Chapter VI

Other Names for Roses

I

The second point that emerges as very significant when we analyze the attitude of the colleges toward modern atomic theory is that they find the Bohr atom more suitable for the applications with which they are particularly concerned than its highly sophisticated successors: a fact which helps to explain their coolness toward the more recent developments. The atomic picture for which the textbook finds so much “physical and chemical evidence” is the original Bohr picture, which all of the leaders in the field, including Bohr himself, have long since characterized as wrong.

Just offhand, this seems ridiculous. How can there be “much physical and chemical evidence” of the correctness of a theory that is admittedly wrong? The answer to this question goes back to a point which was brought out in the introductory chapter: the fact that prevailing practice tends to interpret observations which are consistent with a particular hypothesis as proof of that hypothesis. If we require the textbook authors to restrain their enthusiasm for currently accepted ideas and to limit their assertions to statements which they are prepared to back up with facts, they will have to amend their comments and say, in effect, “There is much physical and chemical evidence which is consistent with the modern atomic picture.” But this, of course, will not support the previous conclusion that “there can be no reasonable doubt of its validity.”

It not infrequently happens that a particular set of facts is consistent with many theories, and on the basis of present practice, the protagonists of all of these theories can (and sometimes do) offer exactly the same facts as “proof” of their respective contentions. The original Bohr theory is wrong, as the front-line theorists now admit, because it is inconsistent with some physical facts, but these fatal contradictions are not apparent in the less complex applications with which the elementary physics textbooks deal, and hence these text books can still offer evidence which is consistent with the original Bohr theory as “proof” of that theory.

It is the aim of this present chapter to show that most of the “physical and chemical evidence” to which the textbook writers refer is equally as consistent with many other hypotheses as with the theory of the nuclear atom, and that it therefore is not a proof of any hypothesis. Since this is the case, collapse of the nuclear theory does not cause the widespread dislocation that would ordinarily be expected; in general the previous conclusions expressed in terms of the nuclear atom remain just as valid as ever; all that is necessary is to change the language in which they are expressed. This does not weaken the previous conclusions in any essential respect. To borrow an expression from another field of human activity, “A rose by any other name would smell as sweet.” All that we need to do in this instance to accommodate our experimental findings to the absence of the nuclear theory is to provide some new names for our old roses.

One major class of items of this kind is illustrated by Moseley’s Law, which is widely hailed as one of the bulwarks of modern atomic theory. Holton tells us, for example, “In the year 1913… there came yet another profound contribution (to the theory of the nuclear atom).”⁶⁰ Let us see just how “profound” this contribution actually is.

Moseley’s work, in essence, established a mathematical relationship between the atomic number and the frequencies of the characteristic x-rays of the various elements. His unimpeachable conclusion, as quoted by Holton, is that “We have here a proof that there is in the atom a fundamental quantity, which increases by regular steps as we pass from one element to the next.” But then he, too, falls into the trap unintentionally set by Rutherford, and goes on to say, “This quantity can only be the charge on the central positive nucleus, of the existence of which we already have definite proof.”

Let us bear in mind that this conclusion was reached in 1913, only two years after the formulation of the nuclear postulate, and the “definite proof” to which Moseley refers was furnished by Rutherford’s interpretation of the results of his scattering experiments, which we now see is wholly unjustified. Here, and in the original work of Bohr, carried on contemporaneously, we can see the beginning of the great build-up, in which a conclusion of Rutherford’s, never properly substantiated and now completely refuted, has been pyramided step by step into the great mass of detail that now constitutes the nuclear theory of the atom. Like Bohr’s theory, which is preposterous unless the existence of a nucleus is previously established beyond all reasonable doubt, this second conclusion of Moseley’s falls flat unless it is preceded by the “definite proof” of which he speaks. But since Rutherford’s hypothesis as to the existence of a nucleus was accepted without question, these two subsidiary theories, Bohr’s and Moseley’s, which could not have been entertained at all if the nuclear hypothesis had been subjected to any reasonably careful analysis, were likewise accepted. In the next step these Bohr and Moseley concepts were utilized to “prove” still other conclusions, and the same process was repeated over and over again until the present imposing structure was built up.

