Chapter V

Postulates Unlimited

I

The four preceding chapters present the primary thesis of this work. They show that when the arguments in favor of the nuclear atom concept, developed fifty years ago on the basis of a very limited amount of experimental information, are reexamined in the light of the immense store of factual knowledge now available, they collapse completely and leave the theory entirely without support. However, during the half century that the nuclear theory has been the accepted doctrine in its field, it has become entwined and intermeshed with many other phases of physical theory, and it cannot be summarily discarded without a certain amount of effect in these other fields. Indeed, it is generally believed, quite erroneously, that these collateral items furnish some corroboration for the nuclear theory itself. Some discussion of these related items is therefore appropriate.

One of the most interesting and revealing features of present-day atomic physics is the fact that the original Bohr theory, already buried deep under successive layers of modifications and revisions, is still the picture of atomic structure that is presented to all those who undertake a study of physics. “This (Bohr) atom… is wrong. It is, alas! still taught in school and university,”⁵⁰ laments a British observer. “There is no much physical and chemical evidence for the correctness of the modern atomic picture that there can be no reasonable doubt of its validity,”⁵¹ says one elementary physics textbook, which then goes on to present pure Bohr theory, apparently oblivious to the fact that such a statement is the height of absurdity when the “modern atomic picture” to which it refers is flatly repudiated by the leading theorists in the physical field.

Here is an extraordinary situation that deserves some thoughtful consideration. Two points stand out particularly. First, it is quite significant that those who are responsible for the college curricula deliberately choose not to include any of the post-Bohr developments in their basic physics courses. The textbook from which the foregoing quotation was taken has 1271 pages, including one complete section on “Modern Physics”—surely space enough to permit at least some mention of the “official” doctrines of the present day. But nowhere in all of these pages is the student given the slightest inkling that, according to the acknowledged leaders in the field, his efforts to understand the “modern atomic picture” are in vain; that “the atom of modern physics can only be symbolized by a partial differential equation in an abstract multidimensional space…”, and that “an understanding of the ‘first order’ is… almost by definition, impossible for the world of atoms.”¹⁸

One can only speculate as to the reasons why this policy is being followed, but whatever they are, they certainly demonstrate a decided lack of confidence in the work of the modern theorists. This is a very curious phenomenon, yet, on reflection, it is quite understandable that those who undertake to teach the subject of physics should be somewhat less than enthusiastic about presenting to an audience of youthful skeptics a theory that has severed all ties with everyday experience and has gone on an uncontrolled excursion into a weird land of fantasy completely divorced from physical reality: a theory which has “made the atom into something inaccessible to our senses or to our imagination.”⁵² The university of today has enough of a task on its hands in attempting to give its students an understanding “of the first order” of so many subjects for which such an understanding is possible. It can hardly be blamed for reluctance to undertake the assignment of teaching a theory which admittedly cannot be clearly understood. The Principle of Incomprehensibility which Heisenberg, in effect, enunciated in making the statement quoted in the preceding paragraph, may actually have had a more profound effect on the physics curricula than his famous Principle of Uncertainty.

Even the most casual consideration of the history of the development of the nuclear concept, if undertaken by someone who is not so close to the subject that the trees interfere with his view of the forest, will inevitably suggest a direct connection between this incomprehensibility and the unprecedented degree to which established physical principles have been thrown overboard in the course of the development. Many centuries of experience in the pursuit of scientific knowledge should have made it abundantly clear by this time that one of the most hazardous assumptions that can be made in scientific research is that “things are different here.” An imaginative approach and a “certain daring in considering and testing new ideas,” to use the words of John A. Wheeler, are essential to progress, but the lesson to be learned from history is that the new ideas which are actually productive are those which lead to methods of fitting the points at issue into the existing structure of knowledge, not those which dodge the problem by postulating that existing knowledge does not apply to the matters in question. This point can be demonstrated by consideration of a few examples.

The discovery of the neutrino has already been mentioned as an illustration of a hypothesis which was completely unsupported when originally advanced, yet has achieved both general acceptance and experimental confirmation. The important aspect of this case, so far as the present discussion is concerned, is that the neutrino hypothesis did not involve postulating any deviation from established physical laws; on the contrary, the primary objective of postulating the new particle was to avoid the necessity of assuming the violation of an established physical principle: the conservation of energy.

