The preceding discussion has developed the point that we have no picture of the atom; we have only atom-models. All of these models are limited in scope and, for that reason, the more specific they attempt to be, the less validity they possess. The simple nuclear model, which attempts to set up a detailed account of the atomic structure, has been shown to be completely erroneous; the billiard-ball atom is in agreement with the facts in its own field, but this is a very restricted field; the Copenhagen version of the nuclear atom also agrees with the facts in certain mathematical areas, but it has withdrawn completely from any attempt to fit the non-mathematical aspects of the physical atom. None of these models can give us any actual information about the atom; whatever conclusions are drawn from the model are conclusions about the model.
In the light of these facts much of the current discussion about the impact of modern physics on philosophy is simply meaningless. An enormous crop of literature has grown up, all based on the assumption that a “revolution” has occurred in our understanding of basic physical processes, and that the nature of this revolution is such as to necessitate revision of many previously accepted concepts in philosophy—even in religion. But the newly developed items upon which this assumption is based are not facts from experimental sources; they are conclusions drawn from theory or interpretations of the experimental facts in the light of current theories. In other words, this new information to which such extraordinary importance has been attached is not information about the physical world; it is information about the incomplete and purely speculative models that have been set up to represent the physical realities. It follows that the “revolution” that has taken place has not been a change in the physicists’ understanding of nature, as we are led to believe, but in their thinking about nature. The profound alteration of the philosophical outlook now visualized by the philosophers is thus based on nothing more substantial than a shift in the direction of the physicists’ imaginations.
By far the majority of these revolutionary philosophical implications have been drawn from the various applications of the quantum ideas to the behavior of the atom, the Copenhagen atom-model in particular. Contrary to statements that are often made, these implications do not come from the quantum concept itself. The scientific world was already familiar with many physical entities which exist only in discrete units, matter being the most prominent, and all that Planck did in formulating his theory was to add radiant energy to this list. This came as quite a surprise, but it was certainly not the kind of a radical change in outlook which justifies reconstruction of basic philosophical ideas, and it was not so interpreted at the time. The revolutionary implications have not come from this experimentally verified concept of the existence of quanta of radiation, but from purely theoretical aspects of the atom-models invented in an effort to apply quantum ideas to events on the atomic level.
Of all these inventions, the favorite from the standpoint of philosophical speculation is Heisenberg’s Principle of Uncertainty, or Principle of Indeterminacy, as some prefer to call it. This principle asserts that because of the quantum considerations which enter into the structure of matter, there is an inherent and unavoidable uncertainty in our knowledge of specific physical situations, the magnitude of which is related to Planck’s constant h. If we attempt to be more accurate in our definition of some particular magnitude, the principle says, we can achieve this only at the expense of becoming less accurate in our definition of some conjugate magnitude. Thus an attempt to obtain exact information as to the momentum of a particle necessarily introduces an uncertainty into our knowledge of its location.
An even more important and far-reaching development is the abandonment of the causal concept that underlies the entire structure of science outside of the modern atomic theory: the principle that “from nothing nothing comes.” In the happy, carefree land of the quantum theories things just happen; there does not have to be any reason for the happening, as in the dull and prosaic realms of everyday life. Nor do these events need to be of a rational or reasonable character. As Bridgman explains, in the statement previously quoted, “The world is not intrinsically reasonable or understandable” in the “realm of the very little.” There appears to be some difficulty in formulating an acceptable “principle” which will express this assumption that the atomic events do not follow any fixed principles, but some authors talk about a Principle of Anomaly,89 the gist of which seems to be that strange things can be expected to happen in the atomic regions. The philosophical discussions that are concerned with the repudiation of causality are often rather vague as to the point of departure from which the speculations take off. Not infrequently the Principle of Uncertainty gets the credit (or the blame, depending on the point of view) for something that is more legitimately chargeable to the “anomaly” concept.
