Chapter I

Introduction

History shows clearly that the advances of science have always been frustrated by the tyrannical influences of certain preconceived notions which were turned into unassailable dogmas. For that reason alone, every serious scientist should periodically make a profound reexamination of his basic principles.

Louis de Broglie
New Perspectives in Physics
Basic Books, New York, 1962

I

A familiar American aphorism that has been attributed to practically everyone from Abraham Lincoln to Will Rogers asserts that “It’s not what we don’t know that hurts us, it’s what we do know that isn’t so.” Like many another statement ostensibly uttered in a spirit of jest, this one contains a very large element of truth, and nowhere is that truth more evident than in the field of scientific theory.

In retrospect it is easy to recognize many glaring examples, and from the vantage point afforded us by the labors of the intervening centuries we are rather prone to underestimate the intellectual abilities of those who formulated and those who accepted these ideas that are now so thoroughly discredited. We smile indulgently at the egocentric astronomers of ancient Greece and the Arab countries who made man the focus of the physical universe and set up theories wherein the whole universe revolved around the tiny planet which the human race inhabits, but we are inclined to forget that the Ptolemaic theories of the universe met all of the demands upon them for more than a thousand years: a record that few of our modern theories are likely to equal. Then again, our present-day textbooks refer to the phlogiston theory in such terms as “a false, almost ludicrous, hypothesis,” but they fail to bring out the fact that it is ludicrous only in the light of present-day knowledge; in the terms of reference provided by contemporary scientific knowledge it was a plausible and quite consistent explanation of the phenomena to which it applied, and it was accepted by the leading scientists of the era: such men as Priestley, Scheele, and Cavendish, whose intellectual stature does not suffer by comparison with that of the leaders of modern science. Much the same can be said about the caloric theory, the theory of the ether, and dozens of similar, though perhaps less striking, examples.

It might logically be expected that the principle of “once bit, twice shy” would apply in this case, and that the disastrous fate of so many presumably firmly-established scientific theories of the past would have a salutary effect in the way of discouraging over-confidence in the currently fashionable theories and concepts of science, but oddly enough, this is not true. If anything, present-day scientists are more cocksure than ever before. To be sure, they admit the existence of contradictions and weaknesses in existing theory, and they concede, at least in principle, that changes must take place, perhaps “radical changes,” but almost to a man they stoutly contend that these changes must not alter the general framework of currently accepted theory; that they must be extensions or revisions of present-day ideas, not replacements for them. Here are some expressions of the prevailing viewpoint: From Pascual Jordan, “The author, therefore, is convinced that the new conceptions must be considered conclusive…”¹ From N. F. Mott, “…it now appears that we have in quantum mechanics a body of knowledge which in its proper field is likely to last just as long… as scientists and engineers have a place in civilized communities.”² From Werner Heisenberg, “…we must assume that even the less palatable features of the laws of quantum mechanics will remain integral parts of theoretical science.”³ From George Gamow, “In my opinion and in the opinion of many other theoretical physicists, the uncertainty principle will stand its ground indefinitely.”⁴ A. J. Hymans sums up the situation in these words, “The conventional view at the moment appears to be that the state of affairs revealed by Quantum Mechanics is final and ultimate.”⁵

When viewed in the perspective of history this is a curious attitude. It is true, of course, that the areas in which knowledge is essentially complete and final are gradually expanding, and it is not unreasonable to envision the day when these completely-defined areas will embrace all or practically all of the physical universe. Some observers disagree, contending that the universe is qualitatively infinite, and that a complete understanding can never be attained, but even if we accept the more optimistic hypothesis that such an understanding is possible, it is obvious that we are still far from it. Consider the situation in elementary particle physics, for instance. As Heisenberg points out, “It is obvious that at the present state of our knowledge it would be hopeless to try to find the correct theory of the elementary particles,”⁶ and it is freely conceded that we cannot even formulate the problem, to say nothing of finding the answer, since “we do not really know how to define an elementary particle.”⁷ H. Margenau says that the word “elementary” is now equivalent to perplexing, enigmatic, etc. Some theorists are beginning to doubt whether an adequate physical theory can ever be constructed. C. N. Yang, for example, was quoted in a recent news item as “expressing some doubts about the ability of the human brain in general, and his in particular, to accomplish this task.”⁸

