The principle of stationary action

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Dated: 8 September 2018

This arose from a discussion, in which my interlocutors defended the idea that physics makes particles follow a path of least action always (whenever we have a Hamiltonian description). I show by a simple counterexample that often the action is only stationary, i.e. neither a minimum nor a maximum, rather a saddle point. With pre-relativistic Lagrangians of the form L=T-V, the action is never a local maximum (but can be a saddle point). The standard form of the relativistic Lagrangian, on the other hand, leads, for finite-mass particles to either a saddle point or a maximum of the action, never a local minimum.

The principle of stationary action, 08.09.2018

Next: Potentials in Newtonian mechanics   Up: Introduction science education project    Previous: Identically accelerating twins

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