The fact is that, beside the two quantum rules for energy and angular momentum, there is a third analogous rule for the linear momentum, established by W. Duane in 1923. Though this rule is generally accepted, there is no trace of recognition in the literature that it yields a consistent unitary particle explanation of all those phenomena of diffraction and coherence, e.g., of the two-slit experiment, which allegedly can be accounted for only by the fiction of a dual nature of matter, with transmutation of particles into waves and back into particles again. The usual method of solving this dilemma has admittedly been that of “refining the language of physics,” beginning with replacing the physical idea of a forth and back transformation by the term “dual manifestation,” thereby shunning any “real” constitution of matter, which then requires a specially adjusted philosophy of knowledge. In contrast, the quantum rule for the linear momentum solves the apparent contradictions in a physical manner without alternating manifestations. It introduces a great simplification which should also influence the method of teaching the theory. The purpose of the present article is to give due credit to the American pioneer of quantum mechanics, W. Duane, whose contribution to solving the duality paradox is a shining example of the scientific method, in contrast to the purely semantic approach in vogue for more than a generation.
The fact is that, beside the two quantum rules for energy and angular momentum, there is a third analogous rule for the linear momentum, established by W. Duane in 1923. Though this rule is generally accepted, there is no trace of recognition in the literature that it yields a consistent unitary particle explanation of all those phenomena of diffraction and coherence, e.g., of the two-slit experiment, which allegedly can be accounted for only by the fiction of a dual nature of matter, with transmutation of particles into waves and back into particles again. The usual method of solving this dilemma has admittedly been that of “refining the language of physics,” beginning with replacing the physical idea of a forth and back transformation by the term “dual manifestation,” thereby shunning any “real” constitution of matter, which then requires a specially adjusted philosophy of knowledge. In contrast, the quantum rule for the linear momentum solves the apparent contradictions in a physical manner without alternating manifestations. It introduces a great simplification which should also influence the method of teaching the theory. The purpose of the present article is to give due credit to the American pioneer of quantum mechanics, W. Duane, whose contribution to solving the duality paradox is a shining example of the scientific method, in contrast to the purely semantic approach in vogue for more than a generation.
Niels Bohr has often pointed out that already the simplest quantum rule, ΔE = hν, is irrational insofar as ΔE stands for a timeless energy jump, whereas a frequency ν is defined only over a long time span. However, when this irrational relation is accepted as a mainstay of the quantum theory, one cannot reject a corresponding irrationality for momentum jumps Δp connected with periodicities in space, the less so as it yields a unitary mechanical explanation of all wavelike-looking phenomena of matter, in particular those of the diffraction of electrons, without resorting to any wave interference in space. (This has nothing to do with the complex–imaginary wave function ψ, which has a purely statistical significance.) We therefore propose to regard matter particles as real physical entities as always, in contrast to the matter waves with λ = h/p as a suggestive yet expendable fiction, permitting a return from dualism to unity, a simplification of the customary interpretation of standard quantum effects, also suggesting a long overdue reform in the teaching of the elements of quantum mechanics. Editor’s note: This is the fourth and last in a series of articles begun ten years ago in this Journal. Earlier parts in the series may be found in American Journal of Physics 33, 123 (1965); 34, 1160 (1966); and 37, 541 (1969).
(1) The idea that diffraction of matter particles can only be understood in terms of a temporary wave transformation or ‘double manifestation’ is an uneconomical ad hoc hypothesis, shattered already in 1923 by the unitary quantum theory of diffraction of Duane which in 1926 became part of the quantum mechanics, with a statistical interpretation of wave-like appearances. (2) Bohr's re-interpretation of Heisenberg's uncertainty of prediction as an indeterminacy of existence rests on an illegitimate literal translation of a wave result into particle language which is at variance with experience as well as with the statistical interpretation. (3) The fact that one can transform the simple and unitary particle mechanics into a complicated wavelike form is only a weak substitute for genuine dualism — as if one would see dualism in the transformability from the geo- to the heliocentric reference system. (4) The strongest argument against a symmetry of the particle and the wave theory of matter is the explainability of the former in terms of simple postulates of invariance, leaving the wave formalism as a purely ad hoc construction.
Electron diffraction was shown in Part I to be due to the quantum-mechanical activity of the diffractor rather than to a fictional wave-picture manifestation of the diffracted particles. Part II aims at eliminating further fictional elements, most of them based on inconsistency of interpretation. The controversy between the extremist views of Schrödinger and Born, either frequency resonance or quantum jumps, is removed by showing that consistency compels one to admit both to occur simultaneously. Attempts at saving duality and other fictions are criticized, such as the contention that (1) “duality is a fact” seen in the contrast of obvious particle effects and not so obvious particle effects, (2) that particles are material and waves are expectations by observing subjects, (3) that statistical law means the end of the sharp separation between subject and object, (4) that Heisenberg's empirical rule for the uncertainty of prediction means indeterminacy of existence. It is pointed out that quantum mechanics can be derived as a necessary consequence of general nonquantal postulates, known from deterministic mechanics, but applied now to the construction of a probabilistic schema of connection between events.
