The relativistic boltzmann equation and two times

L. P. Horwitz

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We discuss a covariant relativistic Boltzmann equation which describes the evolution of a system of particles in spacetime evolving with a universal invariant parameter τ. The observed time t of Einstein and Maxwell, in the presence of interaction, is not necessarily a monotonic function of τ. If t(τ) increases with τ, the worldline may be associated with a normal particle, but if it is decreasing in t, it is observed in the laboratory as an antiparticle. This paper discusses the implications for entropy evolution in this relativistic framework. It is shown that if an ensemble of particles and antiparticles, converge in a region of pair annihilation, the entropy of the antiparticle beam may decreaase in time.

Original languageEnglish
Article number804
Issue number8
StatePublished - 22 Jul 2020

Bibliographical note

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  • Antiparticles
  • Einstein-Maxwell time
  • Entropy flow
  • Invariant world time
  • Relativistic boltzmann equation
  • SHP theory


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