We propose an interpretative framework for quantum mechanics inspired by Louis de Broglie's double-solution theory. The principle is to decompose the evolution of a quantum system into two wave functions: an external wave function corresponding to the evolution of its center of mass along with other macroscopic degrees of freedom, and an internal wave function corresponding to the evolution of its internal variables in the center-of-mass system. These two wave functions will have different meanings and interpretations.The external wave function ``pilots'' the center of mass of the quantum system: it corresponds to the de Broglie pilot wave. For the internal wave function, we argue in favor of the interpretation proposed by Erwin Schrödinger at the Solvay Congress in 1927: the particles are extended and the square of the module of the (internal) wave function of an electron corresponds to the density of its charge in space.
We propose an interpretative framework for quantum mechanics inspired by Louis de Broglie's double-solution theory. The principle is to decompose the evolution of a quantum system into two wave functions: an external wave function corresponding to the evolution of its center of mass along with other macroscopic degrees of freedom, and an internal wave function corresponding to the evolution of its internal variables in the center-of-mass system. These two wave functions will have different meanings and interpretations.The external wave function ``pilots'' the center of mass of the quantum system: it corresponds to the de Broglie pilot wave. For the internal wave function, we argue in favor of the interpretation proposed by Erwin Schrödinger at the Solvay Congress in 1927: the particles are extended and the square of the module of the (internal) wave function of an electron corresponds to the density of its charge in space.
We propose an interpretative framework for quantum mechanics corresponding to the specifications of Louis de Broglie's double-solution theory. The principle is to decompose the evolution of a quantum system into two wave functions: an external wave function corresponding to the evolution of its center of mass and an internal wave function corresponding to the evolution of its internal variables in the center-of-mass system. Mathematical decomposition is only possible in certain cases because there are many interactions linking these two parts. In addition, these two wave functions will have different meanings and interpretations. The external wave function "pilots" the center of mass of the quantum system: it corresponds to the Broglie pilot wave. When the Planck constant tends to zero, it results mathematically from the convergence of the square of the module and the phase of the external wave function to a density and a classical action verifying the Hamilton-Jacobi statistical equations. This interpretation explains all the measurement results, namely those yielded by interference, spin measurement (Stern and Gerlach) and non-locality (EPR-B) experiments. For the internal wave function, several interpretations are possible : the one of the pilot wave can be applied in cascade to the internal wave function. However, the interpretation proposed by Erwin Schr{ö}dinger at the Solvay Congress in 1927 and restricted to the internal wave function is also possible. For Schr{ö}dinger, the particles are extended and the square of the module of the (internal) wave function of an electron corresponds to the density of its charge in space. We present many arguments in favour of this interpretation, which like the pilot wave interpretation is realistic and deterministic. Finally, we will see that this double interpretation serves as a frame of reference by which to better understand the debates on the interpretation of quantum mechanics and to review the relationships between gravity and quantum mechanics.
We present a new interpretation of quantum mechanics, called the double-scale theory, which expends on the de Broglie-Bohm (dBB) theory. It is based, for any quantum system, on the simultaneous existence of two wave functions in the laboratory reference frame : an external wavefunction and an internal one. The external wave function corresponds to a field that pilots the center-of-mass of the quantum system. The external wave spreads out in space over time. Mathematically, the Schrödinger equation converges to the Hamilton-Jacobi statistical equations when the Planck constant tends towards zero and the Newton trajectories are therefore approximations of the dBB trajectories. The internal wave function corresponds to the interpretation proposed by Edwin Schrödinger for whom the particle is extended. Then, the internal wave remains confined in space. Its converges, when h -> 0, to a Dirac distribution. Furthermore, we show that non-stationary solutions can exist such that the 3N-dimensional configuration space of the internal wave function can be rewritten as the product of N individual 3-dimensional internal wave functions.
We present a semiclassical gravity in the framework of the double scale theory, a new interpretation of quantum mechanics which expands on the de Broglie-Bohm (dBB) theory. In this interpretation, any quantum system is associated with two wave functions, one external and one internal. The external wave function drives the center-of-mass, as in the dBB theory, and spreads with time. The internal wave function corresponds to the density of an extended particle. It remains confined in space and its average position corresponds to the center of mass of the particle. We define, for an N-body system, new semi-classical gravity equations called Einstein-de Broglie equations. The external wave function of each body depends only on the internal wave functions of the N--1 others. They are deduced from Einstein's semi-classical equation by using the internal wave functions instead of the usual wave function. If we restrict to the dBB interpretation, we find the Newton-de Broglie equations that Struyve and Lalo{ë} have recently proposed independently. We show that the Newton-de Broglie and Einstein-de Broglie equations converge to Newton's gravity when h → 0, which gives a theoretical validation.
