Off-mass-shell dynamics in flat spacetime

Foundations of Physics 27 (3):389-414 (1997)
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In the covariant Hamiltonian mechanics with action-at-a-distance, we compare the proper time and dynamical time representations of the coordinate space world line using the differential geometry of nongeodesic curves in 3+1 Minkowski spacetime. The covariant generalization of the Serret-Frenet equations for the point particle with interaction are derived using the arc length representation. A set of invariant point particle kinematical properties are derived which are equivalent to the solutions of the equations of motion in coordinate space and which are functions of either the proper time or the dynamical time. Expressions for the quantities are given for the example of the covariant harmonic oscillator and comments are offered regarding the measurability of the dynamical time



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Relativity: The Special Theory.John Lighton Synge - 1965 - Interscience Publishers, New York,].
Statistical mechanics analysis of the “twins paradox”.Uri Ben-Ya'acov - 1995 - Foundations of Physics 25 (12):1733-1740.

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