Against this background, the prevailing attitude that the currently popular basic theories of physical science are incontestable articles of faith not subject to challenge, an attitude which every innovator encounters, is nothing short of preposterous. There is every reason to believe that the historical pattern of scientific progress is still fully operative and that many, probably most, of the currently popular theories will ultimately fall as that progress continues. If a theory is solid and well-rounded it can resist attack successfully, and some of our modern theories will no doubt hold their own, but no theory should ever be exempt from the necessity of demonstrating its ability to meet whatever challenge is offered. Neither long years without question nor universal acceptance in present-day practice justifies any such exemption; on the contrary, theories of long standing are particularly vulnerable in that their original acceptance many years ago was necessarily based on information which, according to present standards, is very meager.

P. W. Bridgman once pointed out that there are important deficiencies in the type of examination to which scientific theories are usually subjected. The ordinary scientist does not normally feel that he can take the time to examine basic scientific concepts thoroughly. Many of the ideas to which he subscribes “have not been thought through carefully but are held in the comfortable belief… that some one must have examined them at some time.”⁹ This belief is not always justified, and even if such an examination has actually been made “at some time,” this is not necessarily enough. Experimental knowledge is advancing so rapidly, in some areas at least, that it is not safe to place full trust in any theory unless it has had a thorough and critical examination recently.. According to Sir C. V. Raman, “The progress being made is so rapid that even the most eminent leaders of the science have had scarcely time to comprehend or understand, in its totality, the meaning of all the new knowledge. They can only just glimpse the general trends of progress and hope that they will live long enough to be able to understand it all a little better some day.”¹⁰

One of the aspects of the “meaning of all the new knowledge” which is the most difficult to grasp, particularly under present-day conditions when all branches of science are so highly specialized, is the full effect of new discoveries on existing scientific thought, especially basic concepts and theories. It can easily happen, and indeed has happened, as will be demonstrated in the following pages, that new discoveries completely demolish the foundations of some accepted physical theory seemingly without anyone being aware of the fact, and the world of science moves along for the time being accepting both the new discovery and the totally incompatible idea of long standing.

In order to prevent this situation from getting completely out of hand it is obviously desirable to review the status of existing concepts and theories from time to time, paying special attention to the fields where the most rapid experimental progress is being made. An area that naturally suggests itself in this connection is the question of the structure of the atom. More than a half century has elapsed since Rutherford formulated his hypothesis of a nuclear atom: a period in which experimental science has made enormous strides. The physicist of today has at his command a huge store of knowledge of which Rutherford and his contemporaries had no inkling whatever. In the light of this situation it is no longer safe to assume that the conclusions reached in 1911 on the basis of the experimental knowledge which existed at that time—a very small fraction of that available today—are still valid, and it becomes pertinent to ask whether we might not arrive at some altogether different conclusions if we carried out a thorough reexamination of the subject with the benefit of all of the information now at our disposal. If the nuclear atom had been uniformly successful and if the present status of the theories of the atom and its structure were beyond reproach, such a question could be considered academic, but under existing conditions it can hardly be denied that it is very much to the point.

Actually we will find, when we examine present-day atomic theory carefully and critically, that it is a curious and contradictory mixture of half-century-old ideas with up-to-date conclusions based on the latest experimental evidence. We will find the textbook authors trustingly accepting the theories formulated by Rutherford and his contemporaries on the basis of the relatively few facts then available, and building a vast and complex theoretical structure on these highly imaginative basic concepts, then a page or a hundred pages later calmly and unblushingly stating conclusions derived from the immense body of experimental evidence now at hand which flatly contradict the previous statements and strike directly at the underpinnings of the basic theories so confidently expounded. We will find that the foundations of large and important portions of existing theory, originally thought to be secure against all attack, have been completely destroyed by the advances in the experimental field, leaving these sections of the theoretical structure suspended without any support; we will find assumption piled upon assumption in a manner unprecedented elsewhere in science; in short, we will find a theory that is inextricably enmeshed in difficulties of its own making, and hopelessly behind the times.