After formulating these “revolutionary” principles on the basis of purely theoretical considerations, the originators have naturally tried to find some physical evidence to support their conclusions, and it may be worth while to take a look at what they have dredged up. The argument that is advanced to support the Principle of Uncertainty is that events at the atomic level cannot be observed without radically changing them by the act of observation, since the agencies by means of which the observation is made, light for example, are composed of units (photons) which are of the same order of magnitude as the phenomena that are to be observed. Speaking specifically of electrons, Reichenbach asserts, “When you observe them, you have to disturb them; and therefore you do not know what they did before the observation.”90 Thus, say the theorists, there is an actual physical uncertainty corroborating the theoretical uncertainty represented by Heisenberg’s principle.
Now let us stack this against the work of the investigators who actually discovered the electron and determined its major properties. These experimenters worked primarily with scintillation screens, in which the impact of the electron causes a flash of light that is visible to the observer. Here we have exactly what the present-day theorists are talking about; the only way by which Thomson and his contemporaries were able to observe the electron involved a violent collision which completely altered its behavior. But did this prevent the investigators from obtaining the information they were seeking? Definitely not. They were able to establish the magnitudes of the major properties of the electron, and the nature of the response of the particle to various forces that might be applied to it, so that we can now proceed with confidence to the construction of devices such as the electron microscope, in which the entire utility of the device depends on our being able to define the behavior of the electrons with extreme precision.
The essential point here is that the scientific investigator does not attempt to determine the behavior of an individual electron, or an individual molecule, or an individual projectile, from observations of that electron, molecule, or projectile. What he does is to make observations of many members of each class, thousands of them if necessary, until he has accumulated sufficient information to reveal the characteristics of the behavior of the individual entities and to enable him to set up general principles and mathematical equations describing their behavior. When it then becomes desirable to know what will happen to some particular individual, a ballistic missile, for example, the path which this individual will follow is determined by calculation, not by observation. Whether or not the observations involved in the original study “disturb” the individuals being studied is entirely immaterial. In many instances the only methods that are available not only disturb, but destroy, the subject of observation, but this has no bearing on the validity of the results that are obtained.
These facts are well known to the scientists and philosophers who are advancing the “disturbance” argument in an effort to bolster the Uncertainty Principle, and it is rather odd that such an empty argument would be used so widely by competent people. Here again, however, we encounter the same situation that was the subject of comment earlier in this volume: the fact that those who are thoroughly convinced of the validity of a theory are inclined to accept at face value any arguments which support that theory, without making any real effort to determine whether these arguments are actually sound. Reichenbach, for example, follows his statement of the “disturbance” argument with a discussion of the question as to whether the desired information might be obtained in some way that did not involve a disturbance of the subject. He admits that this would be possible if the entities being investigated follow the usual physical laws, but he dismisses this possibility with the statement that “The analysis of quantum mechanics, however, has given a negative answer….” In essence he is telling us that the assertion of quantum theory with respect to uncertainty is verified by the fact that quantum theory itself says that any alternative is impossible. Here is a plain case of circular reasoning that would not be given the slightest consideration if it were presented as an argument in anything other than a case that had already been pre-judged before the evidence was submitted.
Ernest Nagel discusses this “disturbance” argument at considerable length in his book The Structure of Science and concludes that it is “neither entirely clear nor persuasive.” He emphasizes particularly that the argument rests primarily on the contention that the disturbances which the electrons or other entities under observation are alleged to suffer in the act of observation are “uncontrollable” and “unpredictable,” but that these uncontrollable and unpredictable aspects are not factual items derived from experimental evidence; they are “part of the consequences drawn from the [uncertainty] relations”:91 another instance of the circular reasoning that is far too prevalent in the atomic domain.
If there actually were any electrons in the atomic structure, their properties and behavior characteristics could no doubt be determined in the same way that the properties of electrons or other particles are determined wherever they do exist. But since the atomic electron is non-existent, it is no wonder that the modern physicists have been forced to conclude that it “is not a material particle in space and time but, in a way, only a symbol…”,17 as Heisenberg says. We could very appropriately rewrite the Principle of Uncertainty in this manner: The properties of non-existent particles cannot be determined with precision.
The stock argument in support of the contention that causal relationships do not apply to individual events on the atomic level is radioactivity. It is pointed out that although we can predict accurately what proportion of the atoms of a radioactive substance will disintegrate during any particular period of time, we have no knowledge whatever of the fate of any particular atom. From this it is argued that there are no rational considerations governing the behavior of the individual atom; that the orderly and predictable behavior of the aggregate is simply a statistical effect.
