Are elementary particles vortices in a 'vacuum' fluid?
Daniël Bischoff van Heemskerck
Quantum theory and relativity exhibit several formal analogies with fluid mechanics. This paper examines under which conditions a classical fluid model may reproduce the simplest formulations of both theories. By identifying the angular momentum of irrotational vortices in an inviscid, barotropic, isothermal fluid with sound speed c with the reduced Planck constant, and incorporating Korteweg capillary stress, a complex wave equation describing the momentum and continuity fields of a vortex is obtained. When uniform convection is introduced, the weak field approximation of this wave equation is equivalent to Schrödinger’s equation. The model is shown to yield classical analogues for de Broglie wavelength, the Einstein–Planck relation, the Born rule and the uncertainty principle. Accounting for the retarded propagation of the wavefield of a vortex in convection yields the Lorentz transformation and the Klein–Gordon equation, with Schrödinger’s equation appearing as the low-Mach-number limit. These results demonstrate that, under explicit assumptions, a classical continuum can reproduce quantum and relativistic theory in their simplest form, without assuming the postulates principal to those theories.
•Dec 20, 2025•0 citations