On the Uncertainty Principle for Proper Time and Mass
Abstract
Description
In [J. Math. Phys. {\bf 40}, 1237 (1999)] Kudaka and Matsumoto derive the uncertainty relation $c^2 Δm Δτ\geq \hbar/2$ between the rest mass $m$ and the proper time $τ$, by considering the Lagrangian $M(\dot τ- c^{-1} \sqrt{-g_{μν} \dot x^μ\dot x^ν}) + e A_μ(x) \dot x^μ$. In this note we give an alternative derivation based on a special case of the time-like geodesic equation obtained using the general relativistic Lagrangian $g_{μν} \frac{dx^μ}{d τ}\frac{dx^ν}{d τ}$.
9 pages, uses subeqn.sty
9 pages, uses subeqn.sty