Spontaneous predictivisation

Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 162)


In the first section of this paper we define the concept of an Attractor of a hereditary first order differential equation as an ordinary differential equation whose solutions are solutions of the hereditary one and can be interpreted as the asymptotes of its generic solutions. We define also the concept of Predictive Differential Equations associated with a class of hereditary ones depending on a coupling constant G as a first order differential equation which is such that all its solutions are solutions of the corresponding hereditary one and which is analytic in the neighbourhood of G = 0. We report some numerical work proving that for some hereditary equations the corresponding predictive ones are Attractors.

In the second section we consider the retarded electromagnetic equations of two point charges and we prove numerically in a particular case that the associate Predictive Poincaré Invariant System defined in previous papers is an Attractor in an obviously generalized sense. Roughly speaking this means that the retarded electromagnetic equations of motion have a built-in mechanism which causes a spontaneous predictivisation of the causal interaction.


Physical Review Order Differential Equation World Line Causal Interaction Neutral Type 
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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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • L. Bel
    • 1
  1. 1.Institut Henri Poincaré - 11Equipe de Recherche Associée au C.N.R.S. n° 533ParisFrance

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