"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."
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[ 3.2 ms ] story [ 21.0 ms ] threadI 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
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.
Also, something interesting I came across - the Euler-Lagrange equations do have a quantum analogue as well: https://en.wikipedia.org/wiki/Schwinger%E2%80%93Dyson_equati...
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."
https://www.dbooks.org/foundations-of-quantum-theory-3319517...
(beware of the Bohr Topos)