Perhaps the most surprising discovery that awaits anyone who turns the light of critical inquiry on the current theory of the atom is the extent to which the scientific profession has been willing to sacrifice logic and consistency in order to keep this cherished theory from being destroyed by the advance of knowledge. It is almost incredible that anyone would advance, in all seriousness, some of the arguments that are commonly presented in favor of the nuclear theory or particular aspects of that theory. A very common practice, for example, is to draw a conclusion favorable to the theory from an experiment or observation which actually has no relation at all to atomic theory. One contemporary physics textbook tells us, “…since the same value (of the ratio e/m) was obtained whatever gas was contained in the tube, the particle identified (the electron) was clearly a sub-atomic particle—that is, a constituent particle of atoms.”¹¹ Now it is perfectly obvious that this experiment tells us nothing of the sort; it is evidence that all electrons are alike, but the further conclusion that they are constituents of atoms is wholly gratuitous. One might be inclined to think that the authors do not mean what they say, were it not for the fact that we find them saying exactly the same thing in slightly different words a few pages farther on, and we encounter the same statement over and over again in scientific literature.

Circular reasoning which bases the “proof” of a proposition on initial premises that assume the validity of the proposition is widespread. One text undertakes to prove the existence of ions in the solid state, and gives us a diagram of the NaCI crystal; then says, without further argument, “The only possible interpretation of such a structure… is that the atoms are charged and are therefore ions.”¹² As it stands, this statement is utterly ridiculous. It can be justified only by first assuming the validity of the electrical theory of the cohesion of matter, and this, of course, is equivalent to assuming the point which is to be proved. Another text considers the relation of the positron to the atomic picture, and answers the question as to why the positron does not occur in nature as frequently as the electron in this manner, ”The reason is that soon after a positron is created it disappears as a result of a collision with an electron.”¹³ In order to give this explanation any meaning at all, we have to assume that the universe is overpopulated with electrons to begin with: exactly the situation that the text is undertaking to explain.

Then again, we find in the textbooks a perfectly astounding number of assertions in support of the atomic theory which are completely without foundation, such as the following: “…later work, particularly that of H. Moseley in 1913… has shown that… the atomic number of an element represents the number of electrons outside the nucleus of the atom and also the number of protons in the nucleus of the same atom.”¹⁴ Even a minimum consideration of Moseley’s work is sufficient to show that the only fact which he established is that the atomic number represents the number of units of some “fundamental quantity,” as Moseley expressed it, which the atom contains, and to make it clear that this work does not give us the slightest indication as to the nature of that fundamental quantity. The identification of the atomic number with protons and electrons is pure hypothesis devised in an attempt to explain the findings of Moseley and other investigators, and the present-day tendency to twist the results of this and similar experimental work into a verification of the explanatory hypotheses is a barefaced distortion of the facts.

Surely the authors of the foregoing, and a great many other statements of a similarly indefensible character contained in modern textbooks, a considerable number of which will be discussed in subsequent chapters, know better. About the only possible explanation that comes readily to mind is that they are so thoroughly convinced of the validity of the theory—“Everybody knows that matter consists of nuclei and electrons,”¹⁵ says another textbook—that they consider it unnecessary to exercise any particular care with respect to the validity of the arguments that are advanced to support it. It is high time, therefore, that we strip away the veneer of unsupported assumptions and worthless “proofs,” and subject the underlying structure of theory to a close enough scrutiny to determine just how sound it actually is.

II

As a background for the discussion which follows, it will be desirable to review briefly the history of the various steps which ultimately culminated in the currently accepted theory of the nuclear atom. Since the existence of atoms, as such, is not being questioned in this presentation, it will not be necessary to follow the long and checkered career of the atomic theory itself, and we can begin with the situation as it existed in the middle of the nineteenth century, by which time the work in connection with the development of the kinetic theory of gases had placed the atomic theory on a firm footing. In this era the atom was regarded much as it was envisioned by Democritus: a hard spherical bit of matter, the indivisible ultimate unit of physical reality.

Although the possible existence of some kind of an internal structure within the atom was a subject of speculation much earlier (Prout’s Hypothesis, for instance, was advanced in 1815), the first experimental indication that the ”billiard ball” atom might be an oversimplification came with the discovery of the electron and the determination of its major properties in the closing years of the nineteenth century. Here, for the first time, a particle smaller than an atom was observed, and although there was as yet no good reason to believe that the electron could be identified as matter, or as a constituent of matter, there were obvious possibilities in this connection which led to a great deal of discussion and speculation. But only a few years later radioactivity was discovered, and in the burst of experimental activity that followed, it was soon determined that one of the “rays” that originated from the radioactive disintegrations was a stream of electrons. Subsequently the alpha particles, which also emanated from the radioactive materials, were identified as positively-charged helium atoms.

