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Canadian Journal of Research

THE FOUNDATIONS AND PHILOSOPHICAL IMPLICATIONS OF WAVE MECHANICS

Seyuan Shu

Published Mar 1, 1947• 0 citations
Publisher

Abstract

This paper attempts to show:(a) The nature of the basic assumptions made either explicitly or implicitly by L. de Broglie in arriving at the fundamental formula, [Formula: see text], of wave mechanics, and that at least some of these assumptions are open to criticism.(b) That it is a little too hasty to regard as demonstrated the non-localization of photons or electrons in motion and the lack of determinism with respect to them.(c) That the presuppositions which lead to the 'relations of incertitude' involve highly arbitrary elements and these 'relations' are read into or arbitrarily imposed upon the physical world rather than really found to be in it.(d) That it is an unwarranted claim that the new mechanics can contribute to the solution of the age-long philosophical problem of free will.(e) That it is possible to render the foundations of wave mechanics logically independent of the theory of relativity.

DOI
10.1139/cjr47a-012

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This paper attempts to show:(a) The nature of the basic assumptions made either explicitly or implicitly by L. de Broglie in arriving at the fundamental formula, [Formula: see text], of wave mechanics, and that at least some of these assumptions are open to criticism.(b) That it is a little too hasty to regard as demonstrated the non-localization of photons or electrons in motion and the lack of determinism with respect to them.(c) That the presuppositions which lead to the 'relations of incertitude' involve highly arbitrary elements and these 'relations' are read into or arbitrarily imposed upon the physical world rather than really found to be in it.(d) That it is an unwarranted claim that the new mechanics can contribute to the solution of the age-long philosophical problem of free will.(e) That it is possible to render the foundations of wave mechanics logically independent of the theory of relativity.
There are several important philosophical problems to which quantum mechanics is often said to have made significant contributions: Determinism: quantum theory has been taken to refute determinism;Free Will: in turn, this is thought to open the door to free will;The mind-body problem: relatedly, it is sometimes said to shed light on consciousness;Idealism: more radically, quantum theory is assumed to have refuted realism and to have placed the observer at the centre of the world;Reductionism: even granting realism, it has been claimed that quantum theory undermines reductionism.Our main thesis in this paper is that none of this is either necessary or desirable. By adopting the de Broglie–Bohm theory (or Bohmian mechanics), one can straightforwardly account for quantum phenomena without endorsing any of these claims.
This work is an attempt to recreate Quantum Mechanics conceptual foundations. First, we claim that the wave function in quantum mechanics is a definition of random discontinuous particle motion, and that the wave function's modulus square gives the particle probability density at some space locations. First, we demonstrate that the linear, non-relativistic evolution of an isolated system's wave function obeys the free Schr ̈odinger equation due to the spacetime translation invariance and relativistic invariance requirements. Thirdly, we argue that the discontinuous random motion of the particles will lead to a stochastic, nonlinear collapse of the wave function. A discrete model of the energy-conserved collapse of the wave function is proposed and demonstrated to be consistent with current experiments and our macroscopic experience. We also offer a crucial review of the de Broglie-Bohm theory, the explanation of several worlds and other theories of dynamic collapse, and briefly discuss the question of the incompatibility between quantum mechanics and particular relativity.
On the Creation of a Deeper Insight Into What May Underlie Quantum Physical Law.- The Measurement Theory of Everett and de Broglie's Pilot Wave.- Quantum Mechanics and Determinism.- On Hidden Variables and Quantum Mechanical Probabilities.- Experimental Status of Hidden Variable Theories.- Pre-Quantum Mechanics Introduction to Models with Hidden Variables.- On the Foundations of Quantum Physics.- Quantum Logic: Is It Necessarily Orthocomplemented ?.- The Stochastic Interpretation of Quantum Mechanics and the Theory of Measurement.- Statistical Ensembles in Quantum Mechanics.- Conditional Probability in Wave Mechanics.- Classical Electrodynamics in Terms of a Direct Interparticle Hamiltonian.- Theory of One-Dimensional Relativistic Elastic Continuum for the Model of Particles and Resonances.- On the Photon Theory of L. de Broglie.- From the Photon to the Graviton and to a General Theory of Corpuscular Waves.- Possible Implications of de Broglie's Wave-Mechanical Theory of Photon Behaviour.- Index of Names.
