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Astrophysics

, Volume 61, Issue 3, pp 370–374 | Cite as

Note on the Interpretation of Proper Mass as a Constant Lagrange Multiplier

  • R. A. Krikorian
Article
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The timelike world line C0 of a free particle is a maximizing curve for the integral I = ∫ds in the class Γ of neighboring admissible timelike curves joining the events A, B, and satisfying the side-condition imposed on the 4-velocity \( \upvarphi ={g}_{ij}\ {\overset{\cdot }{x}}^i{\overset{\cdot }{x}}^j=1\left({\overset{\cdot }{x}}^i={dx}^i/ ds\right) \). Considering the problem of extremizing integral I as a time optimal problem, we show that the multiplier λ (s) associated with the equation φ = 1 is constant along C0 and may be identified with the proper mass m of the free particle. The constancy of m can thus be regarded as a consequence of the path dependence of proper time.

Keywords

proper mass: Lagrange multiplier 

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Collège de France - Sorbonne Université, CNRS, Institut d’Astrophysique de ParisParisFrance

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