Comment on ``On Derivations of the Uncertainty Principle''

Ralph Klingbeil

Shoju Kudaka, Shuichi Matsumoto

DaeKil Park, Eylee Jung

Recently in Phys. Rev. D 99, 104010 (2019), the nonrelativistic Feynman propagator for a harmonic oscillator system was presented when the generalized uncertainty principle is employed. In this short Comment we show that the expression is incorrect, and we derive its correct form.

Ernest R. Davidson

R. A. Krikorian

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.