Equivalent quantum equations in a system inspired by bouncing droplets experiments

Abstract

In this paper we study a classical and theoretical system which consists of an elastic medium carrying transverse waves and one point-like high elastic medium density, called concretion. We compute the equation of motion for the concretion as well as the wave equation of this system. Afterwards we always consider the case where the concretion is not the wave source any longer. Then the concretion obeys a general and covariant guidance formula, which leads in low-velocity approximation to an equivalent de Broglie-Bohm guidance formula. The concretion moves then as if exists an equivalent quantum potential. A strictly equivalent free Schrödinger equation is retrieved, as well as the quantum stationary states in a linear or spherical cavity. We compute the energy (and momentum) of the concretion, naturally defined from the energy (and momentum) density of the vibrating elastic medium. Provided one condition about the amplitude of oscillation is fulfilled, it strikingly appears that the energy and momentum of the concretion not only are written in the same form as in quantum mechanics, but also encapsulate equivalent relativistic formulas.

15 pages, 1 figure, Foundations of Physics (2017)

References in corpus (5)

• Chaos driven by interfering memory
• Interaction of two walkers: Wave-mediated energy and force
• de Broglie's double solution program: 90 years later
• Generalized guidance equation for peaked quantum solitons and effective gravity
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Cited by in corpus (5)

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• Revisiting de Broglie's Double-Solution Pilot-Wave Theory with a Lorentz-Covariant Lagrangian Framework
• Quantum solitodynamics: Non-linear wave mechanics and pilot-wave theory
• Bouncing oil droplets, de Broglie's quantum thermostat and convergence to equilibrium
• Effective gravity and effective quantum equations in a system inspired by walking droplets experiments