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.
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.
(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.
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).
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.
A deterministic quantum mechanics theory is presented in a series of papers starting with the present one. The proposed theory is shown to be consistent with the current mainstream statistical quantum theory as well as with classical physics. It produces solutions, which demonstrate that causality, physical reality, and determinism are restored and can explain in simple form concerns that are raised by results from the current mainstream statistical quantum theory. The meaning of particle- wave duality and complementarity, the possibility of a particle, like the electron, to cross through the nucleus as it does when the angular momentum of the electron is zero at the ground state of the hydrogen atom, the possibility of a point-size particle to have an “intrinsic spin”, the possibility of “quantum jumps” as the electron transitions instantaneously from one stable orbital to another without passing through the space in between the orbitals and does that at irregular time intervals, and the natural collapse of the wave function as part of the solution are some of the results that emerge from the proposed deterministic quantum mechanics theory. The phenomenon of entanglement is shown to be consistent with the proposed deterministic quantum mechanics theory. The Bohr-Schrödinger energy levels leading to the experimentally confirmed spectral lines, as well as the fine structure constant emerge directly from the solution of the equations governing theproposed deterministic quantum mechanics presented in Part II of these series of papers.