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Iranian Journal of Physics Research

Using Bohmian trajectories in gravitational reduction of the wave function

Rahmani, Faramarz, Sadeghi, Mehdi

Published Jun 1, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.47176/ijpr.24.1.11791

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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.
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.
Quantum mechanics is often praised as a theory which unifies classical mechanics and classical wave theory. Quanta are said to behave either as particles or waves, depending on the type of experiment they are subjected to. But where in the standard formalism can a pointlike particle structure actually be found? Perhaps only to some degree in the reduction postulate applied to position measurements. In reaction to this unsatisfactory state of affairs, Bohmian mechanics introduces a mathematically precise particle concept into quantum mechanical theory. The fuzzy wave functions are supplemented by sharp particle world-lines. Through this additional structure some quantum phenomena like the double slit experiment have lost their mystery.
Abstract The recent experimental proposals by Bose et al. and Marletto et al. (BMV) outline a way to test for the quantum nature of gravity by measuring gravitationally induced differential phase accumulation over the superposed paths of two ∼ 10−14 kg masses. These authors outline the expected outcome of these experiments for semi-classical, quantum gravity and collapse models. It is found that both semi-classical and collapse models predict a lack of entanglement in the experimental results. This work predicts the outcome of the BMV experiment in Bohmian trajectory gravity - where classical gravity is assumed to couple to the particle configuration in each Bohmian path, as opposed to semi-classical gravity where gravity couples to the expectation value of the wave function, or of quantized gravity, where the gravitational field is itself in a quantum superposition. In the case of the BMV experiment, Bohmian trajectory gravity predicts that there will be quantum entanglement. This is surprising as the gravitational field is treated classically. A discussion of how Bohmian trajectory gravity can induce quantum entanglement for a non superposed gravitational field is put forward.
The aim of this book is to provide a comprehensive guide to the metaphysics of Bohmian mechanics. Bohmian mechanics is a quantum theory that describes the motion of particles following trajectories that are determined by the quantum wave-function. The key question that the theory has to face relates to the ontological interpretation of the quantum wave-function. The main debate has mostly centered around two opposing views, wave-function realism on the one hand, and the nomological view on the other hand. The supporters of the former believe that the wave-function is a physical field living in a high-dimensional space; the supporters of the latter regard the wave-function as just an entity that appears in the laws of nature and lacks physical status. This monograph discusses both views open-mindedly, illuminating their tacit problems and providing new insight into how they can be overcome. Moreover, it discusses the structuralist view, which is often neglected and which can be regarded as a reconciliation of the two main opposing camps.
In the last few years the hydrodynamic formulation of quantum mechanics, equivalent to the Bohmian equations of motion, has been used to obtain numerical solutions of the Schrodinger equation. Problems, however, have been experienced near wave function nodes (or low probability regions). Here we attempt to compute wave functions and Bohmian trajectories for the interference of one particle or of two identical particles. It turns out that the large number of nodes (i.e. interference minima) makes the hydrodynamic equations impractical, whereas a more straightforward solution of the Schrodinger equation gives very good results.