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The question in question: Why isn't the principle of least action named as "the principle of optimization"?

I suppose that one solution is to define what optimization/optimal state/optimized state is. This brings to a new question: would asking "How is optimization/optimal state/optimized state defined in physics?" be opinion-based?

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    $\begingroup$ What sort of answer are you looking for? Names are determined historically by what sticks, and it seems that you are inherently asking for people's opinion on other possible names. $\endgroup$
    – fqq
    Aug 15, 2021 at 8:15
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    $\begingroup$ Related: physics.meta.stackexchange.com/q/1083/2451 $\endgroup$
    – Qmechanic Mod
    Aug 16, 2021 at 7:11

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Your question is asking about a name, and the names of ideas in physics are often historical accidents that have little significance. So in general it's a bit pointless asking why a particular name was chosen.

In this case the name principle of least action is actually appropriate - well almost. It's because for any trajectory we can calculate the action and then we find the trajectory for which this value is least. Hence least action.

I say almost because we actually extremise the action i.e. it can be a minimum or a maximum, but as I said the names for things in physics are often not especially appropriate. Anyhow, principle of extreme action sounds like a gangster movie :-)

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  • $\begingroup$ I understand why the name "principle of least action" is appropriate. Hmm, maybe I should ask "would it still correct to call the principle of least action the principle of optimization?"? Or "Does principle of least action imply optimization?"? Because optimization is, at least, a different concept to action $\endgroup$
    – Ooker
    Aug 15, 2021 at 9:48
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    $\begingroup$ @Ooker "optimisation" is finding the "best" value for something, but "best" is a rather meaningless concept because it depends on what you consider to be "good". By contrast "least" is unambiguous. $\endgroup$
    – John Rennie
    Aug 15, 2021 at 10:38
  • $\begingroup$ I see. I wonder if saying that "the universe finds least action is good" is a stretch? Also, why not "the principle of minimal action"? $\endgroup$
    – Ooker
    Aug 15, 2021 at 10:59
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    $\begingroup$ I doubt the universe cares what we think is "good" :-) $\endgroup$
    – John Rennie
    Aug 15, 2021 at 11:00
  • $\begingroup$ @Ooker, I think anchovies and pineapple are "good" on pizza, while other people think differently. That makes the word "good" opinion-based. It's not allowed in questions on Stack Exchange sites. ¶ Well, it is, but only when it is specifically defined first, as in "assuming a 'good' result is one that is within 5% of reality, would … produce a good result?" or as in "assuming 'goodness' means the square root of the absolute value of error, does method 'X' produce a better result than method 'Y'. $\endgroup$
    – Ray Butterworth
    Aug 15, 2021 at 13:12
  • $\begingroup$ To quote John Rennie: > "optimisation" is finding the "best" value for something, but "best" is a rather meaningless concept because it depends on what you consider to be "good". By contrast "least" is unambiguous. <-- I didn't think about that. In retrospect the reason I didn't see why "optimisation" opinion-based was because I assumed that the least action was a "good" value already. $\endgroup$
    – Ooker
    Aug 15, 2021 at 14:32
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Perhaps it can be asked on chat?

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