Hydrodynamic Quantum Field Theory: The Onset of Particle Motion and the Form of the Pilot Wave
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fphy-08-00300.pdf
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1.3 MB
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Adobe PDF
Checksum (MD5)
3feee2ade5a52a35af0f83722d00abb5
Author(s)
Durey, Matthew
Bush, John W. M.
Date Issued
August 2020
Journal
Frontiers in Physics
Publisher
Frontiers Media SA
Citation
Durey, Matthew and John W. M. Bush. "Hydrodynamic Quantum Field Theory: The Onset of Particle Motion and the Form of the Pilot Wave." Frontiers in Physics 8 (2020 August): 300. © 2020 Durey and Bush
Version
Final published version
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution 4.0 International license
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DOI of Published Version
https://doi.org/10.3389/fphy.2020.00300