Even before the positive identification of the alpha particles, Rutherford and Soddy had demonstrated that atoms of a radioactive element are transformed into atoms of some other element lower in the atomic scale, and when it was established that electrons and helium atoms are ejected from the original atom in the radioactive disintegration process, this naturally led to the conclusion that the atoms are constructed of such particles. This conclusion was all the more plausible because the existence of oppositely directed charges on these two ”atomic building blocks” also furnished an indication of the nature of the force that holds the building blocks together. With such points in its favor, this concept of an atom constructed of positively and negatively charged particles was almost immediately accepted, and has never been seriously challenged since.

The next question, that of the way in which the constituent particles are arranged in the atom, was resolved to the satisfaction of the scientific world almost as quickly. For a brief period the Thomson atom, which has been compared to a plum pudding, with the electrons corresponding to the raisins, occupied the center of the stage, but Rutherford’s experiments around 1911 showed that this concept was untenable. His results on the scattering of alpha particles showed conclusively that if the atom is constructed of electrons and positively charged particles, the latter must be concentrated in an extremely small region. He therefore postulated an atom roughly analogous to the solar system, with a minute positively charged nucleus, around which electrons are distributed in some manner in sufficient numbers to create an equal and opposite charge, thus making the atom as a whole electrically neutral. Disregarding details, this Rutherford atom of 1911 is still the “official” concept of atomic structure: the nuclear atom of the present day.

But while we can thus disregard details in taking a birds-eye view of the situation, the question as to details must be faced sooner or later, and this has proved to be full of difficulties. It was quickly recognized that the simple picture originally conceived was not capable of representing all of the known facts, and that the nucleus must contain something more than the positively-charged particles. The first hypothesis that was proposed as a means of meeting this situation was that some electrons existed in the atomic nucleus in addition to the extra-nuclear electrons originally postulated, and this was the accepted view for the next twenty years or so. There are, however, some very serious objections to the idea of electrons inside the nucleus, and the theorists gave a sigh of relief in 1932, when the discovery of the neutron supplied a new building block that could be substituted for the nuclear electron. Since 1932 the atomic nucleus has been assumed to consist of protons and neutrons in the appropriate proportions for each element and isotope.

In the meantime, even greater trouble was encountered with the orbital electrons in the outer regions of the nuclear atom. As soon as detailed calculations were made on the Rutherford atom, it became apparent that this atom was not stable and could not even maintain itself if undisturbed, to say nothing of surviving thermal collisions. Niels Bohr met this problem in an unprecedented way by boldly postulating that the atomic electrons do not follow the usual laws of physics, conforming instead to certain unique behavior characteristics of their own, which he defined to fit the existing situation. In spite of the wide latitude afforded by this chance to write his own physical laws, Bohr found his atom enmeshed in constantly growing difficulties, and it ultimately had to be abandoned, or at least modified beyond all recognition. The present “official” view of the atom, of which more will be said later, regards it as something which, as Heisenberg says, does not “exist objectively”¹⁶ and is “in a way, only a symbol.”¹⁷

The strange and tortuous path which the revisions of the original Bohr theory have taken has left the scientific world somewhat bewildered, and as matters now stand the physicists are strung out all along the line of development. At one end are the educators, particularly those teaching elementary physics, who present the Bohr atom in all of its pristine glory as if every feature of the atomic structure were known specifically and in detail. At the other end are the theorists of the Copenhagen school, who deny the reality of the “elementary particles” and even of the atom itself, and tell us that anything other than a mathematical picture of the atom is impossible; that “…the atom of modern physics… has no immediate and direct physical properties at all, i.e., every type of visual conception we might wish to design is, eo ipso, faulty.”¹⁸ Somewhere in between are the majority of the individual physicists, who realize that the advance of knowledge has destroyed the original Bohr theory, but are nevertheless unwilling to go along with the extreme views of the Copenhagen group and concede that the ultimate units of the physical world are nothing but mathematical phantoms.

