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 would argue that there's no more fundamental principle. it's one of those things that has remained true from classical mechanics all the way down to quantum field theory
it's a principle because there's no (as we now know) any a priori reason why Nature chooses the path that makes the integral over kinetic *minus* potential stationary
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We do though, although it hasn't been made very pedagogical. It's basically because we want to make this exact differential: dL = p dv + F dx, and also have the convention that F = - dU/dx https://physics.stackexchange.com/questions/86008/motivation-for-form-of-lagrangian … and https://web2.ph.utexas.edu/~mwguthrie/t.lagrangian.pdf …
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i wouldn't call this an a priori reason though. it just seems to say that it's because it returns the right EOM, but what the 'right' EOM are is an empirical fact
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but that is a bit circular. in the end, you choose the lagrangian that gives you the right equation.
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you're missing the point .. you choose the *general* form of something called a lagrangian and assert that nature must respect the trajectories that make the action stationary .. you need to make definitions some how, right? defining something is not circular
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in a sense, potentials are arbitrary functions, kinetics is just another way to speak about derivatives.
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I believe biology violates it. (See Attila Grandpierre)
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