Holton’s characterization of Moseley’s findings as a “profound contribution” to the nuclear theory is an example of a widespread misconception as to the true status of the so-called “evidence” in favor of the theory. This statement reveals a mental image, apparently shared by most physicists, in which the various items of “evidence” are regarded as independent and cumulative. Rutherford first arrives at a conclusion. Moseley makes some further discoveries and arrives at another conclusion, based on these discoveries, which is consistent with that of Rutherford. Bohr does the same, and so on. According to this popular point of view, each additional finding reinforces what has gone before. The findings of Rutherford plus those of Moseley are more secure than those of Rutherford alone. Bohr’s results add still more solidity to the structure, etc.

If these various findings were truly independent, this point of view would be entirely justified. The work of Einstein on the photoelectric effect, previously mentioned, is in this category. Einstein utilized the theory developed by Planck, but his findings were not in any way contingent on any previous proof of that theory; on the contrary, his demonstration of the validity of Planck’s theory in application to the photoelectric effect would have remained valid even if Planck’s own conclusions with respect to the distribution of frequencies in black-body radiation had turned out to be in error. Under these conditions Einstein’s work actually was a “profound contribution” in support of Planck’s theory. But the findings of Moseley, so far as they have any bearing on the nuclear atom theory, are not independent of those of Rutherford. Unless the “definite proof” of the validity of Rutherford’s hypothesis, to which Moseley refers, is forthcoming, Moseley’s experimental results cannot be connected with the nuclear atom at all. Similarly, Bohr’s conclusions, as already pointed out, are completely dependent on the validity of Rutherford’s hypothesis. Hence Rutherford plus Moseley plus Bohr are no stronger than Rutherford alone. Since he falls, then all fall. This is a general principle, applicable in all cases where an entire structure of theory is pyramided on one basic hypothesis and is completely dependent on the validity of that hypothesis.

Pursuing this subject further, let us examine the nature of Moseley’s results. Since he was unable to look behind the facade and see that Rutherford’s hypothesis might be wrong, Moseley concluded that the “fundamental quantity,” the existence of which was indicated by his experiments, was the nuclear charge. But the charge, as such, does not enter into Moseley’s mathematical expressions of his results. In these expressions the “fundamental quantity” enters only as a dimensionless number. Clearly this represents a number of units of some kind, but the nature of these units is not indicated by Moseley’s findings, and the kind of unit involved is completely immaterial so far as the relationship expressed by Moseley’s Law is concerned. The element potassium, for instance, must contain 19 units of some kind in order that the relationships which Moseley established may be satisfied, but they can be 19 units of any kind, without restriction.

It is quite obvious that any atomic theory that might be seriously proposed in the light of present factual knowledge must provide for some quantity corresponding to the atomic number: some quantity which, as Moseley says, “increases by regular steps as we pass from one element to the next.” But this means that this theory, whatever it may be, is automatically in conformity with Moseley’s Law. The contention that Moseley’s findings constitute a “profound contribution” to the nuclear theory is thus completely erroneous. These findings are consistent with any plausible atomic theory and they cannot be uniquely connected with the nuclear theory unless that theory is first proved correct by some other means.

Essentially the same thing can be said about every item of this kind that is now being advanced as “proof” of the modern atomic theory or some specific phase of that theory. All of these items purport to show that the observed relationships confirm the existence of certain numbers of electrons, protons, neutrons, electric charges, etc., in the atom, but when we examine the alleged evidence we find that in no case do such particles or charges actually enter into the relations that are established experimentally. The entities which appear in the mathematical expressions are dimensionless numbers in all cases, just as in Moseley’s Law, and the observed facts give us no indication as to what kind of units might be involved. The labels that are currently attached to these numbers come from the theory, not from experiment. The mathematical expressions that have been derived from the experimental work are consistent with the currently accepted theories, to be sure, but they are equally consistent with any other theory which arrives at the same numerical values, regardless of the names which such other theory may attach to the units, and since these numerical values are all related to some quantities such as the atomic number or atomic weight, for which any theory must furnish an explanation, agreement with the observed mathematical relations is no problem for any theory. If it does not come automatically, as in the case of Moseley’s Law, it can certainly be achieved with no more manipulation than is required in current practice.

The situation is altogether different in the case of relationships in other areas of physical science where the pertinent terms in the mathematical expressions that define these relations have specific dimensions. If our answer has the dimensions of force, then we must somewhere have a term with the dimensions of mass, and where ten units of this kind are involved they must be ten units of mass; they cannot be ten units of any other kind. But the relations which are supposed to involve numbers of electrons, etc., are not of this character. These electrons, or other hypothetical particles, do not have any unique significance in relation to the experimental results; the numbers are dimensionless, so far as the experimentally observed relations are concerned, and if anyone chooses to say that they refer to some units other than electrons, this is equally consistent with the observed facts.

