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arXiv · hep-th/9604106

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

L. Burakovsky·L. P. Horwitz
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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.

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L. Burakovsky, L. P. Horwitz. 1996-04-18. Mass - Proper Time Uncertainty Relation in a Manifestly Covariant Relativistic Statistical Mechanics. https://arxiv.org/abs/hep-th/9604106

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