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Is the electron's charge 2e? A problem of the de Broglie-Bohm theory

Shan Gao

Published Apr 10, 2012• 0 citations
OpenAlex

Abstract

It is shown that the de Broglie-Bohm theory has a potential problem concerning the charge distribution of a quantum system such as an elec-tron. According to the guidance equation of the theory, the electron’s charge is localized in a position where its Bohmian particle is. But ac-cording to the Schrödinger equation of the theory, the electron’s charge is not localized in one position but distributed throughout space, and the charge density in each position is proportional to the modulus square of the wave function of the electron there. Although this tension may be resolved by assuming that the electron’s charge is not e but 2e, one for its Bohmian particle and the other for its wave function, the resolution will introduce more serious problems. The de Broglie-Bohm theory is an alternative to standard quantum mechan-ics initially proposed by de Broglie (1928) and later developed by Bohm (1952). According to the theory, a complete realistic description of a quantum system is

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It is shown that the de Broglie-Bohm theory has a potential problem concerning the charge distribution of a quantum system such as an elec-tron. According to the guidance equation of the theory, the electron’s charge is localized in a position where its Bohmian particle is. But ac-cording to the Schrödinger equation of the theory, the electron’s charge is not localized in one position but distributed throughout space, and the charge density in each position is proportional to the modulus square of the wave function of the electron there. Although this tension may be resolved by assuming that the electron’s charge is not e but 2e, one for its Bohmian particle and the other for its wave function, the resolution will introduce more serious problems. The de Broglie-Bohm theory is an alternative to standard quantum mechan-ics initially proposed by de Broglie (1928) and later developed by Bohm (1952). According to the theory, a complete realistic description of a quantum system is
It is shown that the de Broglie-Bohm theory has a potential problem concerning the mass and charge distributions of a quantum system such as an electron. According to the de Broglie-Bohm theory, the mass and charge of an electron are localized in a position where its Bohmian particle is. However, protective measurement indicates that they are not localized in one position but distributed throughout space, and the mass and charge density of the electron in each position is proportional to the modulus square of its wave function there.
We show that the de Broglie-Bohm theory is inconsistent with the established parts of quantum mechanics concerning its physical content. According to the de Broglie-Bohm theory, the mass and charge of an electron are localized in a position where its Bohmian particle is. However, protective measurement implies that they are not localized in one position but distributed throughout space, and the mass and charge density of the electron in each position is proportional to the modulus square of its wave function there.
There are three possible interpretations of the wave function in the de Broglie-Bohm theory: taking the wave function as corresponding to a physical entity or a property of the Bohmian particles or a law. In this paper, we argue that the first interpretation is favored by an analysis of protective measurements. The de Broglie-Bohm theory is an alternative to standard quantum mechan-ics initially proposed by de Broglie (1928) and later developed by Bohm (1952). According to the theory, a complete description of a quantum system is provided by the configuration defined by the positions of its particles together with its wave function. The wave function follows the linear Schrödinger equation and never collapses. The motion of the particles, which are usually called Bohmian particles, follows the so-called guiding equation. Although the de Broglie-Bohm theory is mathematically equivalent to quantum mechanics, there is no clear consensus with regard to its physical interpretation. In particular, the interpre-
Bohmian mechanics also known as de Broglie-Bohm theory is the most popular alternative approach to quantum mechanics. Whereas the standard interpretation of quantum mechanics is based on the complementarity principle Bohmian mechanics assumes that both particle and wave are concrete physical objects. In 1993 Peter Holland has written an ardent account on the plausibility of the de Broglie-Bohm theory. He proved that it fully reproduces quantum mechanics if the initial particle distribution is consistent with a solution of the Schrödinger equation. Which may be the reasons that Bohmian mechanics has not yet found global acceptance? In this article it will be shown that predicted properties of atoms and molecules are in conflict with experimental findings. Moreover it will be demonstrated that repeatedly published ensembles of trajectories illustrating double slit diffraction processes do not agree with quantum mechanics. The credibility of a theory is undermined when recognizably wrong data presented frequently over years are finally not declared obsolete.
A de Broglie-Bohm like model of Dirac equation, that leads to the correct Pauli equations for electrons and positrons in the low-speed limit, is presented. Under this theoretical framework, that affords an interpretation of the quantum potential, the main assumption of the de Broglie-Bohm theory--that the local momentum of particles is given by the gradient of the phase of the wave function--wont be accurate. Also, the number of particles wont be locally conserved. Furthermore, the representation of physical systems through wave functions wont be complete.
According to Standard Quantum Mechanics (SQM), known as the Copenhagen Interpretation, the complete description of a system of particles is provided by its wave function. However, in the de Broglie-Bohm theory of Bohmian Quantum Mechanics (BQM), the additional element which is introduced apart from the wave function is the particle position, conceived in the classical sense as pursuing a definite continuous track in space-time. In BQM formulation, depending on the configuration of the potential barrier and the energy of the packet, the particle trajectories have been shown to take distinct paths. We will consider several barrier heights and show that in a Bohmian interpretation of the problem, there is no such thing as Quantum Tunnelling.