Chapter X

Facts and Fancies

I

The objective of this present discussion is simply to make a long overdue critical examination of the status of the nuclear theory of the atom in the light of present-day experimental knowledge, and to show that this theory is now completely untenable, however satisfactorily it may have met the less exacting requirements that prevailed in its youth. The act of making such an examination imposes no obligation to provide an acceptable substitute for any theories which may have to be discarded as a result of the findings; clearing away the dead wood is a necessary preliminary to the erection of a new structure, but it is an entirely separate operation. Nevertheless, there are those who feel that destroying an existing theory without putting something in its place is, in some way, immoral, and in deference to this school of thought the final three chapters will be devoted to an examination of the road ahead. Chapters 10 and 11 will discuss some of the conditions that need to be corrected to clear the way for the development of a new and adequate theory of the atom, and Chapter 12 will indicate the general features that such a theory must possess in order to be compatible with present-day experimental knowledge.

The findings of the investigation on which this present work is based point very definitely to the conclusion that the most serious obstacle standing in the way of scientific research in general and the formulation of a satisfactory theory of atomic structure in particular is the lack of a clear distinction between factual and non-factual material in present-day practice. In theory, the most distinctive feature of science is its reliance upon the established facts as the ultimate authority. Speculation and hypothesis play an important part in scientific research, to be sure, but the products of such activity are not supposed to be considered in any way authoritative unless and until they are verified by experiment or observation. As it happens, however, scientists are not only scientists, they are also human beings, and in the latter capacity they are subject to the ordinary weaknesses of the human race, including a strong bias in favor of familiar and commonly accepted ideas, a totally unscientific reliance on presumably authoritative pronouncements, and a distinct reluctance to admit ignorance. All of these add up to a marked tendency to regard general acceptance as equivalent to proof, a tendency that has had the effect of diluting the firmly established factual material of science with a large admixture of matter of an unproved and uncertain character.

The strangest feature of the whole situation is that this confusion of fact with fancy is not only completely at odds with the basic philosophy on which all science rests; it is so utterly unnecessary. It is possible to understand why there might be a tendency in some other fields where actual verifiable facts are few and far between, to stretch a point and make broader claims for some of the currently popular ideas than can actually be substantiated, but science needs no padding of this kind. The factual knowledge in the scientific field is already so greatly in excess of that in any other sphere of human activity that exaggerating its extent is pointless.

Nevertheless, the exaggerations are widespread. Even the most casual survey discloses an almost incredible number of non-factual items masquerading as facts. This statement is not made on the strength of any unusually strict definition of the term “fact.” It is true that if we split enough hairs we can set up rigid definitions of such concepts as “proof,” “truth,” and “fact,” which will exclude almost everything. But the present discussion is based on the rather liberal interpretation of the nature of practical scientific proof outlined in the introductory chapter: a viewpoint which recognizes that as a practical matter some relaxation of the theoretically correct standards of proof is necessary in order to build up any body of scientific knowledge at all. It is not the intention here to contest the adequacy of the proof where proof is offered; the point which is to be emphasized is that a substantial part of present-day scientific “knowledge” consists of items which admittedly cannot be proved at all, or for which the alleged proofs that are offered are clearly inapplicable. In short, the scientist has developed a habit of saying “We know…” when he should say “We think….”

Probably no other single item has been more costly in terms of its effects in diverting scientific research from the straightforward path and turning it into unproductive detours than the failure to recognize and explore alternatives. All too often, as soon as an explanation is offered, the job is considered done, and possible alternatives, even if they are in plain sight, are ignored. As brought out in Chapter 2, the basic error made in the construction of present-day atomic theory was the failure to consider the possibility of an alternate explanation of Rutherford’s scattering experiments. Not until such possibilities have been thoroughly explored and rejected is it legitimate to say that the original explanation is correct, no matter how liberal we may make the standards of proof. In the Rutherford case, if any attempt at all had been made to look for possible alternatives, it would have been almost immediately obvious that such an alternative not only existed, but was a much better explanation of the facts than the original theory.

Bohr had an opportunity to rectify this mistake when he found that Rutherford’s atom was irreconcilable with established physical laws. For him there were clearly two alternatives; either one or the other of the conflicting structures of thought must be wrong. But, as Rutherford had done before him, Bohr looked at only one of the alternatives and, as is now evident, chose the wrong one. Beyond this point the situation became more complicated. Those who undertook to solve the many problems faced by the Bohr atom in its subsequent development no longer had a clear-cut case of choosing between alternatives. By this time it had become a matter of fighting it out on the lines already laid down or of questioning the validity of the whole structure of existing theory.

