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arXiv:quant-ph/0307179

There is no first quantization - except in the de Broglie-Bohm interpretation

Hrvoje Nikolić

Published Jul 25, 2003• 3 citations
arXivHTMLPDF

Abstract

The relativistic effects of the integer-spin quantum field theory imply that the wave functions describing a fixed number of particles do not admit the usual probabilistic interpretation. Among several most popular interpretations of quantum mechanics applied to first quantization, the only interpretation for which this fact does not lead to a serious problem, and therefore the only consistent interpretation of first quantization, is the de Broglie-Bohm interpretation.

DOI
10.48550/arxiv.quant-ph/0307179

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The relativistic effects of the integer-spin quantum field theory imply that the wave functions describing a fixed number of particles do not admit the usual probabilistic interpretation. Among several most popular interpretations of quantum mechanics applied to first quantization, the only interpretation for which this fact does not lead to a serious problem, and therefore the only consistent interpretation of first quantization, is the de Broglie-Bohm interpretation.
We define the de Broglie-Bohm (dBB) weak interpretation as the dBB interpretation restricted to particles in unbound states whose wave function is defined in the three-dimensional physical space, and the dBB strong interpretation as the usual dBB interpretation applied to all wave functions, in particular to particles in bound states whose wave function is defined in a 3N-dimensional configuration space in which N is the number of particules. We show that the current criticisms of the dBB interpretation do not apply to this weak interpretation and that, furthermore, there are theoritical and experimental reasons to justify the weak dBB interpretation. Theoretically, the main reason concern the continuity existing for such particles between quantum mechanics and classical mechanics: we demonstrate in fact that the density and the phase of the wave function of a single-particle (or a set of identical particles without interaction), when the Planck constant tends to 0, converges to the density and the action of a set of unrecognizable prepared classical particles that satisfy the statistical Hamilton-Jacobi equations. As the Hamilton-Jacobi action pilots the particle in classical mechanics, this continuity naturally concurs with the weak dBB interpretation. Experimentally, we show that the measurement results of the main quantum experiments (Young's slits experiment, Stern and Gerlach, EPR-B) are compatible with the de Broglie-Bohm weak interpretation and everything takes place as if these unbounded particles had trajectories. In addition, we propose two potential solutions to complete the dBB weak interpretation.
The appearance of single-particle wave functions as field operators or arguments of a field functional in quantum field theory is often regarded as a second quantization, since these wave functions were themselves obtained by quantizing mass points (“particles”). I argue here that this language, though reflecting the historical development, is misleading. Spatial fields must be regarded as the true and only physical variables (in quantum theory becoming the arguments of a fundamental wave functional). This includes spinor and other fields which never become classical. Apparent particles are no more than the result of decoherence in the measuring device or by means of other environmental scattering processes, without playing any fundamental conceptual rôle in the theory or its interpretation. A remark on gauge fields is added.
In this work we apply the de Broglie-Bohm interpretation of quantum mechanics to the quantized spherically symmetric black-hole coupled to a massless scalar field. The wave-functional used was first obtained by Tomimatsu using the standard ADM quantization and a gauge that places the observer close to the black-hole horizon. Using the causal interpretation, we compute quantum trajectories determined by the initial conditions. We show that the quantum trajectories for the black-hole mass can either increase or decrease with time. The quantum trajectories that show increasing mass represent the usual black-hole behavior of continuous energy absorption. The mass-decreasing quantum trajectories are a purely quantum mechanical phenomena. They can be physically interpreted as describing a black-hole that evaporates.
With all its remarkable achievements, Quantum Mechanics as established in the fundamental papers written by Heisenberg, de Broglie, Schro¨dinger, Dirac, etc. contains some inconsistencies and internal contradictions. Quantum mechanics deals with quantum processes in which the number and the type of particles do not vary during their interaction, but only their energy and momentum states. The formalism of Quantum Mechanics is not capable of describing neither the variation of the number of particles, nor the transformation of one type of particle into another type. Even if in some cases the number of particles is allowed to change, this is somewhat forced and inconsistent. For example, Quantum Mechanics is not able to give a satisfactory explanation of the spontaneous emission, in which an electron situated on an excited energy level emits a quanta γ and decays to a lower energy level.
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-