In the subsequent pages it will be necessary to discuss matters relevant to each of these points of view at one time or another, but in such cases the particular theory involved will be specifically indicated, and it should be understood that wherever reference is made to the “nuclear theory of the atom” without special qualification, this represents the general concept on which the physicists of all schools of thought are currently agreed; that is, an atom which consists of a nucleus, composed of protons and neutrons and hence positively charged, and an outer structure composed of negatively-charged electrons distributed around the nucleus in some manner.

III

Before beginning an examination of the observations and conclusions upon which the concept of the nuclear atom rests, it will be helpful to consider the general question as to how the validity of such a concept can be proved. Since science recognizes the observed facts as the ultimate authority, this proof must be based on correlations with observed or measured facts, unless the item is itself something that can be observed or measured and thus proved directly. Two types of indirect proof are available, one of which rests upon the antecedents of the concept in question, the other on its consequences.

A scientific proposition may be proved by showing that it is a necessary and unavoidable consequence of certain positively established facts, or of some other proposition or propositions that have been proved previously. Alternatively, it may be proved by showing that its consequences are consistent with all of the pertinent facts. Since one can rarely, if ever, be sure that all of the pertinent facts are known, this latter type of proof must rely upon probability considerations, and in order to reduce the probability of a hidden conflict somewhere in the system to the point where it is negligible, it must be shown that the consequences of the proposition in question are consistent with the known facts in a large number of random cases throughout the area involved, without exception, and without the use of contrived methods of evading contradictions or inconsistencies.

Practical considerations necessitate a certain amount of relaxation of these rigorous standards of proof, since our factual knowledge is still far from complete and few scientific principles could qualify as true if we were to demand strict mathematical and logical compliance with the requirements set forth in the preceding paragraph. In order to establish any body of scientific knowledge at all, we must compromise to some extent and accept those propositions which are established beyond what we consider a reasonable doubt, even though we know that there is a possibility that these propositions may be overturned by future additions to scientific knowledge. Unfortunately, when it becomes necessary to open the door at all, there is always a temptation to open it still wider and, in particular, to accept certain hypotheses which do not even come close to meeting the requirements, simply because they appear to be the best explanations of the observed facts currently available. The distinction between fact and assumption thus becomes blurred, and there is a very definite tendency in present-day scientific practice to regard general acceptance as equivalent to proof. In undertaking a critical reexamination of currently accepted ideas it is, of course, essential to distinguish clearly between those items which have actual factual support and those which owe their present standing merely to general acceptance.

Another of the loose practices with which we will be particularly concerned in this discussion is that of interpreting evidence which is consistent with a particular hypothesis as proof of the validity of that hypothesis. Where only one explanation of a set of facts can be found on the basis of existing knowledge, we are justified, from a practical standpoint, in accepting this explanation as true, at least tentatively, even though we recognize that there may be some other explanation at present unknown. But where more than one possible explanation can be derived from existing knowledge, there is no justification for considering the observed facts as proof of any one of them. Furthermore, this situation is not materially altered if an explanation is consistent with many such facts, as long as alternative explanations are available for each of them, unless all of the requirements for a proof by the probability method can be met.

Both of these practices, that of accepting inconclusive evidence in lieu of proof and that of accepting today’s best guess as the equivalent of an established fact, are so foreign to the spirit of scientific inquiry that unless one has had reason to make a critical examination of the situation it is hard to believe that they would be allowed to enter into scientific work to any significant extent. Actually, however, they are not only widespread, but they are symptomatic of a general change of attitude that has taken place in the scientific community in the current century. What this change amounts to is the subordination of all other considerations to the maintenance of the status quo in the field of basic theory.

We are taught that a scientific theory is valid only so long as it agrees with the facts derived from observation and measurement, and that when and if the time comes that a substantial body of new facts is discovered which cannot be reconciled with the theory, it must step aside in favor of something more adequate. Thus the Ptolemaic theory of the universe, the caloric theory of heat, and other once highly valued concepts of earlier days have faded from the picture. Thus, too, it can logically be expected that many of the theories of the present day will ultimately be superseded.