Nous proposons une grille de lecture de la mécanique quantique correspondant aux spécifications de la théorie de la double solution de Louis de Broglie. Le principe est de considérer l’évolution d’un système quantique sous la forme de deux fonctions d’onde : une fonction d’onde externe correspondant à l’évolution de son centre de masse et une fonction d’onde interne correspondant à l’évolution de ses variables internes dans le référentiel du centre de masse. La décomposition mathématique exacte n’est possible que dans certains cas car de nombreuses interactions relient ces deux parties. En outre, ces deux fonctions d’onde vont avoir des sens et des interprétations différentes.La fonction d’onde externe pilote le centre de masse du système quantique : elle correspond à l’onde pilote de Broglie. Elle découle mathématiquement de la convergence, lorsque l’on fait tendre la constante de Planck ~ vers zéro, du carré du module et de la phase de la fonction d’onde externe vers une densité et une action classique vérifiant les équations statistiques d’Hamilton-Jacobi. Cette interprétation explique tous les résultats de mesure, comme les expériences d’interférences, de mesure du spin (Stern et Gerlach) et de non-localité (EPR-B).Pour la fonction d’onde interne, plusieurs interprétations sont possibles : celle de l’onde pilote peut s’appliquer en cascade à la fonction d’onde interne. Cependant l’interprétation proposée par Erwin Schrödinger au congrès Solvay de 1927 et restreinte à la fonction d’onde interne est également envisageable. Pour Schrödinger, les particules sont étendues et le carré du module de la fonction d’onde (interne) d’un électron correspond à la densité de sa charge dans l’espace. Nous présentons les nombreux arguments en faveur de cette interprétation, qui comme celle de l’onde pilote est réaliste et déterministe.Nous montrons que cette double interprétation est une grille de lecture pour mieux comprendre les débats sur les interprétations de la mécanique quantique et de revoir les relations entre gravité et mécanique quantique.
In the 1927 Solvay conference, three apparently irreconcilable interpretations of the quantum mechanics wave function were presented: the pilot-wave interpretation by de Broglie, the soliton wave interpretation by Schrödinger and the Born statistical rule by Born and Heisenberg. In this paper, we demonstrate the complementarity of these interpretations corresponding to quantum systems that are prepared differently and we deduce a synthetic interpretation: the double-preparation theory. We first introduce in quantum mechanics the concept of semi-classical statistically prepared particles, and we show that in the Schrödinger equation these particles converge, when , to the equations of a statistical set of classical particles. These classical particles are undiscerned, and if we assume continuity between classical mechanics and quantum mechanics, we conclude the necessity of the de Broglie–Bohm interpretation for the semi-classical statistically prepared particles (statistical wave). We then introduce in quantum mechanics the concept of a semi-classical deterministically prepared particle, and we show that in the Schrödinger equation this particle converges, when , to the equations of a single classical particle. This classical particle is discerned and assuming continuity between classical mechanics and quantum mechanics, we conclude the necessity of the Schrödinger interpretation for the semi-classical deterministically prepared particle (the soliton wave). Finally we propose, in the semi-classical approximation, a new interpretation of quantum mechanics, the 'theory of the double preparation', which depends on the preparation of the particles.
This paper provides a detailed and unified historical account of early debates over wave-function realism, the modern term for the view that the wave function of quantum theory is physically real. As this paper will show, the idea of physical waves associated with particles had its roots in work by Einstein and de Broglie, who both originally thought of these waves as propagating in three-dimensional physical space. De Broglie quickly turned this wave--particle duality into an early pilot-wave theory, on which a particle's associated ``phase wave'' piloted or guided the particle along its trajectory. Schrödinger built on de Broglie's phase-wave hypothesis to provide a comprehensive account of the nascent quantum theory. However, Schrödinger's new ``undulatory mechanics'' came at the cost of replacing de Broglie's phase waves propagating in physical space with a wave function propagating in a system's abstract configuration space. The present work will argue that this move from three-dimensional physical space to a many-dimensional configuration space was a decisive reason why the founders of quantum theory uniformly abandoned the physical reality of the wave function. This paper will further clarify that de Broglie introduced two distinct pilot-wave theories, and will then argue that it was Bohm's rediscovery of the second of these two pilot-wave theories over two decades later, as well as Bohm's vociferous defense of wave-function realism, that were responsible for resurrecting the idea of an ontological wave function. Finally, this paper will describe how the influence of Schrödinger and Bohmended up playing a central role in Everett's development of the ``many worlds'' interpretation.