How would you apply the lagrangian in special relativity? How do you interpret the expression?
The action is given by: $$S=-mc^2 \int d\tau$$
where $m$ is the rest mass. If I understand correctly the relativistic stationary principle maximizes the proper time of a particle. In other words a particle takes the path between two points in spacetime that maximises the spacetime interval.
However what does the mass term change about that exactly? Does a particle rather 'prefer' being massive or rather not? For example if we look at a pion that decays into 2 photons. It seems the preference is to transform the rest mass into energy. Is this true?
How do you interpret the relativistic action and how does the mass $m$ change it?
I am looking for a proper interpretation.
