"All known theories of physics - from classical mechanics all the way to general relativity quantum field theory - can be written in this way: a collection of objects and a recipe to build a Lagrangian from those objects, with the movement of those objects determined by a path that minimizes the Lagrangian."
I think Quantum Mechanics doesn't reduce to this, it's a probabilistic theory.
Thanks for the link! I'm a huge fan of Peter Woit - his blog especially.
So my understanding is that while the way Lagrangians are written in classical theory doesn't extend directly to quantum mechanics, the concept of a Lagrangian is still useful since the Lagrangian can be fed into the path integral formulation (as opposed to being used as an input to the Euler-Lagrange equations). Also, in quantum field theory the starting point for canonical second quantization is typically a Lagrangian, where the fields are changed to operator fields.
A while ago I read in Klaas Landsman's Book, it is very nice: "This book studies the foundations of quantum theory through its relationship to classical physics."
I think Quantum Mechanics doesn't reduce to this, it's a probabilistic theory.
A similar take from Peter Woit:
https://www.math.columbia.edu/~woit/laguardia.pdf