Self-turbulence in the motion of a free particle

Research output: Contribution to journalArticlepeer-review


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
Issue number9-10
StatePublished - Oct 1978


Dive into the research topics of 'Self-turbulence in the motion of a free particle'. Together they form a unique fingerprint.

Cite this