But now a new element has entered into the situation, and dislodgement of a firmly entrenched theory has become an almost impossible task, even when the theory is completely erroneous. The supporters of the older theories had to capitulate when the contradictory facts became too numerous, but the ingenious and resourceful modern theorist is no longer at the mercy of the facts. He has invented a whole new armament of novel weapons that can be used against any challenger. If only a single inconvenient fact has to be faced, the answer is an ad hoc assumption, tailor-made to remove the obstruction; if some established physical law stands in the way, the theorist simply postulates that the law does not apply to this particular situation; if the theory fails to solve a problem, all that is necessary is to proclaim a principle of impotence, according to which a solution to this problem is impossible, or alternatively, to assert that the problem has been solved “in principle” and that only the extraordinary mathematical complexity of the solution prevents getting answers that are applicable to specific cases.

The skeptic may be reluctant to accept results obtained by such means, but he has little on which to hang an objection, since these devices are of such a nature that they are inherently immune to attack. Besides which, there are not very many sincere skeptics to be found. The great majority of scientists go along willingly with the currently accepted basic theories and raise no inconvenient questions. It would probably be difficult to find even a handful who would question the validity of the nuclear theory itself. The quantum development of the basic theory brings out a few more dissenters. Some are inclined to echo Cornelius Lanczos’ complaint that “strange and obscure principles are forced on us”¹⁹; others would second Erwin Schrodinger’s fervent hope that we may find “something better than the mess of formulas which today surrounds our subject,”²⁰ but few are ready to discard any major portion of existing theory. Whenever the accepted theory arrives at a crisis, the alternatives are either to abandon the entire theoretical structure or to avoid the necessity for so doing by using one of these somewhat questionable recent inventions. In view of the extreme reluctance to abandon ideas of long standing, which is characteristic not only of the scientist, but also of the entire human race to which he belongs, there is little doubt as to which alternative will prevail.

It is obvious, however, that this situation is made to order for perpetuation of any error that may have been made in the formulation of a basic theory. Such an error will inevitably lead to a series of contradictions and inconsistencies as the development of the theory progresses. In earlier years the accumulation of a number of these contradictions would necessitate abandoning the theory, but today, when a wide variety of devices for evading the contradictions is at the command of the theorist, the erroneous basic theory can remain intact almost indefinitely. Under these circumstances, it would be nothing short of a miracle if all of the basic theories of the present day were sound and free from error. The analysis of the nuclear theory of the atom that will be made in the pages that follow will demonstrate that the Age of Miracles has not yet arrived. It will be shown that a serious mistake in interpretation of the observed facts was made in the initial formulation of this theory. As could be expected, the theory built upon this error was in conflict with established physical laws almost immediately. This conflict was brushed aside by postulating that the established laws did not apply, and the theory proceeded on its way, until it encountered another of the inevitable recalcitrant facts. This, in turn, was removed by the use of another of the ingenious modern techniques, permitting the theory to move on to the next crisis, and so on and on.

In the kaleidoscope of changing patterns during the course of this development, the basic nuclear theory has come to occupy a position as the one permanent element in the picture. Established principles may be repudiated, interpretations of observed facts may be altered beyond recognition, hypothetical forces and behavior characteristics may come and go, even physical reality itself may be questioned, but through it all the concept of the nuclear atom remains intact, simply because this is the one thing to which all else is subordinated. As matters stand, it is no wonder that the standards of proof have been relaxed; that our “delicacy of feeling with reference to such questions has been blunted,” as Schrödinger puts it. Why worry about whether our arguments are sound and logical—the general attitude seems to be—since they are only perfunctory anyway? We know the answer before we start. This attitude reaches a fitting climax in the strange upside-down thinking of the author who solemnly assures us that “Quantum physics presents a strong case against traditional logic.”²¹

In undertaking a critical reexamination of the validity of the nuclear theory it will be necessary to take an altogether different approach. Since we will be looking for an answer, rather than working toward an answer already defined in advance, the prevailing carefree policy of accepting every favorable argument at face value without anything more than a casual scrutiny can no longer be tolerated; it will be necessary to demand strict conformity with logical principles and reasonably rigid standards of proof. We can no longer assume that because an idea is generally accepted that it is necessarily true, nor that an explanation of an observed fact is necessarily the correct explanation. On the contrary, the fact that the accepted theories are sheltered behind a series of assumptions and postulates which by their very nature lend themselves readily to abuse, but cannot be attacked directly, makes it all the more imperative that we hold these theories to a strict accounting wherever they are exposed and can be subjected to the usual tests that distinguish truth from falsity.