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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You can derive the PoLA from Feynman path integrals. This would suggest to me that it, or at least quantum interference, is more fundamental.
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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Writing the Lagrangian for your system gets you the action. It's already something you do before you attempt to minimize it. The point is that you don't have to minimize it, you can just sum over all histories, and the interfernece reproduce the classical least action principle.
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ahh i'm remembering this now .. that's fascinating and would indeed be more fundamental in my book .. 'interference' though i'm not sure i would call quantum interference .. iirc isn't it just that when h->0 you can use steepest descent cause of the ever more rapid oscillations?
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But this approach doesn't make any attempt to minimize it. The only thing that happens is that the paths near the least-action path constructively interfere, and all other paths destructively interfere. But I don't know about more sophisticated approaches, that's your field. :)
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