The validity of this argument depends entirely on an assumption which is necessary to complete the chain of reasoning: the assumption that since we do not know the reason for the disintegration now, we will never know it; that is, there is no reason. Here is a manifestation of the egotism that is characteristic of the human race; a trait that science tries to subdue, with considerably less than complete success. “We cannot say of any grain [of plutonium] whether it will fall into the decayed or the surviving half,” says Bronowski. “There are no physical laws to tell us—and there cannot be.”92 These last four words tell the story—“and there cannot be.” From the vantage point of our minuscule knowledge of the physical world-a knowledge which Newton compared to a few pebbles on the shore of the great ocean of truth—the human race, at least a substantial part of it, feels competent to lay down dicta for all time to come.
Such statements are simply nonsense. As matters now stand we know essentially nothing about the radioactive disintegration process, other than that it happens. We do not know what the structure of the atom was to begin with, what changes take place in the process, or what initiated the radioactive event in the first place. Any claim to omniscience on the subject of what can be or cannot be is ridiculous.
On the strength of these curious principles, the Principle of Uncertainty and the somewhat nebulous Principle of Anomaly, the philosophers have had a field day. After arguments have gone on for centuries in some philosophical areas, it now appears from these “discoveries” in the field of physics that nature has taken a hand in the game and has laid down some rules. To be sure, the exact meaning of these rules is still uncertain and controversial, but irrespective of details, if there is a limit to the precision with which the properties of physical entities can be specified, and if phenomena at the atomic level are determined by statistical rather than causal considerations, these are matters which are clearly of great significance to philosophy.
But all this is based on the assumption that nature is speaking, whereas the truth is that the speakers are Bohr, Heisenberg, and their associates. Uncertainty is not a property of the physical atom or the physical electron; it is a property of the Copenhagen atom-model. Heisenberg is uncertain, but this is no proof, or even a good indication, that nature is uncertain. Likewise we have no evidence that physical events involving atomic or sub-atomic entities are determined solely by statistical laws; this again is a property of the atom-model, not of the atom. The philosophers, in spite of their rigorous training in the art of avoiding logical pitfalls, have fallen into a trap; they have simply been talked into accepting an atom-model, a very incomplete atom-model, as a true picture of the atom.
This is all the more remarkable in that these philosophers have come very near a recognition of the true situation. Ernest Nagel, for example, tells us that “a model may be a potential intellectual trap as well as an invaluable intellectual tool.”93 Here is a statement that is so very much to the point that one might easily get the impression that Nagel had a full realization of the kind of a package that the physicists were handing to him, particularly since, as pointed out previously, he has noted that some physicists are inclined to place quantum theory even lower in the scale than a model. But when we follow the development of his line of thought we find that he is referring to something altogether different. In this present work the terms “theory” and “atom-model” are used interchangeably, following the general practice in the field of physics. Nagel, however, draws a distinction between the theory itself and any kind of a conceptual model that might be used as an aid in visualizing-the theory, and his concern is that such a conceptual model might not be a true representation of the theory, and that improper conclusions might result from confusing the two. Whatever merit this point may have, it is totally irrelevant to the present issue. All that has been said about atom-models applies equally as forcibly to the theory and to any conceptual model that might be devised to represent the theory. No theory or model of the atom yet proposed even comes close to qualifying as a picture of the atom, and consequently no statement about such a theory or model is a statement about the physical atom. Whatever its authors may claim, it is a statement about the theory or about the model, and nothing more.
This seems to be the stumbling block that has tripped up all those who have examined the situation from the philosophical standpoint. It has been generally recognized that the Uncertainty Principle and associated concepts are purely creatures of the quantum theory. Ernst Cassirer, for instance, admits that “… the limitation… expressed in the uncertainty relations is only valid relative to the quantum principle and to the general formalism of quantum mechanics.”94 This, of course, carries with it the realization that if the quantum theory topples, all of the philosophical implications collapse with it. Cassirer goes on to say that if the advance of empirical knowledge ultimately requires replacement of the quantum theory by “some other basic assumption, the question of observability would then also appear in a different light.”
