Hydrodynamic Quantum Field Theory: The Onset of Particle Motion and the Form of the Pilot Wave

Abstract

We consider the hydrodynamic quantum field theory proposed by Dagan and Bush, a model of quantum dynamics inspired by Louis de Broglie and informed by the hydrodynamic pilot-wave system discovered by Couder and Fort. According to this theory, a quantum particle has an internal vibration at twice the Compton frequency that generates disturbances in an ambient scalar field, the result being self-propulsion of the particle through a resonant interaction with its pilot-wave field. Particular attention is given here to providing theoretical rationale for the geometric form of the wave field generated by steady, rectilinear particle motion at a prescribed speed, where signatures of both the de Broglie and Compton wavelengths are generally evident. While focus is given to the one-dimensional geometry considered by Dagan and Bush, we also deduce the form of the pilot wave in two dimensions. We further consider the influence on the pilot-wave form of the details of the particle-induced wave generation, specifically the spatial extent and vibration frequency of the particle. Finally, guided by analogous theoretical descriptions of the hydrodynamic system, we recast the particle dynamics in terms of an integro-differential trajectory equation. Analysis of this equation in the non-relativistic limit reveals a critical wave-particle coupling parameter, above which the particle self-propels. Our results provide the foundation for subsequent theoretical investigations of hydrodynamic quantum field theory, including the stability analysis of various dynamical states.

Real surreal trajectories in pilot-wave hydrodynamics

“…Prior work [21,22] has shown that the walking-droplet system is closer in form to de Broglie's original doublesolution pilot-wave theory [38], according to which a quantum particle has an internal vibration at the Compton frequency that generates its own guiding wave, and the resulting pilotwave dynamics gives rise to emergent statistics described by the standard quantum theory. Our study provides further motivation for the revisitation and extension of de Broglie's double-solution program, informed by the walking-droplet system [39][40][41][42].…”

Real surreal trajectories in pilot-wave hydrodynamics

“…Prior work [21,22] has shown that the walking droplet system is closer in form to de Broglie's original doublesolution pilot-wave theory [37], according to which a quantum particle has an internal vibration at the Compton frequency that generates its own guiding wave, and the resulting pilot-wave dynamics gives rise to emergent statistics described by the standard quantum theory. Our study provides further motivation for the revisitation and extension of de Broglie's double-solution program, informed by the walking-droplet system [38][39][40][41].…”

Uma tradução comentada do artigo “A Termodinâmica Oculta das Partículas” de Louis de Broglie

“…De qualquer maneira "destacamos que nossos resultados não fecham a porta para a busca de difração e interferência das [gotas] errantes, apenas para as condições de contorno consideradas aqui, para o qual o comportamento do sistema é dominado pelas interações gota errante-anteparo" [37, p. 1152]. Além desse último artigo, vale a pena destacar outros trabalhos também de John W. M. Bush e colaboradores que têm se debruçado sobre essa analogia de maneira meticulosa, tal como o Hydrodynamic quantum field theory: the free particle e o Hydrodynamic quantum field theory: The onset of particle motion and the form of the pilot wave [38,39], a ponto de estabelecerem um modelo hidrodinâmico para a spintrônica em Emergent order in hydrodynamic spin lattices, observando uma histerese na transição de antiferromagnético para ferromagnético [40].…”