We introduce the de Broglie-Bohm causal interpreation of quantum mechanics and compare it to the standard interpretation of quantum mechanics, the Copenhagen interpretation. We examine the possibility of experimentally distinguishing between the two theories, as well as the potential for the causal interpretation to more easily bridge the gap between the physics of the quantum and classical worlds. We then use the causal interpretation to construct a deterministic model of the helium atom in which the two electrons move along trajectories through space and time about a stationary nucleus. The dynamics are governed by the non-relativistic Schrödinger equation and the spin vectors of both electrons are assumed to be constant along their respective trajectories. We examine the Bohmian trajectories associated with (approximations to) eigenstates of the helium Hamiltonian as well as the trajectories associated with some non-eigenstates. We also compute an approximation to the ground state energy of the helium atom using a representation of the helium wavefunction in terms of hydrogenic eigenfunctions which is motivated by a perturbation approach.

We introduce the de Broglie-Bohm causal interpreation of quantum mechanics and compare it to the standard interpretation of quantum mechanics, the Copenhagen interpretation. We examine the possibility of experimentally distinguishing between the two theories, as well as the potential for the causal interpretation to more easily bridge the gap between the physics of the quantum and classical worlds. We then use the causal interpretation to construct a deterministic model of the helium atom in which the two electrons move along trajectories through space and time about a stationary nucleus. The dynamics are governed by the non-relativistic Schrödinger equation and the spin vectors of both electrons are assumed to be constant along their respective trajectories. We examine the Bohmian trajectories associated with (approximations to) eigenstates of the helium Hamiltonian as well as the trajectories associated with some non-eigenstates. We also compute an approximation to the ground state energy of the helium atom using a representation of the helium wavefunction in terms of hydrogenic eigenfunctions which is motivated by a perturbation approach.

L'interprétation causale de la mécanique quantique a été décrite en premier lieu par les historiens comme une conséquence de l'influence croissante du marxisme chez les physiciens des pays occidentaux. En effet, au cours des années 1950, le noyau du groupe de physiciens impliqués dans le programme causal autour de Jean-Pierre Vigier et Louis de Broglie à l'Institut Henri Poincaré est majoritairement constitué soit de membres, soit de sympathisants du PCF. Leurs travaux sont fortement influencés par les critiques soviétiques contre l'interprétation dominante de la mécanique quantique, l'interprétation dite de Copenhague. Entre autres, Vigier critique le pragmatisme qui règne dans la physique de l'après-guerre et pense que le manque de réflexion philosophique est en grande partie responsable de la crise que traverse la physique fondamentale, telle que le problème de la renormalisation. Le groupe a également porté la question de l'interprétation de la théorie au sein du PCF d'où est née une controverse au sein du parti qui a soulevé la problématique de la relation entre le marxisme et la science.La théorie fait également partie d'un programme de recherche plus global lié aux questions contemporaines en physique. Ce point est souvent oublié, ce qui mène à la conclusion erronée que la motivation du groupe IHP est seulement de nature idéologique et, par conséquent, que leur activité est hors de la science. Dès 1957, en collaboration avec des physiciens japonais, le groupe a proposé une théorie des particules élémentaires et un système de classification, à une époque où une théorie consensuelle manque encore / The Causal Interpretation of Quantum Mechanics was in the first place described by historians as a consequence of the growing influence of Marxism among physicists in Western countries. Indeed, during the 1950s, the core of the group of physicists involved in the Causal program around Jean-Pierre Vigier and Louis de Broglie at the Institut Henri Poincaré was mainly constituted either of members or sympathizers of the PCF. Their works were strongly influenced by critics from Soviet Union against the mainstream interpretation of Quantum Mechanics, the so called Copenhagen interpretation. Vigier criticized the pragmatism which prevailed in the Postwar physics and thought that the lack of philosophical considerations was in great part responsible for the crisis in fundamental physics, such as the problem of renormalization. They also put the issue of the interpretation of the theory inside the PCF and created a controversy inside the party which raised the relationship between Marxism and science. The theory was also part of a more global research program linked with contemporary questions in physics. This point is often forgotten which leads to the erroneous conclusion that the motivation of the IHP group was only ideological and, therefore, their activity was out of science. As early as 1957, in collaboration with Japanese physicists, the group proposed a theory for elementary particles and a method of their classification, in a period in where a standard theory was still missing