Mass - Proper Time Uncertainty Relation in a Manifestly Covariant Relativistic Statistical Mechanics

Abstract

We prove the uncertainty relation $T_{△V}△m\stackrel{>}{\sim }2\pi \hslash /c^2,$ which is realized on a statistical mechanical level for an ensemble of events in $(1+D)$-dimensional spacetime with motion parametrized by an invariant ``proper time'' $\tau ,$ where $T_{△V}$ is the average passage interval in $\tau$ for the events which pass through a small (typical) $(1+D)$-volume $△V,$ and $△m$ is the dispersion of mass around its on-shell value in such an ensemble. We show that a linear mass spectrum is a completely general property of a $(1+D)$-dimensional off-shell theory.

Latex, 13 pages