Comment on “Uncertainty principle for proper time and mass” [J. Math. Phys 40, 1237 (1999)

Abstract

Kudaka and Matsumoto derive the uncertainty relation c2ΔmΔτ≈h between the proper time τ and rest mass m of a material particle by adopting for the description of the particle the Lagrangian L=M(τ̇−c−1−gμνẋμẋν)+eAμ(x)ẋμ, defined on the enlarged space (xμ,τ,M), where M is an additional dynamical variable. A key step in the derivation of their uncertainty relation is the identification of the variable M with the rest mass m. Adopting the point of view of variational analysis, we show that such an identification goes against the relativistic requirement of the path dependence of proper time.