Self-turbulence in the motion of a free particle

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Abstract

A deterministic equation of the Hamilton-Jacobi type is proposed for a single particle:St+(1/2m)(∇S)2+U{S}=0, where U{S} is a certain operator on S, 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 yield random 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.

Original languageEnglish
Pages (from-to)735-744
Number of pages10
JournalFoundations of Physics
Volume8
Issue number9-10
DOIs
StatePublished - Oct 1978

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