The most fundamental principle in physics is called 'The Principle of Least Action'. It also happens to be a good principle to live by during these trying times
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I actually think it is a kinda of a priori reason in a way because I think this really is implicitly defining what we mean by "force".
hmm i think i disagree with you on this one about this being a purely mathematical statement.
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It is a consequence of the convention F = - dU/dx. That minus sign is what caries through to make the minus sign in L = T-U.
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right but the *relative* minus sign, no matter where it goes, is physical. That's the empirical fact i'm talking about. The fact that nature wants to "go downhill", as it were.
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