![]() ![]() Boudaoud Dynamical phenomena: walking and orbiting droplets, Nature, Volume 437 (2005) no. ![]() Our results suggest the potential value of a new hydrodynamically-inspired pilot-wave theory for the motion of quantum particles. The emergent dynamics is strongly reminiscent of that arising in the hydrodynamic pilot-wave system, on the basis of which we anticipate the emergence of quantum statistics in various settings. Speed modulations along the particle path arise with the de Broglie wavelength and frequency c k. The particle locks into quasi-steady motion characterized by a mean momentum p ¯ = ℏ k, where k is the wavenumber of the surrounding matter waves. Resonance is achieved between the particle and its pilot wave, leading to self-excited motion of the particle. We simulate the evolution of the particle position by assuming that the particle is propelled by the local gradient of its pilot wave field. ![]() The particle is modeled as a localized periodic disturbance of the Klein–Gordon field at twice the Compton frequency. Informed by the hydrodynamic pilot-wave system, we explore a variant of de Broglie’s mechanics in which the form of the Compton-scale dynamic interaction between particle and pilot wave is specified. While he developed a guidance equation for the particle, he did not specify how the particle generates the wave. He further proposed that the resulting pilot-wave field satisfies the Klein–Gordon equation. de Broglie proposed that quantum particles are characterized by an internal oscillation at the Compton frequency, at which rest mass energy is exchanged with field energy. We revisit de Broglie’s double-solution pilot-wave theory in light of insights gained from the hydrodynamic pilot-wave system discovered by Couder and Fort . ![]()
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