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arXiv · 1409.7036

Schroedinger vs. Navier-Stokes

P. Fernandez de Cordoba·J. M. Isidro·J. Vazquez Molina
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Abstract

Quantum mechanics has been argued to be a coarse-graining of some underlying deterministic theory. Here we support this view by establishing a map between certain solutions of the Schroedinger equation, and the corresponding solutions of the irrotational Navier-Stokes equation for viscous fluid flow. As a physical model for the fluid itself we propose the quantum probability fluid. It turns out that the (state-dependent) viscosity of this fluid is proportional to Planck's constant, while the volume density of entropy is proportional to Boltzmann's constant. Stationary states have zero viscosity and a vanishing time rate of entropy density. On the other hand, the nonzero viscosity of nonstationary states provides an information-loss mechanism whereby a deterministic theory (a classical fluid governed by the Navier-Stokes equation) gives rise to an emergent theory (a quantum particle governed by the Schroedinger equation).

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P. Fernandez de Cordoba, J. M. Isidro, J. Vazquez Molina. 2014-09-24. Schroedinger vs. Navier-Stokes. https://arxiv.org/abs/1409.7036

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