This rather curious failure to explore alternatives is by no means confined to atomic theory; it is widespread throughout the entire fabric of physical science. The First Postulate of Relativity is a striking example. The real substance of the Relativity Theory is contained in the postulates of the constant velocity of light and the equivalence of gravitational and inertial mass. The validity of these postulates is firmly established; actually they are not postulates at all, they are experimental facts, the authenticity of which most physicists were willing to concede even before Einstein incorporated them into his theory. The First Postulate, on the other hand, is simply a principle of impotence. As such it cannot contribute anything of a positive nature to the theory; it merely serves the purpose of evading the contradiction which otherwise exists between the constant velocity of light and the Newtonian concept of motion. Furthermore, it does not even do a very good job of meeting this quite modest requirement. In the first place, this postulate, which seems rather plausible in application to linear motion, falls flat in application to rotational motion, where the existence of a velocity can often be detected by external means. For instance, we can tell that the galaxies are rotating, and we can even get a general idea as to the relative magnitudes of their rotational velocities, simply by looking at them. This situation has never been reconciled with the First Postulate. “We see at once,” says Eddington, “that a relativity theory of translation is on a different footing from a relativity theory of rotation. The duty of the former is to explain facts; the duty of the latter is to explain away facts.”⁹⁷ Mach has advanced the hypothesis that the rotation is relative to the rest of the universe, rather than absolute, but since we have only one universe (so far as we know), this is merely an exercise in semantics. The other weakness of the First Postulate is that it introduces unnecessary complications of its own making into the operation of the system—a series of “paradoxes.”

On the strength of the evidence available, it can reasonably be concluded that the First Postulate is not an expression of a physical fact; it is, like a model, “only a mental help, a tool of thought.” It is rather strange, therefore, that no serious consideration has been given to the possible alternatives. From a strictly logical standpoint, the best policy would probably be just to accept the fact that a contradiction exists, and to look upon attempts at explanation, such as the First Postulate, simply as interesting speculations, until some fully satisfactory explanation finally does appear. Essentially, this is what is being done in the field of radiation, where there is a similar contradiction between the wave and particle aspects of the photon. Here the physicists, as James B. Conant describes the situation, “have learned to live with a paradox that once seemed intolerable.”⁹⁸

In view of the historical background and the general feeling that even a poor explanation is better than none, a frank recognition of the true situation may be to much to expect. There is no valid excuse, however, for failing to explore the possible alternative explanations. Obviously such alternatives exist. Within the framework of accepted ideas as to the nature of space and time the constant velocity of light is definitely in conflict with the concept of absolute motion. Something therefore has to be modified in order to conform with the observed facts, but this does not mean that the absolute motion concept necessarily has to be jettisoned. It is equally possible to modify the currently accepted space-time concepts and retain absolute motion. There is no a priori reason why one should be preferred over the other, and the experience with Einstein’s choice actually favors the alternative approach, as Einstein found that the denial of absolute motion was not sufficient, and he had to tinker with the space-time concepts as well.

A great many other similar instances of failure to explore alternatives could be cited, but in such cases as those described thus far the fault has been primarily a failure to recognize the existence of the alternatives. This is a serious and costly oversight, to be sure, but criticizing it amounts to essentially nothing more than contending that scientists ought to do a better job: a contention which, even if true, is rather pointless. But in addition to those instances where the alternatives have gone unrecognized, there are many situations in which the existence of alternatives is realized, but where some one of the possible alternative explanations is arbitrarily selected and proclaimed as an established fact. Unlike the failure to recognize the alternatives, which can be excused on the ground that the human brain is far from being a perfect instrument, this equally costly practice of investing pure assumptions with the habiliments of positive facts is wholly unnecessary and inexcusable.