Planck’s theory of the quantum of radiant energy is widely hailed as an imaginative and revolutionary hypothesis, and indeed it does represent a revolution in scientific thinking, probably one of the most significant changes in outlook in all scientific history, but it did not alter any existing physical laws; it merely identified the correct set of existing laws applicable to this particular situation. Science already had laws applicable to continuous phenomena and other laws applicable to phenomena existing only in discrete units (matter, for example). What Planck did was to show that the previously existing concept of radiation as a continuous entity is wrong and that it actually exists in discrete units. The known physical laws applicable to discrete units therefore apply to radiation. This rather prosaic manner of describing the innovation hardly does full justice to the feat of the imagination which Planck exhibited in breaking out of the narrow groove of established thought and formulating his new theory, but it is a correct statement of the situation, nevertheless.

Another celebrated exercise of scientific imagination is Kekule’s hypothesis of the benzene ring, which is said to have been suggested to him by a dream in which he saw a snake with its tail in its mouth. Here is another bold hypothesis, now solidly established, but entirely without experimental support when originally proposed. Again, this successful product of the imagination is an explanation which takes care of the special features of benzene and aromatic compounds in general within the existing framework of physical and chemical theory, and not by postulating that any of the principles applicable to other organic compounds are inapplicable to the aromatics.

Now let us compare Bohr’s original postulates with these three highly successful imaginative hypotheses. In all cases the hypotheses under consideration were totally lacking in direct support to begin with; it would be hard to visualize anything more truly hypothetical than the neutrino when it was first postulated. The difference is that whereas the three successful hypotheses accept existing laws as entirely valid wherever they apply to the phenomena in question, Bohr’s postulates deny the validity of established physical laws so far as application to the atom is concerned. His postulates do not merely elaborate the existing structure of theory in the manner of the hypothesis of the neutrino, or that of the benzene ring; they set up a totally new structure entirely outside the existing system.

This is a very questionable procedure, and it is extremely doubtful whether results obtained in such a manner should ever be recognized on anything more than a speculative basis. It is certainly true that Bohr’s hypotheses were accepted with almost indecent haste. Rutherford’s proposal of the nuclear atom was originally advanced in 1911. Two years later, in 1913, Bohr came forth with his postulates. Now let us ask, can it be contended in all seriousness that two years of study of a totally new hypothesis of a revolutionary nature affecting the very foundations of physical theory is sufficient to establish beyond a reasonable doubt (1) that the new hypothesis is itself sound, and (2) that it cannot be accommodated within the existing framework of physical theory? Would it not be much more in order to insist, where as basic a concept as that of Rutherford’s is involved, that the problem be studied for decades before such a drastic conclusion as number (2) is accepted on anything more than a very tentative basis?

It is now apparent that no serious consideration was ever given to the possibility that Rutherford’s nuclear hypothesis might be unsound, let alone giving it the careful and critical examination that an important theoretical proposal of this kind should have had. Surely if this question had been actively pursued, someone would have seen that it is completely unnecessary to postulate the existence of a nucleus in order to account for the results of the scattering experiments, and that no other basis for such a postulate has ever been suggested. This is merely another of those cases where a plausible and superficially attractive theory appears, and without making any critical examination, the scientific profession simply cries “Eureka!” in the manner of Archimedes, and swallows it whole.

Instead of demanding a thorough and exhaustive study of the entire situation before jettisoning any established physical laws, a study which in all probability would have revealed the true status of the nuclear hypothesis sooner or later, and thus would have stopped the Bohr development in its tracks, the physicists promptly embraced Bohr’s theory, and this acceptance, by pushing Rutherford’s nuclear hypothesis into the background, had the effect of exempting the nuclear hypothesis from any further questioning. Later, when the inevitable difficulties arose, these were taken to indicate the necessity of revising some of Bohr’s ideas, instead of being recognized in their true significance as results of an erroneous basic hypothesis. And so the modification and revision has continued, retreating farther from reality with every change, apparently without a suspicion that the whole complex structure rests on a totally fictitious foundation.

