward with confidence to additional successful applications of this same hypothesis in other physical areas, which will not only represent further advances in scientific knowledge, but will still further strengthen the already strong position of the hypothesis itself. For instance, in one of the many such applications discussed in the subsequent pages, it will be shown that the photon of light, like the distant galaxy, behaves in exactly the manner required by the hypothesis of spacetime progression.

This completes the first phase of our committee assignment. Since the conclusion that both space and time have all of the properties observed in either space or time individually has been derived by means of processes which are entitled to a high degree of confidence, and since there is no factual evidence that is inconsistent with this conclusion, whereas there is strong evidence supporting the validity of the innovations which it introduces into physical relations, we are justified in considering this conclusion as correct. This extends our knowledge of space and time very substantially, and when all of the knowledge that we now possess is explicitly stated in systematic form we will have arrived at the kind of a basic theory of the structure of the universe that our committee was instructed to produce. Before we can express this theory in a suitable form, however, there are a few additional points to be considered.

One question that we will want to examine is whether space and time are continuous or exist in discrete units. Here we find that throughout the history of science there has been a steady growth in the recognition of discontinuity in the physical world. At the time the atomic structure of matter was first proposed, all other primary physical phenomena were thought to be continuous and infinitely divisible. As knowledge has grown, however, more and more of these have been found to exist only in units. The discrete nature of electric charge and of radiant energy are already well confirmed, and there is increasing evidence for the existence of basic units in other phenomena, such as magnetism, for instance. If we project this trend, we can reasonably arrive at the conclusion that when all of the facts are known, the basic entities, space and time, will also be found to exist only in discrete units.

Further mathematical development will show that the limitation of space and time to discrete units is a necessary consequence of the postulates previously formulated, particularly the reciprocal postulate, but for the present it will be preferable to regard this as an additional assumption justified by projecting existing trends in the increase of physical knowledge, as indicated in the preceding paragraph. We will therefore add such an assumption to our list.

Another issue which requires consideration is whether space and time, as we now see them in the light of our new knowledge, together with the consequences that necessarily ensue because of the existence of these two entities with the properties which we now know that they possess, have a broad enough scope to constitute a complete physical universe, or whether the existence of some additional basic entities, such as matter, for example, must be postulated in order to complete the theoretical picture. Here we have no option but to make a pure assumption. It is clearly undesirable, however, to introduce additional complexity into the theoretical development until the necessity for so doing actually arises, and we will therefore start with the postulate that space and time are the only constituents of the physical universe. Additional factors can be introduced if and when this becomes necessary, without invalidating any progress that may have been made up to the point that such action is taken.

In formulating a statement of this postulate we encounter a question as to whether we should consider space and time as separate but related entities, or as two different aspects of the same basic entity, and in case we choose the latter alternative, a further question as to whether we should call this entity space-time or motion. These questions have no bearing on the development of thought and we are therefore free to make our choice on the ground of convenience.

From this standpoint it seems advisable to select those terms which will be most understandable in the context of existing thought and which will facilitate explaining the new theoretical structure to individuals who are familiar with previously accepted ideas. We will therefore say that the universe has only one component, and for the present, we will call this component space-time, with the understanding that this term is equivalent to motion, when motion is taken in the most general sense.

Although the progression of space-time is one of the items of knowledge obtained by extrapolation of our observations in the known region of the universe, we do not need to include this progression in the postulates because it is a necessary consequence of the other assumptions derived by the extrapolation process. The same is true of the homogeneity and isotropy of space and time and the uniformity of the progression. In our restatement of the basic postulates we will therefore omit these items. It should be understood, however, that they are essential to the theoretical development, and if any question is raised as to the validity of their derivation from the remaining assumptions, this merely means that they must be restored to the basic postulates. The course of the subsequent development will not be altered by any such question.

In addition to the assumptions that have been made concerning the physical nature of the universe, it will also be necessary to make some assumptions as to its mathematical behavior. Here again we will follow the same procedure, extrapolating the relations which we find existing in the region accessible to direct observation, and assuming that they apply to the universe as a whole. In this manner we arrive at the assumptions that the universe in general conforms to the relationships of ordinary commutative mathematics, its magnitudes are absolute, and its geometry is Euclidean.

Our committee is now ready to make its first progress report. In this report we will say that we have found it possible to apply a very reliable process—extrapolation of observed relationships—to the problem assigned to us, and that by utilizing this process exclusively, without introducing any unsupported or ad hoc assumptions we have been able to formulate two postulates as to the basic nature of the physical universe which have a very high degree of probability of being correct. A full development of the consequences of these postulates should lead to a complete definition of the structure of the universe. The postulates can be expressed 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.

Second Fundamental Postulate: The physical universe conforms to the relations of ordinary commutative mathematics, its magnitudes are absolute and its geometry is Euclidean.

At this point we will step out of our super-sapiens roles and return to the more prosaic world of human activities. The super-committee still has ahead of it the task of proving the validity of the postulates, and this can be accomplished by applying similar logical and systematic processes, but the objective of this present volume is to clarify the ideas and concepts of the new theoretical structure, not to prove that it is correct. Most of the requirements for proof have been met in previous publications, and whatever gaps still remain, or may seem to exist, will be handled in future extensions of or additions to those works. The nature of the proof that has been and will be offered is, however, germane to the subject of the present volume, and will be discussed in the next chapter.