This Anti-Copenhagen interpretation [compare with N. R. Hanson, Am. J. Phys. 27, 1 (1959)] submits that the doctrine of an inherent double nature of matter (and of light) is a most uneconomical hypothesis which would never have been proposed (except for heuristic purposes) had it not been for an oversight of the mechanical particle theory of diffraction by Duane (1923), later incorporated into the quantum mechanics of 1926 in Born's unitary statistical interpretation of wavelike phenomena. Bohr's indeterminacy view comes from a verbal translation of a legitimate wave feature; it is contrasted to the uncertainty of prediction of exact results. The latter is supported by the experiment, the former is not, so that various “epistemological lessons” drawn from Bohr's view stand on brittle ground, which can hardly be reinforced by pointing to the transformation from the first to the second quantization, i.e., from one to another form of a complete and unitary theory. The simple quantum rules of the particle theory (first quantization) can be reduced to general postulates of symmetry and invariance.
The simplest but deepest questions of the philosophy of quantum mechanics are these: Are quantum systems waves, or are they particles? Are they both or are they neither? When light bounces an electron out of the surface of an alkali metal it behaves like a particle. Light carries momentum but also a punch. Just as there is no such thing as half a punch, so there is no such thing as half a quantum of light. On the other hand, the shadow formed on a screen by an object has soft edges, edges which get softer as the object is moved away from the screen. Light exhibits the phenomena of diffraction and interference and so is wavelike. This dual behaviour of light, and indeed of matter itself, is called wave-particle duality. The wave nature of a quantum system is reflected in wave mechanics which assigns a wave-function to the system. But the dual nature of light was noticed before Schrodinger developed the wave-mechanical formalism in 1926. In fact, it goes back at least as far as Einsteins explanation of the photoelectric effect in 1905. Wave-particle duality is not something that arises within the quantum mechanical formalism. It is something which is expressed within it, and is something which is best discussed in terms of the paradoxes that quantum experiments force upon physics. In fact, the simplest and most immediately disturbing of the quantummechanical paradoxes arise out of wave-particle duality. We take the two-slit experiment and the delayed-choice experiment as examples.
The difficulties of the old quantum theory were largely dispelled by the development of quantum mechanics in the 1920s. First Heisenberg (1925) developed the rather abstract matrix mechanics and soon after Schro¨dinger (1926; see also Eckart, 1926) developed the physically more appealing wave mechanics. Subsequently he showed them to be mathematically equivalent. The physicists were greatly relieved; now they had once again a mathematical formalism that enabled the results of experiments to be calculated. It was possible to move forward. It is certainly a very elegant and indeed beautiful formalism, and does enable the results of many physical measurements to be calculated with great accuracy. It is used daily by atomic and nuclear physicists; there is no other way to make calculations. From the earliest days there has been intense debate about the interpretation of quantum mechanics, and it shows no signs of being settled; if anything it is becoming more intense over the years. As Penrose has remarked, no one understands quantum mechanics. Feynman (1967; see also Sykes, 1994) also admitted that ‘nobody understands quantum mechanics’, and Einstein once remarked: ‘I have thought a hundred times as much about the quantum problems as I have about general relativity theory’ (Pais, 1994, p. 57). It should therefore be evident that the most that can be done here is to try to show where the real difficulties lie, and how the failure to recognize that quantum mechanics is an essentially statistical theory has led to a series of confusing quantum paradoxes. It is just these paradoxes that have often been used to support theological speculations. It is useful to ask what ‘understanding quantum mechanics’ actually means. Certainly it means being able to calculate the results of many measurements. The same applies to Newton’s theory of gravitation, which we understand in the sense that we can use it as a basis of calculation, although we do not really understand the gravitational force itself. Very often, especially in modern physics, the mathematical formalism does not give us the sort of intuitive physical feeling for what is going on that we often obtain from classical mechanics. Perhaps we can never achieve more than this for quantum mechanics. In classical mechanics we can assume that a property that is measured objectively exists prior to the interaction of the measuring apparatus with the observed system. Quantum mechanics, however, ‘is incompatible with the proposition that measurement discovers some unknown but pre-existing property’ (Peres, 1997, p. 14). There is an important distinction between mysteries and absurdities. We may be forced to live with mysteries, but there is no reason why we should put up with absurdities such as the wave-particle duality, tunnelling through potential barriers, acausal events and the collapse of the wave function. These are the quantum paradoxes that will be discussed later on. They arise within the Copenhagen interpretation of quantum mechanics and are solved by other interpretations. These alternative interpretations enable us to make conjectures about what is going on, even though we cannot understand it in detail. This is acceptable and a stimulus to further research. It is certainly difficult enough to understand quantum mechanics, but there is no need to try to visualize logical absurdities in the effort to do so. Quantum mechanics is a mathematical formalism that makes it possible to calculate the results of some experiments. Anything more than this, such as questions about the interpretation of what is measured and whether it tells us what is actually going on in the system being studied, belongs to philosophy. Thus we are concerned here with what is essentially a philosophical debate; if it were just a matter of physics the debate would have been settled long ago. One of the difficulties is that it invokes the results of experiments and uses the language of quantum mechanics. Inevitably this language uses philosophical terms and then it is easy to give the impression that the philosophical propositions are in some way entailed by the physical results. These in turn can influence theological thinking. In order to be quite clear which arguments are justified and which are not, it is essential to separate the three levels of discourse: physical, philosophical and theological. Our task is to relate these together, and this immediately raises the traditional problems of the philosophy of science, including the relation of experiment to theory, and of theory to explanation. We begin by discussing experiments, distinguishing between those that are real and those that are imaginary.