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Foundations of Physics

, Volume 8, Issue 9–10, pp 735–744 | Cite as

Self-turbulence in the motion of a free particle

  • G. Sivashinsky
Article

Abstract

A deterministic equation of the Hamilton-Jacobi type is proposed for a single particle:St+(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.

Keywords

Energy Level Single Particle Uncertainty Relation Free Particle Classical Trajectory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    J. A. Wheeler, Superspace and Nature of Quantum Geometrodynamics, inTopics in Nonlinear Physics, N. J. Zabusky, ed. (Springer-Verlag, 1968).Google Scholar
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    A. Einstein,Elementare Überlegungen zur Interpretation der Grundlagen der Quanten-Mechanik (Scientific papers presented to Max Born), (Oliver and Boyd, Edinburg, 1953), pp. 33–40.Google Scholar

Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • G. Sivashinsky
    • 1
  1. 1.Department of Mathematical Sciences, Division of Applied MathematicsTel-Aviv UniversityRamat-Aviv, Tel-AvivIsrael

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