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In a recent paper P. Ghose [1] has proposed an experiment addressed to compare de Broglie -Bohm theory and standard quantum mechanics, based on different predictions for coincidence counts in a double slit experiment.

Like any other physical theory, quantum mechanics has two distinct but interrelated components: a mathematical formalism and a physical interpretation. By formalism we mean an algorithmic structure consisting of equations and calculational recipes. However to compare computed results with empirical observations, we need interpretational inputs to connect the formal language of a theory to actual experimental results. An interpretation provides physical content to a theory in terms of some key concepts; e.g., the concept of force as a cause for acceleration is crucial in understanding the basic equation of motion in Newtonian mechanics. In this book we are mainly concerned with interpretational issues in nonrelativistic quantum mechanics. Although we assume the reader to be sufficiently familiar with the basic mathematical technicalities of the subject, we begin by briefly recapitulating some of the key general features of the standard formalism.

This paper attempts to clarify the origin of quantization defined by the Planck’s constant ħ. By introducing the concept of inhomogeneous standing waves, one can derive the Planck-Einstein relation E = ħω and the de Broglie relation p = ħk and explain why quantization can be interpreted as a wave effect.

The possible experiments which lead to conflicting predictions of quantum mechanics and the de Broglie pilot wave theory are presented and discussed. Recently, one of these has been performed by Wang, Zou, and Mandel, and the results are well in agreement with quantum mechanical prediction. The criticisms of this experimental set-up are discussed. In particular, Selleri’s model, based on enhanced photon detection, is analyzed. A proposal of a new experiment to discriminate between the Selleri model and quantun mechanics is presented.

We show that the particle motion in Bohmian mechanics as the solution of an ordinary differential equation exists globally, i.e., the singularities of the velocity field and infinity will not be reached in finite time for typical initial configurations and a large class of potentials, including the physically most relevant potential of N-particle Coulomb interaction with arbitrary charges and masses. The analysis is based on the probabilistic significance of the quantum flux. We point to the connection between the global existence of Bohmian mechanics and the self-adjointness of the Schrodinger Hamiltonian.

Louis de Broglie’s wave-particle duality hypothesis, published in his famous paper(1) in 1924, was verified for electrons only 3 years later by Davisson and Germer(2) and Thomson.(3) No interferometer was available at that time to measure the very short electron wavelengths predicted by the de Broglie relation. The idea underlying their experiment to prove the hypothesis was that if electrons are in some sense represented by waves, they should undergo diffraction from crystalline lattices in a way almost identical to X rays. Crystalline lattices of appropriate periodicity were at hand and therefore a diffraction experiment provided the first evidence of wave-particle duality.

We show that it is possible to give a causal, continuous and deterministic description of the motion of an individual system undergoing a transition between states using the de Broglie — Bohm interpretation of quantum mechanics.