On the Uncertainty Principle for Proper Time and Mass

2002/12/26 by B. Ram, Ram, B.
Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #hep-th #math-ph #math.MP #quant-ph

paper · pdf · doi:10.48550/arxiv.math-ph/0212071

9 pages, uses subeqn.sty

arxiv created 2002/12/26 · arxiv updated 2009/11/30

Abstract

In [J. Math. Phys. \bf 40, 1237 (1999)] Kudaka and Matsumoto derive the uncertainty relation c² Δm Δτ≥ ℏ/2 between the rest mass m and the proper time τ, by considering the Lagrangian M( τ- c^-1 √-g_μν x^μ x^ν) + e A_μ(x) 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 (dx^μ)/(d τ)(dx^ν)/(d τ).

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