We may conclude, therefore, that in general the substitution of some other theory for the present theory of the nuclear atom will not affect relations of the kind just discussed, except that different language will have to be used. Wherever these items are consistent with the nuclear theory, they will be equally consistent with any other plausible theory that may be proposed.

II

The points which have been brought out with reference to the lack of any definite connection between Moseley’s Law and the nuclear theory apply with equal force to the items which are advanced as “proof” of the validity of Bohr’s model of the atom, but in view of the major role which these items have played in building the nuclear atom theory up to its present quite undeserved eminence, it will be in order to discuss this situation more specifically. The exact status of these so-called proofs is, of course, rather vague, now that the original Bohr theory has been officially repudiated. It is not uncommon in scientific practice to have some alleged proof of a theory refuted, without seriously affecting the standing of the theory itself, but here we have the extraordinary situation of a theory being abandoned, leaving its proofs still standing, and still being taught on a wholesale scale in our universities. This has somewhat the same flavor as Victor Borge’s account of the cure for which there is as yet no known disease.

The original and most impressive success scored by Bohr was his interpretation of the line spectrum of hydrogen. J. J. Balmer discovered empirically in 1885 that the principal series of lines in the hydrogen spectrum can be represented by a mathematical formula, which in its modern form is expressed as R (1/4-1/b²), the factor taking successive integral values beginning with 3. Subsequently it was found that this Balmer formula is a special case of a general expression R (1/a²-1/b²) in which both a and b take successive integral values. When a= 2, the Balmer series results. Other values of a produce the Lyman series, the Paschen series, the Brackett series, and so on. Later, in 1908, Ritz extended these findings to line spectra in general by means of his Combination Principle, which asserts that any spectral series can be represented by a similar combination in which the first term remains constant while the denominator of the second term assumes successively higher values.

At this stage Bohr entered the picture and addressed himself to the task of discovering the reason why each spectral series assumes this particular mathematical form. He was convinced from the start that the then very recent discovery by Planck of the existence of discrete units or quanta of radiant energy would provide the key to the problem, and the integral values of the factors a and b in the modified Balmer formula obviously fitted in very well with this idea. The question then arose: What is the nature of these two terms that enter into the Ritz combinations? Bohr’s answer to this question constitutes his major contribution to the theory of spectra. He reasoned that since the quantum of radiant energy is a function of the frequency of the radiation, the frequency represented by the difference between two Balmer or Ritz terms is a quantity of energy. From this it can reasonably be deduced that those terms also represent energy, and Bohr thus arrived at a picture in which the atom is able to assume certain specific energy levels and emits or absorbs radiation when it changes from one of these permissible energy levels to another.

This has been a very fruitful concept, and it has provided a solid foundation upon which it has been possible to build a logical and systematic classification of atomic spectra. As matters now stand, the identification of the terms in the spectral formulas as atomic energy levels appears to be firmly established. Here is a significant scientific accomplishment that can be credited to Bohr and those who have followed in the paths which he originally defined. But the scientific community has not stopped with a well-deserved approbation of this important step forward; it has gone on to accept this accomplishment as evidence confirming the validity of present-day atomic theory: something for which there is absolutely no justification.

It may be mentioned in passing that Planck’s quantum is commonly termed a quantum of “action,” because the constant h has the dimensions energy × time, but there is no indication that this so-called “action” has any significance so far as the atomic spectra are concerned. It is, in fact, quite doubtful if “action” has any physical significance at all. The quantity which enters into the spectral relations is the quantum of energy, which is the product of Planck’s constant h and the frequency of the radiation.

Now let us go back for a moment to Bohr and his original work. Having arrived at the concept of discrete energy levels from an adaptation of Planck’s quantum hypothesis, the next objective was to connect this with Rutherford’s atom-model, the validity of which Bohr accepted without question. In this model the electrons circling around the central nucleus must possess kinetic energy and it seemed logical to assume that the energy level changes corresponding to the observed radiation reflected changes in the electronic motion. Here the established laws of physical science were in direct conflict with the new ideas, but Bohr was already prepared to throw these laws overboard. “…Rutherford’s discovery of the atomic nucleus revealed at once the inadequacy of classical mechanical and electromagnetic concepts ,”⁶¹ he tells us, and on the basis of this philosophy, he postulated that the electrons are able to occupy only certain specific orbits defined by quantum considerations, that they do not radiate while moving in these orbits, and that they possess the ability to jump from one orbit to another and, in so doing, to emit or absorb radiation with a frequency corresponding to the difference between the energy levels of the two orbits.

