Related papers: Global existence and uniqueness of Bohmian traject…
We explain why, in a configuration space that is multiply connected, i.e., whose fundamental group is nontrivial, there are several quantum theories, corresponding to different choices of topological factors. We do this in the context of…
Recently, Bohmian mechanics has been challenged [Nature 643, 67 (2025)] by studying a system in which the motion of particles cannot be associated only with the gradient of phase of the wave function. We point out that, in general, Bohmian…
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 generic Bohmian trajectories are calculated for an isolated particle in an approximate energy eigenstate, for an arbitrary one-dimensional potential well. It is shown, that the necessary and sufficient condition for there to be a…
Here I explore a novel no-collapse interpretation of quantum mechanics which combines aspects of two familiar and well-developed alternatives, Bohmian mechanics and the many-worlds interpretation. Despite reproducing the empirical…
In classical relativistic mechanics, a "preferred" proper direction in spacetime for each particle is determined by the direction of its 4-momentum. Analogously, for each quantum particle we find a local direction uniquely determined by the…
Mermin's "shut up and calculate!" somehow summarizes the most widely accepted view on quantum mechanics. This conception has led to a rather constraining way to think and understand the quantum world. Nonetheless, a closer look at the…
Bohmian trajectories have been used for various purposes, including the numerical simulation of the time-dependent Schroedinger equation and the visualization of time-dependent wave functions. We review the purpose they were invented for:…
We show that one-dimensional Bohmian mechanics is unique, in that, the Bohm trajectories are the only solutions that conserve total left (or right) probability. In Brandt et al., Phys. Lett. A, 249 (1998) 265--270, they define quantile…
Bohmian mechanics is an alternative interpretation of quantum mechanics. We outline the main characteristics of its non-relativistic formulation. Most notably it does provide a simple solution to the infamous measurement problem of quantum…
Quantum hydrodynamics is a formulation of quantum mechanics based on the probability density and flux (current) density of a quantum system. It can be used to define trajectories which allow for a particle-based interpretation of quantum…
The paper shows how the Bohmian approach to quantum physics can be applied to develop a clear and coherent ontology of non-perturbative quantum gravity. We suggest retaining discrete objects as the primitive ontology also when it comes to a…
Quantum gravity aims to describe gravity in quantum mechanical terms. How exactly this needs to be done remains an open question. Various proposals have been put on the table, such as canonical quantum gravity, loop quantum gravity, string…
We consider a Bohmian approach to the Wheeler-DeWitt quantization of the Friedmann-Lemaitre-Robertson-Walker model and investigate the question whether or not there are singularities, in the sense that the universe reaches zero volume. We…
We present a novel perspective on gravity-induced wave function reduction using Bohmian trajectories. This study examines the quantum motion of both point particles and objects, identifying critical parameters for the transition from…
Bohmian mechanics is a nonlocal hidden-variable interpretation of quantum theory which predicts that particles follow deterministic trajectories in spacetime. Historically, the study of Bohmian trajectories has mainly been restricted to…
Recent years have seen increased interest in complexified Bohmian mechanical trajectory calculations for quantum systems, both as a pedagogical and computational tool. In the latter context, it is essential that trajectories satisfy…
It is shown explicitly that in the framework of Bohmian quantum gravity, the equations of motion of the space-time metric are Einstein's equations plus some quantum corrections. It is observed that these corrections are not covariant. So…
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…
It is argued that the world is a dissipative dynamic system, a phase flow of which is formed by conformally-symplectic mapping. The key assumption is that the concept of energy in microcosm makes sense only for the steady motions…