Once again Einstein’s work furnishes a striking example. Throughout scientific literature his theory that mass is a function of velocity is described as having been “proved” by the results of experiment and by the successful use of the predictions of the theory in the design of the particle accelerators. Yet at the same time that a host of scientific authorities are proclaiming this theory as a firmly established and incontestable experimental fact, practically every elementary physics textbook admits that it is actually nothing more than an arbitrary selection from among several possible alternative explanations of the observed facts. The experiments simply show that if a particle is subjected to an unchanged electric or magnetic force, the resulting acceleration decreases at high velocities and approaches a limit of zero at the velocity of light. The further conclusion that the decrease in acceleration is due to an increase in mass is a pure assumption that has no factual foundation whatever.

It should be emphasized that, so far as the present issue is concerned, it is immaterial whether this assumption of an increase in mass at high velocities is ultimately found valid or not valid. The important point is that as matters now stand, we do not know what the ultimate verdict will be, and if the assumption happens to be wrong, which is not at all unlikely, the prevailing arbitrary refusal to consider any alternative places an almost impassible roadblock in the way of further progress. Nothing dampens the enthusiasm of the research worker more, or constitutes a greater obstacle to recognition of the right answer if the researcher does ultimately find it in spite of everything, than this practice of building pure assumptions up to the status of articles of faith whose validity must not be questioned.

This is not intended to imply that there is anything inherently wrong about making assumptions. Newton thought that there was, and he expressed some rather critical opinions about hypotheses in general, but an examination of his work shows that he actually utilized them rather freely. The truth is that we have no option but to use assumptions, unless we restrict our inquiries to the regions accessible to direct observation. The only method that is available for investigating phenomena in inaccessible regions is to make some assumption, then determine what consequences will result in the observable regions if the assumption is valid, and finally compare these theoretical consequences with the results of observation or measurement. We may legitimately take the stand, therefore, that assumptions are indispensable tools of science. The trouble starts only when the distinction between assumptions and facts is allowed to break down.

There are, of course, many kinds of assumptions in scientific practice, and the arbitrary selection from among equally possible alternatives is neither the most prevalent nor the most dangerous. As pointed out in a previous chapter, the latter distinction belongs to the postulates which deny the validity of established physical principles in application to the special classes of phenomena under consideration. The most common is the ad hoc assumption invented for the purpose of overcoming some specific obstacle in the theoretical development. Nothing more than a very elementary knowledge of human nature is required for a full understanding of the immense popularity that the privilege of making such assumptions now enjoys. No scientist likes to face the prospect of spending long years of effort in a fruitless endeavor to solve a difficult problem, and few can achieve such perfect scientific detachment that they are able to contemplate with equanimity the necessity of giving up a cherished concept or theory of long standing. But here is a marvelous device by which the scientist can circumvent both of these distasteful prospects as if by magic. Following the example of Bohr, he “solves” his problems simply by “postulating that they do not exist.”

The ad hoc assumption is the morphine of the scientific world. When used sparingly and in the appropriate circumstances it is invaluable, but when it is used indiscriminately the results are disastrous. Common prudence certainly calls for the exercise of a careful control over any device which is so open to abuse: a close scrutiny of the alleged justification for the assumption, an insistence on adequate study of all possible alternatives, and above all, a permanent and sharply defined line of demarcation between assumptions and positively established facts. But present practice is just the reverse. The scientist who solves a problem receives no more credit than the one who postulates that a solution is impossible; indeed our highest honors are reserved for those who construct evasive postulates of a particularly novel and ingenious character. Furthermore, the current tendency is to elevate these ingenious assumptions to a level where they are on a par with, or even superior to, the established facts.

The most vicious aspect of the present incredibly liberal policy with respect to the employment of ad hoc assumptions is that it perpetuates basic errors when they are once made. The facts that have been brought out in the preceding pages with respect to the nuclear hypothesis provide a graphic illustration of this point. Here is a hypothesis whose antecedents could never have survived any kind of a critical examination, and whose consequences have been one long story of continued and repeated conflict with observed facts and established principles. The mere layman, in his innocence, might think that somewhere along the line someone would suggest that it would be simpler to drop the nuclear idea than to force the rest of physical theory through such a painful series of contortions. But no, the theorist tells us, this is unthinkable. Back on page one of The Book it says that Rutherford discovered the nucleus in 1911 and this, like the laws of the Medes and Persians, cannot be changed. And as long as there are no restrictions on the use of ad hoc assumptions, it will not be changed (unless through the agency of some irreverent work such as this), since the question always comes up in this form: Shall we make another assumption or shall we abandon our entire theoretical structure?

