Causal interpretation and quantum phase space

We show that the de Broglie–Bohm interpretation can be easily implemented in quantum phase space through the method of quasi-distributions. This method establishes a connection with the formalism of the Wigner function. As a by-product, we obtain the rules for evaluating the expectation values and probabilities associated with a general observable in the de Broglie–Bohm formulation. Finally, we discuss some aspects of the dynamics.     

Space–time transformation for the propagator in de Broglie–Bohm theory

A linear space–time transformation proposed to calculate the propagator in the de Broglie–Bohm theory, viewed as an expansion of the guiding wave function over the velocity space. It is shown that the quantum evolution is preserved in its semiclassical scheme through this change. The case of variable-frequency harmonic oscillator is presented as an example.     

Solving the Measurement Problem: De Broglie--Bohm Loses Out to Everett

The quantum theory of de Broglie and Bohm solves the measurement problem, but the hypothetical corpuscles play no role in the argument. The solution finds a more natural home in the Everett interpretation.     

The double slit experiment,the Aharonov-Bohm effect,and a new quantum potential theory: Towards a realistic interpretation of quantum mechanics

In this paper, a new proposal of the quantum potential theory is presented, along with a discussion of the two-slit interference experiment and the Aharonov-Bohm effect, which are explicitly calculated within the scheme adopted. The present formulation holds the notion of particle trajectory and follows the interpretation suggested by de Broglie and Bohm, the quantum potential being a manifestation of the quantum wave. This wave always satisfies the Schrödinger equation and is considered as areal and separate entity from the particle with which is associated. In our approach we try to circumvent some conceptual difficulties that prevent the de Broglie-Bohm's theory from fulfilling a complete objective program. New effects are predicted, specially for the Aharonov-Bohm experiment in the regime of high magnetic fields, and a setup for their detection is proposed.     

Drift wave turbulence in a dense semi-classical magnetoplasma

A semi-classical nonlinear collisional drift wave model for dense magnetized plasmas is developed and solved numerically. The effects of fluid electron density fluctuations associated with quantum statistical pressure and quantum Bohm force are included, and their influences on the collisional drift wave instability and the resulting fully developed nanoscale drift wave turbulence are discussed. It is found that the quantum effects increase the growth rate of the collisional drift wave instability, and introduce a finite de Broglie length screening on the drift wave turbulent density perturbations. The relevance to nanoscale turbulence in nonuniform dense magnetoplasmas is discussed.     

Cosmology and the pilot wave interpretation of quantum mechanics

Bell has recently revived the pilot wave interpretation of de Broglie and Bohm as a possible scheme for interpreting wave functions in quantum cosmology. I argue that the pilot wave interpretation cannot be applied consistently to systems whose wave functions split into macroscopically distinguishable states. At some stage the pilot wave interpretation must either tacitly invoke wave function reduction in the same manner as the Copenhagen interpretation, or else abandon locality by requiring physical particles to move faster than light. Consequently, the many-worlds interpretation is the only known realist interpretation of the quantum mechanical formalism which can be extended to quantum cosmology.     

New Trajectory Interpretation of Quantum Mechanics

It was shown by de Broglie and Bohm that the concept of a deterministic particle trajectory is compatible with quantum mechanics. It is demonstrated by explicit construction that there exists another more general deterministic trajectory interpretation. The method exploits an internal angular degree of freedom that is implicit in the Schrödinger equation, in addition to the particle position. The de Broglie-Bohm model is recovered when the new theory is averaged over the internal freedom. The model exhibits a strong form of entanglement which implies a primary role for the wavefunction of the Universe. The conditions of autonomy are examined, and the viability of the theory is established by application to the measurement problem.     

On the impossible pilot wave

The strange story of the von Neumann impossibility proof is recalled, and the even stranger story of later impossibility proofs, and how the impossible was done by de Broglie and Bohm. Morals are drawn.     

Position measurements in the de Broglie–Bohm interpretation of quantum mechanics

The de Broglie–Bohm interpretation of quantum mechanics assigns positions and trajectories to particles. We analyze the validity of a formula for the velocities of Bohmian particles which makes the analysis of these trajectories particularly simple. We apply it to particle detectors of four different types and show that the detectors of three of these types lead to “surrealistic trajectories”, i.e., leave a trace where the Bohmian particle was not present.     

Quantum-optical predictions for an experiment on the de Broglie waves detection

An experimental apparatus to detect de Broglie waves is discussed. The wave packets of two photons generated in the parametric-down conversion are overlapped in a modified Mach-Zehnder interferometer. The coincidence photodetection rate of photon pairs is evaluated, as a function of path-length of two interferometer arms, both by using the de Broglie concept of a real quantum wave and by the quantum optical approach. The different results of these two theories are compared, and it is shown that the proposed experiment can disprove either the theories.     

Quantization of the space－time with topological defect

We present the classical solution of Lagrange equations for the black hole with a global monopole or with a cosmic string. Then we obtain the wavefunction of the space－time by solving the Wheeler－De Witt equation. De Broglie－Bohm interpretation applied to the wavefunction gives the quantum solution of the space－time. In the end, the quantum effect on Hawking radiation is studied.     

