scholarly journals Drops walking on a vibrating bath: towards a hydrodynamic pilot-wave theory

2013 ◽  
Vol 727 ◽  
pp. 612-647 ◽  
Author(s):  
Jan Moláček ◽  
John W. M. Bush
Keyword(s):  
Wave Field ◽  
Walking Speed ◽  
Critical Role ◽  
Wave Theory ◽  
Special Focus ◽  
Driving Frequency ◽  
Pilot Wave ◽  
Spatio Temporal ◽  
Impact Phase ◽  
Pilot Wave Theory

AbstractWe present the results of a combined experimental and theoretical investigation of droplets walking on a vertically vibrating fluid bath. Several walking states are reported, including pure resonant walkers that bounce with precisely half the driving frequency, limping states, wherein a short contact occurs between two longer ones, and irregular chaotic walking. It is possible for several states to arise for the same parameter combination, including high- and low-energy resonant walking states. The extent of the walking regime is shown to be crucially dependent on the stability of the bouncing states. In order to estimate the resistive forces acting on the drop during impact, we measure the tangential coefficient of restitution of drops impacting a quiescent bath. We then analyse the spatio-temporal evolution of the standing waves created by the drop impact and obtain approximations to their form in the small-drop and long-time limits. By combining theoretical descriptions of the horizontal and vertical drop dynamics and the associated wave field, we develop a theoretical model for the walking drops that allows us to rationalize the limited extent of the walking regimes. The critical requirement for walking is that the drop achieves resonance with its guiding wave field. We also rationalize the observed dependence of the walking speed on system parameters: while the walking speed is generally an increasing function of the driving acceleration, exceptions arise due to possible switching between different vertical bouncing modes. Special focus is given to elucidating the critical role of impact phase on the walking dynamics. The model predictions are shown to compare favourably with previous and new experimental data. Our results form the basis of the first rational hydrodynamic pilot-wave theory.

scholarly journals Geometrical interpretation of the pilot wave theory and manifestation of spinor fields

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Mariya Iv. Trukhanova ◽  
Gennady Shipov
Keyword(s):  
Wave Theory ◽  
Geometrical Interpretation ◽  
Real Field ◽  
Spin Vector ◽  
Spinor Wave Function ◽  
Spinning Particle ◽  
Pilot Wave ◽  
Intrinsic Angular Momentum ◽  
Spinor Wave ◽  
Pilot Wave Theory

Abstract Using the hydrodynamical formalism of quantum mechanics for a Schrödinger spinning particle developed by Takabayashi, Vigier, and followers, which involves vortical flows, we propose a new geometrical interpretation of the pilot wave theory. The spinor wave in this interpretation represents an objectively real field, and the evolution of a material particle controlled by the wave is a manifestation of the geometry of space. We assume this field to have a geometrical nature, basing on the idea that the intrinsic angular momentum, the spin, modifies the geometry of the space, which becomes a manifold, represented as a vector bundle with a base formed by the translational coordinates and time, and the fiber of the bundle, specified at each point by the field of a tetrad $e^a_{\mu}$, forms from bilinear combinations of the spinor wave function. It has been shown that the spin vector rotates following the geodesic of the space with torsion, and the particle moves according to the geometrized guidance equation. This fact explains the self-action of the spinning particle. We show that the curvature and torsion of the spin vector line is determined by the space torsion of the absolute parallelism geometry.

Pilot-wave theory in retrospect

2013 ◽  
pp. 224-241
Author(s):  
Guido Bacciagaluppi ◽  
Antony Valentini
Keyword(s):  
Wave Theory ◽  
Pilot Wave ◽  
Pilot Wave Theory

scholarly journals Bohm Quantum Trajectories of Scalar Field in Trans-Planckian Physics

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Jung-Jeng Huang
Keyword(s):  
Scalar Field ◽  
Wave Theory ◽  
Vacuum State ◽  
Quantum Trajectory ◽  
Quantum Trajectories ◽  
De Sitter ◽  
Pilot Wave ◽  
In Trans ◽  
Schrödinger Picture ◽  
Pilot Wave Theory

In lattice Schrödinger picture, we investigate the possible effects of trans-Planckian physics on the quantum trajectories of scalar field in de Sitter space within the framework of the pilot-wave theory of de Broglie and Bohm. For the massless minimally coupled scalar field and the Corley-Jacobson type dispersion relation with sextic correction to the standard-squared linear relation, we obtain the time evolution of vacuum state of the scalar field during slow-roll inflation. We find that there exists a transition in the evolution of the quantum trajectory from well before horizon exit to well after horizon exit, which provides a possible mechanism to solve the riddle of the smallness of the cosmological constant.

scholarly journals Justifying Born’s Rule Pα = |Ψα|2 Using Deterministic Chaos, Decoherence, and the de Broglie-Bohm Quantum Theory

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1371
Author(s):  
Aurélien Drezet
Keyword(s):  
Quantum Theory ◽  
Kinetic Theory ◽  
Deterministic Chaos ◽  
Wave Theory ◽  
Fast Relaxation ◽  
Pilot Wave ◽  
Born’S Rule ◽  
H Theorem ◽  
Pilot Wave Theory ◽  
De Broglie Bohm

In this work, we derive Born’s rule from the pilot-wave theory of de Broglie and Bohm. Based on a toy model involving a particle coupled to an environment made of “qubits” (i.e., Bohmian pointers), we show that entanglement together with deterministic chaos leads to a fast relaxation from any statistical distribution ρ(x) of finding a particle at point x to the Born probability law |Ψ(x)|2. Our model is discussed in the context of Boltzmann’s kinetic theory, and we demonstrate a kind of H theorem for the relaxation to the quantum equilibrium regime.

scholarly journals Energy velocity and reactive fields

2018 ◽  
Vol 376 (2134) ◽  
pp. 20170453 ◽  
Author(s):  
Hans G. Schantz
Keyword(s):  
Electromagnetic Fields ◽  
Logical Consequence ◽  
Plane Waves ◽  
Wave Theory ◽  
Radiation Reaction ◽  
Electromagnetic Theory ◽  
Subsequent Work ◽  
Pilot Wave ◽  
The Waves ◽  
Pilot Wave Theory

Conventional definitions of ‘near fields’ set bounds that describe where near fields may be found. These definitions tell us nothing about what near fields are, why they exist or how they work. In 1893, Heaviside derived the electromagnetic energy velocity for plane waves. Subsequent work demonstrated that although energy moves in synchronicity with radiated electromagnetic fields at the speed of light, in reactive fields the energy velocity slows down, converging to zero in the case of static fields. Combining Heaviside's energy velocity relation with the field Lagrangian yields a simple parametrization for the reactivity of electromagnetic fields that provides profound insights to the behaviour of electromagnetic systems. Fields guide energy. As waves interfere, they guide energy along paths that may be substantially different from the trajectories of the waves themselves. The results of this paper not only resolve the long-standing paradox of runaway acceleration from radiation reaction, but also make clear that pilot wave theory is the natural and logical consequence of the need for quantum mechanics correspond to the macroscopic results of the classical electromagnetic theory. This article is part of the theme issue ‘Celebrating 125 years of Oliver Heaviside's ‘Electromagnetic Theory’’.

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