As the origins of the currently accepted versions of the theory have receded farther and farther into the background, any thought of questioning the validity of the basic concepts has become more and more inconceivable, even though, at the same time, it has become increasingly clear that there were some very definite and serious irregularities in the early work on the theoretical structure. The effect of this has been to turn the current thinking of the scientific profession into some strange and devious channels. C. N. Yang, for instance, comments on the work of the founders of present-day atomic theory in this manner, “We could only wonder what it was like when to reach correct conclusions through reasonings that were manifestly inconsistent constituted the art of the profession.”⁵³ An unprejudiced observer can hardly avoid doing a little wondering on his own account: wondering why it should be necessary to accept this altogether implausible paradox with such complete docility and without giving any consideration at all to the obvious possibility that the conclusions reached by these faulty reasoning processes are, in fact, erroneous, as the products of faulty reasoning almost always are. It is apparent that one of the characteristics of the present-day “art of the profession” is an excessive timidity in taking issue with the conclusions of earlier eras.

Before passing on to another phase of the subject under discussion it may be well to point out that a repudiation of established physical principles of the scope and magnitude of that involved in the hypotheses of Bohr and his successors, is unprecedented in physical science. There is a general tendency to couple these modern atomic theories with Einstein’s Theory of Relativity as conceptual revolutions of a similar nature, but it should be emphasized that Einstein’s hypotheses are of a totally different character, and irrespective of whether or not they are actually valid, they are not open to the same objections that apply to the hypotheses of Bohr et al.

Einstein does not say that the properties of objects moving with high velocities, the phenomena with which he is primarily concerned, follow laws that are different from those applicable to objects moving at relatively low velocities. According to his postulates, all objects follow exactly the same laws, but the expressions of these laws previously deduced for objects moving at low velocities are simplified forms of the generally applicable expressions, and they are valid only where the other terms of the general expression are negligible.

Except for the fact that Einstein’s postulates apply to some of the fundamental entities of physical science, and therefore have unusually far-reaching consequences, they are no different from many another new development in science. This is, in fact, the way in which scientific knowledge normally develops. Studies in a restricted area first show that the particular phenomenon under consideration follows a certain pattern of behavior, and a mathematical expression is developed to represent this behavior. Later these studies are extended to a wider field and it is discovered that the original pattern is a special case of a more general pattern, and that by modifying the original mathematical expression, usually by means of additional terms which are negligible in the special case, a new expression can be obtained which is applicable to the entire field. Each of these generalized expressions, including Einstein’s, must justify itself in the usual manner, but this procedure by which they are developed is entirely sound and logical.

Such hypotheses as Einstein’s still leave us with but one universe. We may have differences of opinion as to whether or not these hypotheses correctly express the behavior of the one universe to which we all subscribe, but this is a question which we can reasonably expect will be resolved in due course. On the other hand, the hypotheses advanced by Bohr and those who have modified and enlarged upon his work have had the effect (to the extent that these theories are accepted) of splitting the universe into separate parts, each with its own set of laws. From some standpoints it can no doubt be argued that there is no valid reason why there should not be two separate universes, or for that matter, an infinity of universes. At the moment it is fashionable to take the attitude that those who expect the same physical laws to be followed everywhere are simply naive. “Indeed, we should not expect,” says F. Waismann, “in a field which lies so far outside the reach of our senses, to find the same sort of relations and laws as those which hold in our large-scale world.”⁵⁴. But the arguments which are advanced in support of this view are singularly unconvincing; they have a very definite odor of sour grapes. As Lande points out in connection with the attempts to justify another of these new viewpoints, “It is significant, however, that this detached neutrality was accepted by the theorists only after their efforts to establish a unitary theory of matter had failed—temporarily at least.”⁵⁵

The inference that the “reach of our senses” has a bearing on the range of applicability of physical laws is merely another of those anthropomorphic concepts from which science has been trying to free itself for centuries. There is no sound basis for believing that we occupy any preferred or unique position, or that the region accessible to our direct observation is in any way set off from the rest of the universe. So far as we know, there is only one universe, a single all-embracing universe, and it is reasonable to believe that the laws applicable to any one part of this universe are applicable to all. Certainly we are not justified in assuming anything to the contrary merely to save some pet theory from collapse, or to accommodate theorists who have failed in their attempt to solve the problems with which they are confronted, which is essentially what the proponents of present-day atomic theory are asking us to do.

II

Another modern technique of equally dubious character which has been employed freely in the development of the currently accepted theory of the atom, along with the repudiation of established physical laws, is the use of principles of impotence, which rationalize failure to solve difficult problems by setting up postulates that solutions to these problems are impossible. Again quoting Alfred Lande, “in short, if you cannot clarify a problematic situation, declare it to be ’fundamental,’ then proclaim a corresponding ’principle.”⁵⁶ “Such propositions (principles of impotence) play a very large part at the present time in the fundamental theories of physics,”⁵⁷ says R. B. Braithwaite.

