In this investigation, we have considered two thought experiments to make a comparison between predictions of the standard and the Bohmian quantum mechanics. Concerning this, a two-particle system has been studied at two various situations of the entangled and the unentangled states. In the first experiment, the two theories can predict different results at the individual level, while their statistical results are the same. In the other experiment, not only they are in disagreement at the individual level, but their equivalence at the statistical level also breaks down, if one uses selective detection. Furthermore, we discuss about some objections that can be raised against the results of the two suggested experiments.
On the Weak Measurement of Velocity in Bohmian Mechanics
在最近的一篇文章（New Journal of Physics 9，165，2007）中，怀斯曼提出了使用所谓的弱测量来确定量子粒子在给定位置的速度，并表明根据量子力学，这种过程的结果是粒子的玻姆速度。虽然Bohmian力学在经验上等同于基于不同于Bohmian的速度公式的变体，并且虽然已经证明Bohmian力学中的速度是不可测量的，但我们在这里争论的是有点矛盾的结论，即怀斯曼的弱测量过程确实构成了Bohmian力学中速度的真正测量。我们调和了明显的矛盾，并详细阐述了一些不同的测量意义在这里发挥作用。
According to Bohmian mechanics, we see the particle, not the pilot wave. But to make predictions we need to know the wave. How do we learn about the wave to make predictions, if we only see the particle? I show that the puzzle can be solved, but only thanks to decoherence.
Tunneling photons pose no challenge to Bohmian mechanics
Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China（合肥微尺度物质科学国家研究中心和物理科学学院，中国科学技术大学）；Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China（上海量子科学研究中心和中国科学院量子信息重点实验室，中国科学技术大学）；Hefei National Laboratory, University of Science and Technology of China（合肥国家实验室，中国科学技术大学）
This chapter provides a comprehensive overview of the Bohmian formulation of quantum mechanics. It starts with a historical review of the difficulties found by Louis de Broglie, David Bohm, and John S. Bell to convince the scientific community about the validity and utility of Bohmian mechanics. Then, a formal explanation of Bohmian mechanics for nonrelativistic, single-particle quantum systems is presented. The generalization to many-particle systems, where the exchange interaction and the spin play an important role, is also presented. After that, the measurement process in Bohmian mechanics…
Bohmian mechanics, also known as pilot-wave theory or de Broglie-Bohm theory, is a formulation of quantum mechanics whose fundamental axioms are not about what observers will see if they perform an experiment but about what happens in reality. It is therefore called a "quantum theory without observers," alongside with collapse theories and many-worlds theories and in contrast to orthodox quantum mechanics. It follows from these axioms that in a universe governed by Bohmian mechanics, observers will see outcomes with exactly the probabilities specified by the usual rules of quantum mechanics fo…
We discuss the Bohmian mechanics by means of the deformed Schrödinger equation for position dependent mass, in the context of a $q$-algebra inspired by nonextensive statistics. A deduction of the Bohmian quantum formalism is performed by means of a deformed Fisher information functional, from which a deformed Cramér-Rao bound is derived. Lagrangian and Hamiltonian formulations, inherited by the $q$-algebra, are also developed. Then, we illustrate the results with a particle confined in an infinite square potential well. The preservation of the deformed Cramér-Rao bound for the stationary state…
In this study, we solve analytically the Schrodinger equation for a macroscopic quantum oscillator as a central system coupled to a large number of environmental micro-oscillating particles. Then, the Langevin equation is obtained for the system using two approaches: Quantum Mechanics and Bohmian Theory. Our results show that the predictions of the two theories are inherently different in real conditions. Nevertheless, the Langevin equation obtained by Bohmian approach could be reduced to the quantum one, when the vibrational frequency of the central system is high enough compared to the maxim…
Thermal wave packets are used to analyze transmission probabilities and characteristic times through a parabolic repeller within the dissipative Bohmian mechanics. Thermal arrival, dwelling, transmission and reflection times are defined and calculated by using a Maxwell-Boltzmann distribution for the initial velocities of the incident particles. The dissipation is considered within the Caldirola-Kanai and Kostin approaches where a linear and nonlinear framework is used, respectively. The initial parameters are chosen to have only a dissipative tunnelling dynamics at zero temperature; at any no…
