Revisiting de Broglie’s Double-Solution Pilot-Wave Theory with a Lorentz-Covariant Lagrangian Framework
Name
symmetry-16-00149.pdf
Size
2.5 MB
Format
Adobe PDF
Checksum (MD5)
f5d679f0b93b8239f72b96bd93be3ff5
Author(s)
Darrow, David
Bush, John W. M.
Date Issued
January 26, 2024
Journal
Symmetry
Publisher
MDPI AG
Citation
Darrow, D.; Bush, J.W.M. Revisiting de Broglie’s Double-Solution Pilot-Wave Theory with a Lorentz-Covariant Lagrangian Framework. Symmetry 2024, 16, 149.
Version
Final published version
Abstract
The relation between de Broglie’s double-solution approach to quantum dynamics and the hydrodynamic pilot-wave system has motivated a number of recent revisitations and extensions of de Broglie’s theory. Building upon these recent developments, we here introduce a rich family of pilot-wave systems, with a view to reformulating and studying de Broglie’s double-solution program in the modern language of classical field theory. Notably, the entire family is local and Lorentz-invariant, follows from a variational principle, and exhibits time-invariant, two-way coupling between particle and pilot-wave field. We first introduce a variational framework for generic pilot-wave systems, including a derivation of particle-wave exchange of Noether currents. We then focus on a particular limit of our system, in which the particle is propelled by the local gradient of its pilot wave. In this case, we see that the Compton-scale oscillations proposed by de Broglie emerge naturally in the form of particle vibrations, and that the vibration modes dynamically adjust to match the Compton frequency in the rest frame of the particle. The underlying field dynamically changes its radiation patterns in order to satisfy the de Broglie relation p=ℏk at the particle’s position, even as the particle momentum p changes. The wave form and frequency thus evolve so as to conform to de Broglie’s harmony of phases, even for unsteady particle motion. We show that the particle is always dressed with a Compton-scale Yukawa wavepacket, independent of its trajectory, and that the associated energy imparts a constant increase to the particle’s inertial mass. Finally, we see that the particle’s wave-induced Compton-scale oscillation gives rise to a classical version of the Heisenberg uncertainty principle.
Subjects
Physics and Astronomy (miscellaneous)
General Mathematics
Chemistry (miscellaneous)
Computer Science (miscellaneous)
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.3390/sym16020149