When investigating various interpretations of quantum mechanics one notices that each interpretation contains an element which escapes a complete and full description. This element is always associated with the stochasticity of the individual event in the quantum measurement process. It appears that the implications of this limit to any description of the world has not been sufficiently appreciated with notable exceptions of, for example, Heisenberg, Pauli and Wheeler. If we assume that a deeper foundation of quantum mechanics is possible, the question arises which features such a philosophical foundation might have. It is suggested that the objective randomness of the individual quantum event is a necessity of a description of the world in view of the significant influence the observer in quantum mechanics has. It is also suggested that the austerity of the Copenhagen interpretation should serve as a guiding principle in a search for deeper understanding. In recent years, a significant increase of interest in the foundations of quantum mechanics can be observed. This increase is certainly related to the immense progress made during the last two decades in experiments with individual quantum systems. This technological progress has made it possible to really perform more and more of the famous gedanken experiments which were so important in the early days of the theory. Not only did these experiments confirm the theory in every detail, they also opened up avenues for new experimental directions which might even lead some day to new technology. While such applications are certainly still far away, areas like quantum cryptography[1], quantum computation[2] and interaction-free measurement[3], just to name a few examples, certainly deserve the attention they receive. All this activity has also drawn more attention to the problems of understanding and interpreting quantum mechanics. It seems that there, a definitive consensus has not yet been reached. As witnesses quote authorities like Feynman as saying[4]: I think can safely say that nobody today understands quantum mechanics, whereby he apparently included himself, or like Roger Penrose[5], who describes his opinion remarking that while the theory agrees incredibly well with experiment and while it is of profound mathematical beauty, it makes absolutely no sense. Why did even physicists who have contributed so significantly to quantum theory Feynman was even rewarded the Nobel Prize for one of its mathematical formulations choose such emphatic and strong formulations? Why is it that the average physicist hears very little about such problems during his/her education? Why is the comprehension of the theory very often focused on formalism while questions that probe for deeper meaning are usually not tackled? To take a closer look at the situation, let us turn to a brief analysis of the interpretation of quantum mechanics. We note that there are at least two levels of interpreting a formalism, a physical theory. The first, basic, level supplies the rules that determine which element of the formalism corresponds to which measurable quantity or to which observable fact in a concrete experimental situation. Theses rules are a large, mostly not explicated but only implicit, set of instructions. These instructions concern the manner of working with the statements of the theory in order to obtain predictions for future experiments or events, and they concern the instructions on how to proceed in experiment in order to demonstrate or test a theoretical
The Copenhagen interpretation has been the subject of much criticism, notably by De Broglie and Einstein, because it contradicts the principles of causality and realism. The aim of this essay is to study the wave mechanics as an alternative to traditional quantum mechanics, in the continuity of the ideas of Louis de Broglie: the pilot wave theory of De Broglie (where each particle is associated with a wave which guides it), De Broglie-Bohm theory, stochastic electrodynamics (where the stochastic character of particles is caused by the energy field of the fluctuating vacuum), and the analogies between quantum mechanics and hydrodynamics.
The object of this paper is to give an account of the fundamental principles of wave mechanics in a manner which shall make clear the physical significance of all the quantities and processes involved. The principles are illustrated by discussions of the propagation of free electric waves in uniform electromagnetic fields and of bound electric waves in the hydrogen atom. The paper concludes with relativistic wave mechanics (prior to the work of Dirac and Darwin) and a short account of the Compton effect.