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

Abstract

We prove the uncertainty relation $T_{\triangle V}\triangle m\stackrel{>}{\sim }2π\hbar /c^2,$ 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'' $τ,$ where $T_{\triangle V}$ is the average passage interval in $τ$ for the events which pass through a small (typical) $(1+D)$-volume $\triangle V,$ and $\triangle m$ 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.