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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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.
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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That is our convention of what "down" means.
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yes, but it's the fact that nature chooses one thing over the other no matter what we call it, mathematically represented as a minus sign
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what is physical here is that we are speaking of equations defining some geometry.
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I was speaking about the sign and its relation to simplectic geometry
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