II

An important class of non-factual material that is all too often confused with fact consists of extrapolations from the known to the unknown regions. Here again, the process itself is not open to criticism. Extrapolation is a sound and indispensable tool of science, and as long as the products of the extrapolation process are recognized for what they actually are, this device serves a very useful purpose. As brought out earlier, we must use assumptions in order to deal with regions beyond the reach of direct observation, but if we had to make our assumptions completely at random, the amount of work that would have to be done to test one hypothesis after another until we just happened to hit on the right one would make scientific research practically impossible. Extrapolation is the device that we use to determine the kind of assumption which has the greatest probability of being correct.

Let us assume, for example, that we are doing some work which involves the melting point of iron under pressures on the order of those existing at the center of the earth. We have no direct knowledge of the behavior of matter under such high pressures and we therefore have no option but to make an assumption of some kind. Since we are dealing with the unknown, anything is possible, theoretically, and there is practically no limitation on the assumptions that we could make, but it is clear that here, as is almost always true, there is one possible assumption that is so far superior to all others, so much more likely to represent the true facts, that we are never justified in considering any other possibility until after we have given this one a thorough examination. This greatly superior hypothesis is, of course, the assumption that the same pattern which we find in the known region also prevails in the unknown region; that is, it is an extrapolation from the known to the unknown.

In the example cited, the procedure that is followed is to determine the mathematical relation between pressure and the melting point of iron in the pressure range where direct measurement is possible, and then to extend this relation to a determination of the value in question. In this case, one of the primary uncertainties inherent in the extrapolation process is immediately apparent, as we find that there is much difference of opinion as to just what the true relationship within the experimental pressure range actually is. Several different mathematical expressions of this relationship have been proposed by competent investigators, all of which agree with the observed values within the experimental error, but which arrive at widely different results when extrapolated to the pressures at the earth’s core. Even in those cases where this uncertainty does not exist, and the mathematical formulation of the observed values seems to be beyond question there is always the possibility of an unrecognized term which is negligible within the experimental range, but may be very significant in a long extrapolation. Then, of course, it is also possible that the pattern may change at some point beyond the experimental limit: an unsuspected critical point of some kind. Here again the chance of running into this kind of a situation is much greater if the extrapolation is a long one.

The length of the extrapolation is therefore a very important factor in determining the true status of conclusions which are reached by means of an extrapolation process. If the extrapolation is very short, the results which are obtained can usually qualify as facts under the very liberal definition of scientific proof which has been adopted for purposes of this discussion. But many of the extrapolations now being made are far from short. As Bridgman puts it, some of them are “perfectly hair-raising.” A good example is the almost universal belief that we now “know” the nature of the processes which furnish the energy supply for the stars. Even in a day when “hairraising” extrapolations are somewhat commonplace, this one sets some kind of a record. In view of the gigantic extrapolation that is required to pass from the relatively insignificant temperatures and pressures obtainable on earth to the immensely greater magnitudes which we believe (also through extrapolation) exist in the stellar interiors, even the thought that the answers might be correct calls for the exercise of no small degree of faith in the validity of our processes; any contention that the extrapolated results constitute actual knowledge is simply preposterous.

Actually the currently accepted ideas in this field are based to a considerable degree on atomic theories which, in the light of the points brought out in the earlier chapters, are no longer tenable. This, in conjunction with a number of contradictory items of a factual character, principally from the astronomical field, furnishes enough evidence to justify the conclusion that the present theories as to the nature of the stellar energy generation process are not merely unconfirmed assumptions, but are almost certainly wrong. The current practice of presenting such products of long extrapolations as positive knowledge is a definite and serious hindrance to scientific progress.

It is true that the atomic physicists, who are not themselves deceived, generally dilute their statements with a few qualifying words, and if we read the fine print we can see that they are giving tentative conclusions rather than facts. For example, Robert E. Marshak, in an article entitled “The Energy of the Stars,” makes this assertion “So we can safely assume that the stars produce energy by the combination of light elements through the collisions of their swiftly moving nuclei.”⁹⁹ Technically, this statement is unimpeachable. It does not purport to be a statement of fact; on the contrary, it is specifically labeled as an assumption. But physical science today is highly compartmental. As Leprince-Ringuet describes the situation, a physicist “rarely comments on anything that lies outside of his own well-defined specialty,”¹⁰⁰ to say nothing of questioning the conclusions of specialists in other areas. A confident expression such as Marshak’s, coming from a specialist, therefore acquires the status of gospel truth as soon as it gets into the general realm of physics, and we find the textbooks and semi-popular scientific works repeating it in such uncompromising terms as, “Fusion reactions of light nuclei account for the production of energy in the sun,”¹⁰¹ or “Nuclear fusion … has been generating the power of the sun and other stars for billions of years,”¹⁰² or “Actually we all live by hydrogen fusion, for that is how the sun’s heat and light are generated.”¹⁰³

