5 ms·

> It's extremely unintuitive that classical systems should minimize anything like a time or an action. If I get to define the measure arbitrarily, then I can a

> It's extremely unintuitive that classical systems should minimize anything like a time or an action. If I get to define the measure arbitrarily, then I can always find a measure that something else is always a minimum of. So in that sense it's not surprising at all. The interesting question to me is why should that seemingly arbitrary measure be action? What does that even mean, physically? I have no intuition for it. > Think about it: they travel along the minimum path, I'm already stuck here. What would it even mean for a particle to have an "action" (whatever that is) that is not minimized? Like what would that look like, physically? I understand what it means for distance not to be minimized, but action isn't distance...

lambdatronics 3y ago
>What would it even mean for a particle to have an "action" (whatever that is) that is not minimized? The particle doesn't have an action. The trajectory of a particle is what the action is defined in terms of. One way to think of it would be "it's a measure of how much the trajectory deviates from the one dictated by Newton's equations." Pretty much like what you said: "I can always find a measure that something else is always a minimum of." About what a trajectory with non-minimal action would look like: it would be an arbitrary violation of the equations of motion for the system (ex: free particle moving in a zigzag instead of a straight line at constant velocity). Moving in a straight line at constant velocity is what Newtonian mechanics prescribes, and that trajectory will minimize action for the corresponding Hamiltonian.