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.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.

Journal of Mathematical PhysicsAug 1, 20010 citations

Comment on “The Bohr-Sommerfeld Theory and the Uncertainty Principle”

Ralph Klingbeil

American Journal of PhysicsFeb 1, 19731 citation

On the Uncertainty Principle for Proper Time and Mass

Budh Ram

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 $g_{μν} \frac{dx^μ}{d τ}\frac{dx^ν}{d τ}$ .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 $g_{μν} \frac{dx^μ}{d τ}\frac{dx^ν}{d τ}$.

arXiv:math-ph/0212071Dec 26, 20020 citations

Response to “Comment on ‘Entropy and complexity analysis of hydrogenic Rydberg atoms’” [J. Math. Phys. 58, 104101 (2017)]

Sheila López‐Rosa, I. V. Toranzo, Pablo Sánchez-Moreno +1 more

Entropic uncertainty measures for large dimensional hydrogenic systems

Journal of Mathematical PhysicsOct 1, 20172 citations

Comments on ‘‘When is a quantum measurement?’’ [Am. J. Phys. 5 4, 688 (1986)]

Peter John Bussey

American Journal of PhysicsJun 1, 19880 citations

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}