〈 Berger | Dillon 〉

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

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

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

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.