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.
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.
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.
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).
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.
In 1927 at the fifth Solvay Council, that reunited all the aristocracy of theoretical physics, Einstein, regarding with solicitude the new-born “quantum mechanics” of Louis de Broglie, Schrödinger, Heisenberg and Dirac, discerned with his usual sagacity an indelible mark that was destined to become, with time, a subject of passionate discussion among those whose vocation is to adulate this enigmatic and capricious personality. In 1926 Born had given the prophetic stroke to the portrait. Turning to probability as to the official factotum of the reconciliation of the continuous and the discontinuous-here, the associated wave and particle-he transmuted the waves of de Broglie and Schr6dinger into an undulatory calculus o f probabilities, deducing, from a surprising principle, consequences that were even more surprising but always verified through experiment. Parting from the idea that the intensity of the wave is the probability of the detection of the particle at a given point and time, Born replaced the classic principle of addition of partial probabilities with his “principle of the addition of partial amplitudes” that are, as in classical optics, represented by “complex” dimensions, with one real part and one imaginary part. In general, the square of the module of the sum of amplitudes will be the probability. This expression contains, of course, the terms “square” and “rectangular.” The first, if they were alone, would give the former law; as for the second, they express the existence of phenomena of interference that are at the origin of the thousand and one well verified paradoxes of the “new mechanics “-the one thousand and first being the one under consideration here.
Introduction Although the mathematical structure of quantum mechanics was understood within a few years after it was invented, numerous quantum paradoxes still disturb ‘simple-minded’ physicists. Most of them, as ‘naïve realists’, would probably never take Bohr's own over-philosophical and over-complicated treatment of these paradoxes seriously if they realized the philosophical consequences of the Copenhagen interpretation. To make my meaning clearer, let me quote Bohr's answer to Professor Hoffding's question regarding the double-slit experiment [1]. Bohr was asked: ‘What can the electron be said to be in its travel from the point of entry to the point of detection?’ And he replied: ‘ To be ? To be ? What does it mean to be ?’ However, if one questions the existence of microscopic constituents of macroscopic bodies, then the next logical step would be to question the existence of the macroscopic bodies and even ourselves. Needless to say, very few (if any) of us, when making experiments or analyzing their results, address the question of what it means ‘to be’ every time. Even in the context of elementary particles, probably nobody doubts that the particles exist and somehow travel from the point of entry to the point of detection. Moreover, within the accuracy allowed by the uncertainty relation, these particles can be localized and described just as well as macroscopic ‘classical’ objects.
The Copenhagen Interpretation of quantum mechanics has become the standard way of explaining the physical philosophical meaning of the mathematics of microscopic behavior. It developed from the thought of people who attended the Institute for Theoretical Physics of the University of Copenhagen during the 40 years that Niels Bohr directed it, from 1920 to 1962. Bohr took a large part in developing the Copenhagen Interpretation, he didn't escape all controversy over it (although the quote above is a bit of an exaggeration). Bohr did die before the experimental theoretical developments that have transposed the debate over the appropriateness adequacy of the Copenhagen Interpretation into a new key, he may well have been lucky to have escaped when he did. There is no authoritative codification of CI [the Copenhagen Interpretation], write T Gornitz C. E von Weizsacker of the Max Planck Institute in Starnberg, West Germany in' their formal presentation to the recent Loyola Conference on Mathematical Interpretational Problems in Relativistic Quantum Theory, and under the conditions of its origin there probably could not be one.... All prominent authors of the time who wrote on these questions, like Bohr, [Werner] Heisenberg, [Wolfgang] Pauli, J[ohn] v[on] Neumann on one side, [Albert] Einstein [Erwin] Schrodinger on the other, fell, so we feel, into some stammering when they tried to express their own positions. Nevertheless there is what might be called a Copenhagen attitude. It concentrates on observable phenomena, makes statistics probability central to its understanding, considers quantum mechanics primarily a theory of knowledge or information becomes a kind of physica negativa (analogous to a theologia negativa) in trying not to say too much about things that can't be seen or felt. For example, it doesn't much care whether the orbits of electrons in atoms are real or not and, in fact, tends to regard them as unreal. It appears in most textbooks as the standard way of looking at things.