Least action

dEdt

Hamilton's principle says that the action for the true path that a system follows will be stationary. As I understand it, the action is almost always least. Is there a reason why nature prefers least action rather over greatest action?

Marioeden

Hamilton's principle says that the action will be stationary but we can certainly say that it won't be a maximum because we can always increase S by taking a faster, wiggly path with T>>0 so you know it won't be a maximum.

However it could still be a saddle point but "Principle of stationary action" doesn't sound as cool as "Principle of Least Action"

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dEdt	Least action Hamilton's principle says that the action for the true path that a system follows will be stationary. As I understand it, the action is almost always least. Is there a reason why nature prefers least action rather over greatest action?

Marioeden	Hamilton's principle says that the action will be stationary but we can certainly say that it won't be a maximum because we can always increase S by taking a faster, wiggly path with T>>0 so you know it won't be a maximum. However it could still be a saddle point but "Principle of stationary action" doesn't sound as cool as "Principle of Least Action"