It should hardly be necessary to point out that from their very nature these principles of impotence are incapable of proof and even at best introduce a very large element of uncertainty into any situation wherein they are used. It is actually quite doubtful whether there is adequate justification for recognizing them as legitimate scientific devices, to say nothing of giving them any authoritative standing. Some of them should certainly be barred. The underlying concept upon which all scientific research is based, and without which the application of time and effort to this task would be wholly unjustified, is the conviction that the physical universe is essentially reasonable and operates according to fixed principles. Thus far we have never encountered any actual evidence to the contrary; as scientific knowledge has expanded, one after another of the phenomena that were inexplicable to our ancestors has been found to follow fixed and unchanging laws. But now there is a growing use of a practice which is not only questionable by nature, in that it is an easy way of evading the difficult task of solving complex problems, but also leads to conclusions which are in direct opposition to the philosophical premise which is our only justification for undertaking scientific research in the first place.

Conclusions such as this from Heisenberg, “…the idea of an objective real world whose smallest parts exist objectively in the same sense as stones or trees exist, independently of whether or not we observe them… is impossible,”¹⁶ or this from Bridgman, “The world is not intrinsically reasonable or understandable; it acquires these properties in ever-increasing degree as we ascend from the realm of the very little to the realm of everyday things,”⁵⁸ or this from Herbert Dingle, “The ’real’ world is not only unknown and unknowable but inconceivable—that is to say, contradictory or absurd,”³⁰ are completely at odds with the underlying philosophy of scientific research. If we had some definite and positive evidence that they were true, we would have to accept them, however unpalatable they may be, but accepting them purely on the strength of principles of impotence, or long chains of unsupported and highly questionable assumptions, which actually means that they have no factual support whatever, is totally illogical.

The plain and unvarnished truth is that these principles of impotence are simply stratagems designed to avoid the necessity of admitting failure. The theorists have failed in their attempts to discover the exact physical and mathematical properties of the component parts of the atom, and rather than admit that their approach has been wrong, or as C. N. Yang suggested in the interview previously mentioned, that their abilities are unequal to the task, they prefer to postulate that these properties do not exist and that even the atom itself, as Heisenberg says, “has no immediate and direct properties at all.” The ironic part of it is that this present reexamination of the situation in the light of modern experimental knowledge shows that the task at which the theorists have failed is a completely meaningless task; the nuclear structure for which they have sought in vain to develop a consistent and workable theory simply does not exist at all.

Here is the real reason why physical science has gotten itself into a “mess” as Schrödinger describes it, Reichenbach lets the cat out of the bag when he says, “Only the interior structure of the atom, in which lighter particles like electrons play a leading part, requires the quantum mechanical duality of interpretations.”⁵⁹ This is the answer. It is only when we try to ascertain the details of something that does not exist and conjure up all manner of explanations of wholly imaginary happenings, that we enmesh ourselves in the kind of difficulties characteristic of modern physics. The whole story is one of trying to force the universe into a pre-determined mold. The concept of the nuclear atom has been taken as a fixed, unalterable truth, and anything that conflicts with this concept has been given up, no matter how great the sacrifice. But no amount of manipulation, no exercise of ingenuity, no sacrifice of principle, can make a success of a theory that is based on a false premise. As this work brings out, the nuclear theory is wrong; there never was any sound basis for accepting it in the first place, and the advance of knowledge in the intervening half century has demonstrated that it is completely without foundation. However brilliant and ingenious the work of Bohr and his colleagues has been, their attempt to force all physical knowledge into conformity with this erroneous concept was doomed from the start.

This does not imply that their work has been completely wasted. Many results of genuine value have been accomplished as by-products of the development of this erroneous theory of the atom, since here again the theory is not 100 percent wrong; it contains some elements of truth that have been put to good use. These items of real value can be salvaged for use with whatever new theory replaces the present concepts, and this situation will be given some further consideration in the next chapter, but the theory itself-the concept of the atom that has been derived through modification and revision of Bohr’s original ideas—will have to be discarded. In addition to being completely without factual foundation, now that the true status of the “nucleus” has been revealed, this structure is a tangled mass of unsupported assumptions, principles of impotence, and repudiation of established physical knowledge that is entirely out of harmony with the underlying philosophy of scientific research.