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 always found this principle a bit "strange". Is it about physics or about math? It looks to me like a funny way to write equations in, say, another form, very useful, but I am not sure about its "fundamentality" from the physics point of view.
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
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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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You can derive the PoLA from Feynman path integrals. This would suggest to me that it, or at least quantum interference, is more fundamental.
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how do you get the path integral without writing down the Lagrangian? We also no that the Euler Lagrange equations are not in general satisfied after quantum corrections
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but you can say the same about equations, in the sense that all of physics can be ultimately expressed as equations. the principle of "equations". in fact, it is even more general because there are equations that cannot be derived from the extremization of an action
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no,in physics you climb the ladder of deduction until you arrive at a point where you cannot make predictions until you make at least one measurement .. you can *think* about them as axioms, but at the end of the day the fact that nature obeys the principle of least action is 1/2
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And now there are studies which are trying to apply it in psychology, statistical learning and machine learning. Same principle with different name. https://en.m.wikipedia.org/wiki/Principle_of_least_effort?wprov=sfla1 …
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