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

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SUMMARY

The discussion centers on the Principle of Least Action and its potential to unify various branches of physics, including classical mechanics, electromagnetism, quantum mechanics, and general relativity. It is established that Newton's 2nd law and two of Maxwell's equations can be derived from this principle, indicating its foundational role in physics. The conversation also highlights the transition from classical action principles to quantum mechanics through Feynman's path integral formulation, suggesting a deeper connection across different physical theories.

PREREQUISITES
  • Understanding of Newton's 2nd Law in classical mechanics
  • Familiarity with Maxwell's equations, specifically the Maxwell-Faraday and Maxwell-Ampere laws
  • Knowledge of quantum mechanics and Feynman's path integral formulation
  • Basic concepts of general relativity as presented in Dirac's textbook
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  • Research the derivation of Newton's 2nd Law from the Principle of Least Action
  • Explore the implications of Feynman's path integral in quantum mechanics
  • Study the relationship between action principles and general relativity
  • Investigate how the Principle of Least Action applies to modern physics theories
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Physicists, students of physics, and researchers interested in the foundational principles that unify classical and modern physics, particularly those exploring the intersections of mechanics, electromagnetism, and quantum theory.

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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!
 
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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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