I Can the Principle of Least Action Unify Different Branches of Physics?

AI Thread Summary
The discussion explores the principle of least action as a potential unifying concept across various branches of physics, including classical mechanics and electromagnetism, where it can derive fundamental laws like Newton's second law and parts of Maxwell's equations. The conversation raises questions about its applicability in quantum physics and relativity, suggesting that different actions may be defined in these contexts. It highlights the connection between classical and quantum formulations of the action principle, particularly through Feynman's path integral approach. The dialogue culminates in a philosophical inquiry about whether the principle of least action is the only action that governs physical phenomena. Overall, the principle of least action is posited as a significant candidate for unifying diverse physical theories.
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Does the principle of least action unifies physics in a way that we can say that all the fundamental laws of physics (e.g Newton's 2nd law, Maxwell's equations) we know. can be derived from the principle of least action?
From what I know Newton's 2nd law in classical mechanics can be derived from the principle of least action. Also from what I know, two of the Maxwell's equations (those that contain the time derivatives, i.e. Maxwell-Faraday law and Maxwell-Ampere law) also can be derived from the principle of least action. Of course the action defined is different in these two cases.

I don't know if this can be expanded in quantum physics and relativity, if also there the fundamental laws can be derived from the principle of minimizing some -depending on the case- action.

So is the principle of least action offering some sort of unification of the different branches of physics?
 
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I have the textbook of Dirac on general relativity. There all kind of forces including electromagnetic and gravity are derived from corresponding terms of actions.

Classical version of action principle comes from quantum action principle or integral path method.
 
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In QM, it has to be generalized to Feynman's path integral that sums over all paths. When doing the "saddle-point" approximation to the path integral, we recover the classical principle of extremizing the action.
 
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As we all know...Physics is where the action is!
 
Actually its mostly where the action isn't
 
hutchphd said:
Actually its mostly where the action isn't
Touche'

But isn't the least action ultimately the only action?
 
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