What he is telling us in this statement is that if, at some future time, it develops that the quantum theory is not a true representation of the physical facts, then the conclusions that have been drawn from uncertainty and other features of the quantum concepts must be discarded. But Cassirer and his colleagues apparently fail to see that this is just exactly the situation which exists now. The atom has many different properties, each of which has both physical and mathematical aspects: qualitative and quantitative aspects, as we may say. This we know on the basis of the kind of empirical evidence that Cassirer is talking about—evidence from observation and experiment. But quantum theory makes no pretense of giving us a true representation of the physical atom that has these characteristics, the atom that is studied in the laboratories; it specifically disclaims any resemblance between its atom and any physical object. The atom of quantum theory is “a solution of a wave equation and nothing more.” Regardless of how successful or unsuccessful the theory may have been in the limited area which it attempts to cover, it is not, and never has been, a picture of the physical atom; it is a model which, like the billiard-ball atom, admittedly successful in its own field, has been devised to represent one particular aspect of the physical atom.
Thus we do not need to wait to see whether future experimental discoveries will invalidate the quantum theory. Whether valid or not valid in its limited field, this theory is simply an atom-model and any conclusions that are drawn from it are conclusions about this particular atom-model, not about the atom. Max Planck, who originated the quantum concept, makes this very clear in his “Scientific Autobiography.”95 He emphasizes the same point brought out in the foregoing discussion; that is, we are dealing with two entirely different things. One is the physical atom, which in conjunction with other similar entities Planck calls the “sense world.” The other is the atom-model of the quantum theory, for which Planck uses the term “world picture.” The world picture of quantum mechanics (the atom-model), he says, is a “provisional and alterable creation of the human power of imagination,” and “even a cursory glance shows how far (it) has shifted from the sense world….” He goes on to point out that the conclusions with respect to the need for abandoning causality in the microscopic realm are “founded on a confusion of the world picture with the sense world: ” a confusion, we may say, in which the voice from Copenhagen is mistaken for the voice of nature.
The inferences with respect to free will and other philosophical subjects, which have been drawn from the Uncertainty Principle and other aspects of the Copenhagen atom-model, are not resting on the revelations of nature, as the philosophers are assuming; they are resting upon products of the imagination of Bohr and his associates: exactly the same kind of assumptions and postulates that constitute the starting point for most philosophical speculations. All that the philosophers have actually accomplished in this effort is to substitute the imaginations of the physicists for their own.
As a final comment on the philosophic aspect of atomic theory, it may be well to point out that the whole mass of speculation and controversy over the relation of modern physical theory to the problem of free will is essentially meaningless, no matter how much or how little validity the modern theories may possess. Regardless of whether the course of physical events is governed by a rigid determinism, or is entirely a result of chance processes, or comes about through some combination of the two, it still follows that these physical processes, whatever they are, produce a specific result in each case. This is true irrespective of the extent to which chance may enter into the selection of the particular result. Chance does not produce an indeterminate result; when a chance event does occur, it is just as specific and definite as if it had been produced by a fully determinate process. Free will, if any such thing exists, must be able to overrule this event that would otherwise take place, and substitute some other result which is physically possible. The essence of free will is the option. It must be possible either to allow the normal result to take place or, alternatively, to dictate a course of events which would not result from the normal physical processes, whatever these normal processes may be, whether they are deterministic or indeterministic.
The question of determinism is therefore wholly irrelevant so far as the problem of free will is concerned. It makes no difference how much or how little chance enters into the physical processes that produce specific events in the physical universe; as long as the events are dictated by these processes, there is no free will. Free will exists only if the physical processes can be overruled at the option of that will. The existence of an option to accept or reject the decision of nature is incompatible with Laplacian determinism, to be sure, but it is equally incompatible with chance, and no amount of sophistry or circumlocution can evade this simple and obvious fact. Once again, let us call upon Erwin Schrödinger for a summation:
If these statistics (the statistics which, according to present-day theory, determine the behavior of the atom) are interfered with by any agent, this agent violates the laws of quantum mechanics just as objectionably as if it interfered—in pre-quantum physics—with a strictly causal mechanical law… The net result is that quantum physics has nothing to do with the freewill problem. If there is such a problem, it is not furthered a whit by the latest developments in physics.96