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).
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).
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.
Toward the end of the nineteenth century, it became clear that some experiments cannot be explained on the basis of known physics, now referred to as classical physics. In 1900, Max Planck was able to correctly describe the distribution of blackbody radiation energy as a function of wavelength λ or frequency ν = c/λ. He had to accept the existence of energy packets (quanta) with energy E = hν. A few years later, Albert Einstein found that this unexpected relation between energy and frequency is also necessary in order to understand photoemission from metallic surfaces. A decade later, Niels Bohr arrived at the correct equation for the electronic spectrum of the hydrogen atom by applying “quantum conditions” on the motion of the electron around the nucleus and the Planck’s relation E = hν on the energy difference between the energy levels (1916). A decade later, Heisenberg, Born, and Jordan introduced “quantum mechanics” and de Broglie and Schrödinger (1925-1926) introduced “wave mechanics.”
Part III of this series [A. Landé, Amer. J. Phys. 33, 123 (1965), and 34, 160 (1966), quoted as Parts I and II] continues the critique of the customary interpretation of quantum mechanics. It is directed against the idea that electrons, in opposition to the Born statistical particle interpretation of the wave function, are “wavicles.” Serious conceptual and elementary mathematical defects in Bohr's famous “Discussion with Einstein” are pointed out. The doctrine that position q and momentum p of a particle are blurred over an uncertainty range because both allegedly cannot be measured simultaneously, that q and p do not exist simultaneously, is due to a confusion of analogy with identity of qualities. In its second part, the paper offers a nonquantal derivation of the probability interference law as a necessity under the postulate that the general interdependence between probabilities is to become the ordinary probability addition law in the average. The wave picture of matter violates the postulate of relativity.
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.
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.
he study of the behavior of subatomic particles in this century is supposed to have established at least three exceedingly curious facts about the physical world. First, pure chance governs the innermost workings of nature. Second, although material objects always occupy space, situations exist in which they occupy no particular region of space. Third and perhaps most surprising, the fundamental laws that govern the behaviors of OordinaryO physical objects somehow radically fail to apply to objects that happen to be functioning as Omeasuring instrumentsO or Oobservers.O That at any rate is what the founders of quantum mechanics decided; that is what has since become the more or less oUcial dogma of theoretical physics; and that is what it says, to this day, in all the standard textbooks on that subject. But it is now emerging that those conclusions were settled on somewhat too quickly. As a matter of fact, a radically diÝerent, fully worked-out theory exists that accounts for all known behaviors of subatomic particles. In this theory, chance plays no role at all, and every material object invariably does occupy some particular region of space. Moreover, this theory takes the form of a single set of basic physical laws that apply in exactly the same way to every physical object that exists. That theory is principally the work of the late David J. Bohm of Birkbeck College, London. Although his formulation has existed in the scientiÞc literature for more than 40 years, it has until quite recently been mostly ignored. Throughout that period, the thinking about such matters has been dominated by the standard dogma, usually referred to as the Copenhagen interpretation of quantum mechanics because it can more or less be traced back to the Danish physicist Niels Bohr and his circle. I will begin this article with an outline of the main arguments for the standard dogma. I will then indicate briesy how BohmOs theory manages to get around some of those arguments. Finally, I will say a little about how and where BohmOs theory Þts into contemporary speculation about the foundations of quantum mechanics.