In mechanics, the only physical route a particle can take is the one where action is minimized. Why is this true? Is there a proof?
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The principle of least action is a misnomer. The proper name is the principle of stationary action, because the action is not always minimized. – G. Smith Oct 20 '20 at 17:17
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Whoops. Where does stationary action come from? – Oct 21 '20 at 18:39
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From the same place that any physical law comes from. Nobody knows why there are any physical laws at all. – G. Smith Oct 21 '20 at 18:57
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That is untrue. Newton's second law is derived from this principle, as an example. – Oct 21 '20 at 22:36
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That is a non sequitur. There are equivalent mathematical formulations of various physical laws, but neither the Principle of Stationary Action nor Newton’s Second Law need to hold in the physical world for any a priori reason. – G. Smith Oct 22 '20 at 00:05
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You are right. I suppose that by "law" you meant more of an axiom. However, Newton's Second Law is more of a theorem. I suppose Stationary action is more of an axiom. – Oct 22 '20 at 17:59