By the time this product of a “hair-raising” extrapolation reaches the astronomers it has become an article of faith against which factual evidence is powerless. E. T Opik tells us, “This knowledge is so well founded that it furnishes a reliable basis for the calculation of time rates of stellar evolution.”¹⁰⁴ The high estate to which the assumption and belief of the atomic physicist has now risen is all the more remarkable since Opik admits on the very next page that this “reliable basis” is clearly unreliable. “The energy source of the giants remains a puzzle,” he says, and hence “a more powerful source of energy must be assumed.” A little later he further concedes that “some uneasiness may be felt” about the application of the theory to the white dwarfs. Throughout astronomy this same situation prevails. On every hand facts revealed by astronomical observation are openly or inferentially in conflict with necessary and unavoidable consequences of the energy generation process “safely assumed” by the physicists. “It is no small matter,” says Bart J. Bok, “to accept as proven the conclusion that some of our most conspicuous supergiants, like Rigel, were formed so very recently on the cosmic scale of time measurement.”¹⁰⁵ Cecelia Payne-Gaposchkin tells us that the results of age calculations based on this hydrogen conversion process are “staggering.”¹⁰⁶ Otto Struve even finds it necessary to characterize factual knowledge from his own field as “apparent defiance of the modern theory of stellar evolution.”¹⁰⁷

But rather than question the conclusions of specialists in another field, the astronomers have chosen to ignore the contradictory evidence from their own observations and to distort the entire astronomical picture to fit the “hair-raising” extrapolation of the physicists. This is exactly the same kind of thing that has happened in atomic theory, where all else has been subordinated to the demand that the interpretation of Rutherford’s scattering experiments as the discovery of a “nucleus” be maintained at all costs. Both of these situations furnish eloquent testimony to the serious consequences of the lack of adequate discrimination between factual and non-factual material in present-day scientific practice.

Another type of extrapolation, which is all the more dangerous because the extrapolator does not always realize the true nature of the step which he is taking, is what we may call extrapolation of the negative. Here we find that certain things do not happen in the regions directly accessible (the earth, primarily). We then generalize this observation by extrapolating it to the regions that are not accessible, and we say that such things never happen. A good example of this type of extrapolation is provided by the question of isotopic stability. Under terrestrial conditions the isotope Fe⁵⁶ is stable. In the absence of any evidence to the contrary we assume that stability is an inherent property and that Fe⁵⁶ is always stable. Similarly, we assume that the neutron is always (with one curious exception) unstable because it is unstable in the region where we can observe it.

These are natural and logical assumptions under the circumstances, and as long as it is recognized that they are only assumptions, not facts, they are entirely proper. But here again this important distinction is, for the most part, ignored. Much of the current thinking about the cosmic rays, for instance, follows along lines dictated by the belief that those particles which are short-lived in the terrestrial environment are likewise short-lived in inter-stellar and inter-galactic space. Similarly, we find the neutron relegated to a comparatively minor role in hypothetical atom-building processes because it is short-lived on earth. But the observed instability of neutrons, mesons, and other such particles, under terrestrial conditions does not prove that they are unstable under other conditions; it is evidence suggesting such a conclusion, but we are making an enormously long extrapolation of the negative when we apply this conclusion to the universe as a whole, and it is a serious mistake to assume that the little that we now know closes the door to all other possibilities. In this connection it is interesting to note that however firm the modern physicist may be in his conclusion that the instability of the neutron is an inherent property of the particle, he does not hesitate to throw this firm conviction overboard when it conflicts with some other cherished concept. The same physicist who reacts violently to the suggestion that stability may be a function of the environment and that his conclusions as to atom-building and similar processes in extra terrestrial environments may therefore be wide off the mark, does not hesitate to advance exactly the same hypothesis when he finds this necessary in order to fit his theory that the normally unstable neutron is a constituent of stable atoms.