If we appraise this “solution” of the problem from a cold-blooded scientific viewpoint, it is clear that while it is an answer to the problem, there is nothing at all to indicate that it is the correct answer. Furthermore, it is not even a very plausible answer. In order to accomplish his objective of connecting Rutherford’s atom-model with the discrete atomic energy states, Bohr had to use three completely unprecedented postulates in direct contradiction to established physical principles; that is, it took three wild cards to win the trick. As Lanczos expresses it, “The principles from which he [Bohr] developed his model were incomprehensible and, in fact, hardly credible.”¹⁹ Now after more mature consideration, the front-line theorists, including Bohr himself, tell us that it was all a mistake, that there are no specific orbits, that the electron itself is only a “symbol,” and so on.

The most astounding feature of this whole situation is that after having thrown the only connection between the atomic energy levels and the nuclear atom to the wolves, and putting nothing in its place-even going to the extent of contending that nothing can be put in its place-the physicists still insist on using the genuine successes of the theory of atomic energy levels as evidence of the validity of the nuclear theory to which it is no longer even distantly related. Furthermore, the whole jargon of spectroscopy is based on the features of the original theory that have now been repudiated. While Schrödinger tells us that there really are no electrons in orbit, Heisenberg says that there actually is no physical electron at all, only a “symbol,” and the whole Copenhagen school insists that we cannot conceive of the atom or any of its parts in anything but purely mathematical terms, the spectroscopists tell us just how many electrons there are in the atom and exactly how they are arranged in “shells,” etc., and proceed on this basis with the calculation of spectroscopic terms to an accuracy of eight or nine significant figures. “The terms result from definite configurations and motions of the outer electrons of the atom and are explained by a well-established theory of spectral structure,”⁶² says the National Bureau of Standards.

This utterly ridiculous situation in which one group of physicists is defining specifically and in great detail the properties of entities which, according to an even more eminent group of physicists, have “no immediate and direct properties at all ” and do not even “exist objectively” is another example of the same confusion that was pointed out in connection with Moseley’s Law. Here again, as in the Moseley case, a name derived from currently popular theory has been arbitrarily attached to a particular physical phenomenon, and the scientific profession has fallen into the habit of accepting the connotations of that arbitrary nomenclature on the same basis as the observed properties of the phenomenon itself. The Bureau of Standards tells us, “…the atoms of a gas or vapor, when excited by radiation, absorb certain wavelengths corresponding to transitions of their outer electrons from lower energy levels to higher ones.” Here we have an assertion which contains three statements of totally different origin, all lumped together as if they were equally authoritative. The statement that the atoms absorb certain wavelengths when excited by radiation is a description of an observed fact. The statement that these particular wavelengths correspond to transitions from lower to higher energy levels is a theoretical conclusion which is strongly backed by evidence from experimental sources. The further statement that these energy levels are energies of electrons is pure hypothesis without the least vestige of experimental support. These levels are “Atomic Energy Levels”-the title of the Bureau of Standards publication from which the foregoing statement was taken-and that is all we know. Evidently some kind of units enter into the situation, but applying the name “electrons” to these units is pure guesswork.

Similarly the same N.B.S. circular says, “Each chemical element can emit as many atomic spectra as it has electrons,” but what is actually known is that the number of different spectra is equal to the atomic number; the further conclusion that this represents a number of electrons is wholly gratuitous, and the use of the name “electron” serves no purpose that would not be fulfilled equally well by any other name. As pointed out earlier, any theory of atomic structure that could be given any serious consideration at all must necessarily make some provision for a quantity corresponding to the atomic number, and the name of this “something,” whatever it may be, can be substituted for “electron” in the language of spectroscopy without affecting spectroscopic theory in the least. The current contention that the successful application of the theory of energy levels to the study of spectra constitutes an argument in favor of the nuclear theory of the atom is therefore pure fantasy.

