Lorentz Covariance and Internal Space-time Symmetry of Relativistic Extended Particles

Abstract

The difference between Lorentz invariance and Lorentz covariance is discussed in detail. A covariant formalism is developed for the internal space-time symmetry of extended particles, especially in connection with the insightful observations Feynman made during the period 1969-72. A Lorentz-group formalism is presented for the harmonic oscillator model of Feynman, Kislinger and Ravndal, which was originally based on hadronic mass spectra. This covariant version allows us to construct a parton distribution function by Lorentz-boosting the oscillator wave function of a hadron at rest. The role of the time-separation variable is discussed in detail. It is shown that, due to our inability to make measurements on this variable, it belongs to Feynman's rest of the universe. Our failure to observe the rest of the universe leads to an increase in entropy.