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arXiv:2209.00513 · Indian Journal of Physics

On the gravitization of quantum mechanics and wave function reduction in Bohmian quantum mechanics

Faramarz Rahmani, Mehdi Golshani

Published Feb 15, 2024• 1 citation
arXivHTMLPDF
DOI
10.1007/s12648-023-02997-1

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In objective gravitational reduction of the wave function of a quantum system, the classical limit of the system is obtained in terms of the objective properties of the system. On the other hand, in Bohmian quantum mechanics the usual criterion for getting classical limit is the vanishing of the quantum potential or the quantum force of the system, which suffers from the lack of an objective description. In this regard, we investigated the usual criterion of getting the classical limit of a free particle in Bohmian quantum mechanics. Then we argued how it is possible to have an objective gravitational classical limit related to the Bohmian mechanical concepts like quantum potential or quantum force. Also we derived a differential equation related to the wave function reduction. An interesting connection will be made between Bohmian mechanics and gravitational concepts.
In this research, we study the gravitational reduction of the wave function, which has been investigated in standard quantum mechanics. As a new look at the problem, we investigate the reduction of the wave function by studying the dynamics of the particle motion, which can be defined in the quantum Bohmian framework. In this regard, quantities such as the critical mass of reduction, reduction time, and reduction temperature, which are similar to the Unruh temperature, are systematically obtained.
In this study, we use the concept of Bohmian trajectories to present a dynamical and deterministic interpretation for the gravity-induced wave function reduction. We shall classify all possible regimes for the motion of a particle, based on the behavior of trajectories in the ensemble and under the influence of quantum and gravitational forces. In the usual approaches all the information is obtained from the wave function evolution. But, on the basis of Bohm’s deterministic quantum theory, we can investigate the motion of the particle during the reduction processes. This leads to analytical and numerical results for the reduction time and equation of motion of the particle. In this regard, a new visualization will be provided for the reduction time.