III

The most spectacular research activity currently under way in the physical sciences, aside from the space exploration program, in which the increase of scientific knowledge is a secondary objective, is the concentrated attack that is now being made on the baffling problems of the atomic “nucleus.” A great army of research workers equipped with a vast array of amazingly accurate instruments and ingenious devices of all kinds, including huge and enormously expensive machines unprecedented in scientific research, is making a powerful and determined effort to find the answers to the many unresolved questions in this area. To those who are actively engaged in this interesting and formidable task, the conclusion that there is no such thing as a nucleus is likely to seem the height of absurdity. But they should be reminded that “nucleus” is merely a label, and that natural phenomena do not come equipped with labels; the labels are put on afterward. The experiments and observations only reveal the existence and properties of a “something”; the further assertion that this “something” is a nucleus is tacked on later by the theorists.

The conclusions that have been reached in the preceding pages as a result of a critical and comprehensive analysis of the present state of atomic theory in the light of the vast amount of experimental evidence now available do not deny the reality of the “something” that these workers are investigating or the validity of the experimental information that has been accumulated regarding the properties of that “something.” They merely indicate that when the “something” of the experiments is translated into the language of physical theory, the proper word in that language is “atom,” not “nucleus.”

One group of investigators, for example, is busily engaged in measuring what they call “nuclear cross-sections.” They accelerate particles of various kinds to high velocities and project them against matter, observing in detail the effects produced. But these investigators do not actually know that they are dealing with a “nucleus.” They are measuring cross-sections of a “something,” and the idea that this “something” is a nucleus is a purely theoretical interpretation that is completely independent of the experimental work. Hence rejection of the nuclear theory introduces no complications here. We simply alter the terminology and speak of atomic cross-sections rather than nuclear cross-sections, and everything else goes on just as before. Much the same comments can be made about the greater part of the other experimental work now being done in this area. The properties that are currently attributed to the nucleus are in most instances equally appropriate to the atom. When we measure size, shape, mass, magnetic moment, etc., we can simply change the terminology from “nuclear” to “atomic” and transfer the essential meaning intact from one concept to the other.

In some other instances the theoretical interpretations and labels are introduced at a lower level, and current ideas as to what actually takes place in the experiments are influenced to a considerable degree by the theoretical viewpoint of the investigator. This is not peculiar to studies of atomic structure; it is a general situation encountered in all investigations of a complex nature, and James B. Conant give us this warning, “I think that a certain degree of caution is appropriate in reading some of the popular expositions of the implications of the new physics. For in simplifying a complex experiment, the writer is almost forced to intrude an interpretation before he draws the conclusion from the evidence.”⁶³

A conclusion such as this, “The relative stability of the deuteron… shows that the force between a proton and a neutron… is of appreciable magnitude,”⁶⁴ is not a statement of an experimental finding; it is an interpretation of the experimental results on the basis of the author’s theoretical views. All that the experiment shows is that the deuteron is relatively stable; the rest is theory. In order to be entirely accurate all such statements as the one just quoted should be preceded by the same kind of an introduction which appears in the same textbook a few pages later: “An interpretation of these results has been based on the supposition that….” Statements about properties of the “nucleus” are all interpretations based on suppositions. The collapse of the nuclear theory will make it necessary to discard all of these current interpretations and go back to the actual observed facts for a fresh start. In the case cited, we will simply have to accept the fact that all we know is that the deuteron is relatively stable, in that it takes about 2.18 m.e.v. to break it up, and we will have to build a new theory from there. We cannot even justify calling the 2.18 m.e.v. a “binding energy,” since we are not sure that there are any separate parts to be “bound.”

It is to be expected that the theorists working in this field will take a very dim view of this conclusion that the products of their labors must be relegated to the wastebasket, but this issue must be faced, nevertheless. Even the highest degree of competence cannot derive the right answers from the wrong premises, and Gamow’s statement, previously quoted, that “not a single successful step has been made” in this area “in the last few decades” shows how completely unproductive the present line of approach has been. Now that it has been demonstrated that, whatever the structure of the atom may be, it is certainly not a combination of any of the observed sub-atomic particles, it is obvious that the severe limitation which has been placed on the thinking of the theoretical physicists by the presumed necessity of accommodating the structure of the atom to the properties of these sub-atomic particles has been the major obstacle in the way of forward progress. A new start without the burden of this fatal handicap is essential.