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This theoretical study establishes a mathematical equivalence between fluid-mechanical Euler-Korteweg vortex models and fundamental quantum equations like Schrödinger's and Klein-Gordon. By mapping fluid properties such as angular momentum and capillary stress to quantum constants, the work provides a formal analogue for phenomena including the de Broglie wavelength and the uncertainty principle. While the results offer an elegant mathematical bridge between classical fluid dynamics and quantum mechanics, they remain a theoretical construct rather than a new physical mechanism for quantum computation or engineering.
Euler-Korteweg vortices: A fluid-mechanical analogue to the Schr\"odinger and Klein-Gordon equations
arXiv:2512.23771v4 Announce Type: replace Abstract: Quantum theory and relativity exhibit several formal analogies with fluid mechanics. This paper extends upon known analogies by showing that under specific assumptions, an Euler-Korteweg vortex model can be cast into equations that are mathematically equivalent to the Schr\"odinger and Klein-Gordon equations. By assuming that the angular momentum of an irrotational vortex in an inviscid, barotropic, isothermal fluid with sound speed c is equal in magnitude to the reduced Planck constant, and incorporating Korteweg capillary stress, a complex wave equation describing the momentum and continuity equations of an Euler-Korteweg vortex is obtained. When uniform convection is introduced, the weak field approximation of this wave equation is formally equivalent to Schr\"odinger's equation. The model is shown to yield analogues to de Broglie wavelength, the Einstein-Planck relation, the Born rule and the uncertainty principle. Accounting for the retarded propagation of the wave field of a vortex in convection requires the Lorentz transformation and yields a wave equation mathematically equivalent to the Klein-Gordon equation, with Schr\"odinger's equation appearing as the low-Mach-number limit.
Abstract:Quantum theory and relativity exhibit several formal analogies with fluid mechanics. This paper extends upon known analogies by showing that under specific assumptions, an Euler-Korteweg vortex model can be cast into equations that are mathematically equivalent to the Schrödinger and Klein-Gordon equations. By assuming that the angular momentum of an irrotational vortex in an inviscid, barotropic, isothermal fluid with sound speed c is equal in magnitude to the reduced Planck constant, and incorporating Korteweg capillary stress, a complex wave equation describing the momentum and continuity equations of an Euler-Korteweg vortex is obtained. When uniform convection is introduced, the weak field approximation of this wave equation is formally equivalent to Schrödinger's equation. The model is shown to yield analogues to de Broglie wavelength, the Einstein-Planck relation, the Born rule and the uncertainty principle. Accounting for the retarded propagation of the wave field of a vortex in convection requires the Lorentz transformation and yields a wave equation mathematically equivalent to the Klein-Gordon equation, with Schrödinger's equation appearing as the low-Mach-number limit.
Quantum Physics (quant-ph); General Relativity and Quantum Cosmology (gr-qc); Fluid Dynamics (physics.flu-dyn)
arXiv:2512.23771 [quant-ph]
(or arXiv:2512.23771v4 [quant-ph] for this version)
From: Daniël M.F. Bischoff Van Heemskerck [view email] [v1] Mon, 29 Dec 2025 07:38:30 UTC (48 KB) [v2] Tue, 10 Feb 2026 21:52:11 UTC (48 KB) [v3] Mon, 23 Feb 2026 06:20:00 UTC (48 KB) [v4] Thu, 4 Jun 2026 20:13:50 UTC (19 KB)
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