Aharonov–Bohm effects in magnetohydrodynamics

It is shown that an Aharonov–Bohm (AB) effect exists in magnetohydrodynamics (MHD). This effect is best described in terms of the MHD variational variables (Kats, 2004; Yahalom and Lynden-Bell, 2008; Yahalom, 2010) [1], [10], [12]. If a MHD flow has a non-trivial topology some of the functions appearing in the MHD Lagrangian are non-single-valued. These functions have properties similar to the phases in the AB celebrated effect (Aharonov and Bohm, 1959; van Oudenaarden et al., 1998) [2], [3]. While the manifestation of the quantum AB effect is in interference fringe patterns (Tonomura et al., 1982) [4], the manifestation of the MHD Aharonov–Bohm effects are through new dynamical conservation laws.     

教学研究:介绍量子力学几个基本概念——兼答《关于量子几何相位的评注》中的几个主要问题

介绍了量子绝热定理的物理含义及成立的条件，认为有关主要献（Aharonov-Anandan,Bohm，孙昌璞等）的表述是正确的，而《关于量子几何相位的评注》^[1]（以下简称《评注》）相应的表述不完全正确。在此基础上，认为这些献和教材（R.Shankar)得出的涉及Berry绝热相位的一些论述（不含Berry绝热相因子的瞬时能量本征态不满足含时Schroedinger方程等）也是正确的，而《评注》的论述与此相反。《评注》认为只有γn(C)才是Berry相位。本作则倾向于把γn（t）叫做Berry绝热相位，而把γn（C）=γn（T）-γn（0）叫做几何相位（geometric phase)^[2]。     

Explicit mathematical construction of relativistic nonlinear de Broglie waves described by three-dimensional (wave and electromagnetic) solitons “piloted” (controlled) by corresponding solutions of associated linear Klein-Gordon and Schrödinger equations

Starting from a nonlinear relativistic Klein-Gordon equation derived from the stochastic interpretation of quantum mechanics (proposed by Bohm-Vigier, ⁽¹⁾ Nelson, ⁽²⁾ de Broglie, ⁽³⁾ Guerra et al. ⁽⁴⁾ ), one can construct joint wave and particle, soliton-like solutions, which follow the average de Broglie-Bohm ⁽⁵⁾ real trajectories associated with linear solutions of the usual Schrödinger and Klein-Gordon equations.     

Lorentz Invariance and the retarded Bohm Model

We show how a recently introduced retarded version of the Bohm Model evades the Hardy proof that hidden-variable models must violate Lorentz Invariance. We also discuss a possible test of such models.We are happy to have this article included in a volume honoring Jean-Pierre Vigier, who has long recognized the significance of the hidden-variable model following from the work of L. de Broglie and D. Bohm.S.W.M. would like to thank S.E.R.C. for financial support.     

Observing quantum trajectories: From Mott’s problem to quantum Zeno effect and back

The experimental results of Kocsis et al., Mahler et al. and the proposed experiments of Morley et al. show that it is possible to construct “trajectories” in interference regions in a two-slit interferometer. These results call for a theoretical re-appraisal of the notion of a “quantum trajectory” first introduced by Dirac and in the present paper we re-examine this notion from the Bohm perspective based on Hamiltonian flows. In particular, we examine the short-time propagator and the role that the quantum potential plays in determining the form of these trajectories. These trajectories differ from those produced in a typical particle tracker and the key to this difference lies in the active suppression of the quantum potential necessary to produce Mott-type trajectories. We show, using a rigorous mathematical argument, how the active suppression of this potential arises. Finally we discuss in detail how this suppression also accounts for the quantum Zeno effect.     

Challenges to Bohr’s Wave-Particle Complementarity Principle

Contrary to Bohr’s complementarity principle, in 1995 Rabinowitz proposed that by using entangled particles from the source it would be possible to determine which slit a particle goes through while still preserving the interference pattern in the Young’s two slit experiment. In 2000, Kim et al. used spontaneous parametric down conversion to prepare entangled photons as their source, and almost achieved this. In 2012, Menzel et al. experimentally succeeded in doing this. When the source emits entangled particle pairs, the traversed slit is inferred from measurement of the entangled particle’s location by using triangulation. The violation of complementarity breaches the prevailing probabilistic interpretation of quantum mechanics, and benefits Bohm’s pilot-wave theory.     

Dirac's aether in relativistic quantum mechanics

The introduction by Dirac of a new aether model based on a stochastic covariant distribution of subquantum motions (corresponding to a vacuum state alive with fluctuations and randomness) is discussed with respect to the present experimental and theoretical discussion of nonlocality in EPR situations. It is shown (1) that one can deduce the de Broglie waves as real collective Markov processes on the top of Dirac's aether; (2) that the quantum potential associated with this aether's modification, by the presence of EPR photon pairs, yields a relativistic causal action at a distance which interprets the superluminal correlations recently established by Aspect et al.; (3) that the existence of the Einstein-de Broglie photon model (deduced from Dirac's aether) implies experimental predictions which conflict with the Copenhagen interpretation in certain specific testable interference experiments.