scholarly journals The Many-Object "Pilot Wave" Theory

2011 ◽  
Vol 9 ◽  
pp. 69-77
Author(s):  
Yoav Ben-Dov
Keyword(s):  
Quantum Mechanics ◽  
Wave Theory ◽  
Object A ◽  
Pilot Wave ◽  
Supplementary Variables ◽  
The Many ◽  
Pilot Wave Theory

The "pilot wave." supplementary variables version of quantum mechanics diacusaed. It is claimed that in the many-object a semi-class picture of particles "guided" in their motion by waves m 3-spaces is difficult to maintain-Other interpretative schemes are suggested

scholarly journals Hamiltonian formulation of the pilot-wave theory

2019 ◽  
Vol 97 (4) ◽  
pp. 431-435
Author(s):  
Dan N. Vollick
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Scalar Field ◽  
Relativistic Particle ◽  
Hamiltonian Formulation ◽  
Wave Theory ◽  
Schrödinger’S Equation ◽  
Pilot Wave ◽  
Schrödinger's Equation ◽  
Pilot Wave Theory

In the pilot-wave theory of quantum mechanics particles have definite positions and velocities and the system evolves deterministically. The velocity of a particle is determined by the wave function of the system (the guidance equation) and the wave function evolves according to Schrödinger’s equation. In this paper I first construct a Hamiltonian that gives Schrödinger’s equation and the guidance equation for the particle. I then find the Hamiltonian for a relativistic particle in Dirac’s theory and for a quantum scalar field.

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.

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