Abstract
A deterministic equation of the Hamilton-Jacobi type is proposed for a single particle:S t+(1/2m)(∇S)2+U{S}=0, whereU{S} is a certain operator onS, which has the sense of the potential of the self-generated field of a free particle. Examples are given of potentials that imply instability of uniform rectilinear motion of a free particle and yieldrandom fluctuations of its trajectory. Galilei-invariant turbulence-producing potentials can be constructed using a single universal parameter—Planck's constant. Despite the fact that the classical trajectory concept is retained, the mechanics of the particle then admits quantum-type effects: an uncertainty relation, de Broglie-type waves and their interference, discrete energy levels, and zero-point fluctuations.
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Sivashinsky, G. Self-turbulence in the motion of a free particle. Found Phys 8, 735–744 (1978). https://doi.org/10.1007/BF00717503
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DOI: https://doi.org/10.1007/BF00717503