In [J. Math. Phys. { \bf 40}, 1237 (1999)] Kudaka and Matsumoto derive the uncertainty relation $c^2 \Delta m \Delta \tau \geq \hbar/2$ between the rest mass $m$ and the proper time $\tau$, by considering the Lagrangian $M(\dot \tau - c^{ -1} \sqrt{ -g_{ \mu \nu} \dot x^\mu \dot x^\nu}) + e A_\mu (x) \dot x^\mu$. 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 $g_{ \mu \nu} \frac{ dx^\mu}{ d \tau}\frac{ dx^\nu}{ d \tau}$.
Categories: math-ph hep-th math.MP quant-ph