Is the concept of quantum probability consistent with Lorentz covariance?

Abstract

Lorentz-covariant harmonic oscillator wave functions are constructed from the Lorentz-invariant oscillator differential equation of Feynman, Kislinger, and Ravndal for a two-body bound state. The wave functions are not invariant but covariant. As the differential equation contains the time-separation variable, the wave functions contain the same time-separation variable which does not exist in Schr\"odinger wave functions. This time-separation variable can be shown to belong to Feynman's rest of the universe, and can thus be eliminated from the density matrix. The covariant probability interpretation is given. This oscillator formalism explains Feynman's decoherence mechanism which is exhibited in Feynman's parton picture.