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

Click For Summary

Discussion Overview

The discussion centers on the potential of the principle of least action to unify various branches of physics, including classical mechanics, electromagnetism, quantum mechanics, and general relativity. Participants explore whether fundamental laws across these domains can be derived from a common action principle.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant notes that Newton's 2nd law and certain Maxwell's equations can be derived from the principle of least action, suggesting a connection between classical mechanics and electromagnetism.
  • Another participant references Dirac's textbook on general relativity, indicating that various forces, including electromagnetic and gravitational forces, can be derived from corresponding action terms.
  • A participant mentions that in quantum mechanics, the principle must be generalized to Feynman's path integral, which sums over all possible paths, and that the classical principle emerges through the saddle-point approximation.
  • Some participants engage in a light-hearted exchange about the nature of "action" in physics, with one asserting that it is where the action is, while another counters that it is mostly where the action isn't.
  • A later reply questions whether the least action is ultimately the only action, adding a layer of philosophical inquiry to the discussion.

Areas of Agreement / Disagreement

Participants express various viewpoints on the unifying potential of the principle of least action, with no clear consensus reached. Some agree on its applicability across different domains, while others introduce skepticism or alternative interpretations.

Contextual Notes

There are unresolved assumptions regarding the applicability of the principle of least action in different contexts, particularly in quantum physics and relativity. The discussion also reflects a dependence on specific definitions of "action" across different theories.

Who May Find This Useful

This discussion may be of interest to those studying theoretical physics, particularly in the areas of classical mechanics, electromagnetism, quantum mechanics, and general relativity, as well as those interested in the philosophical implications of unifying principles in physics.

Delta2
Homework Helper
Insights Author
Messages
6,002
Reaction score
2,628
TL;DR
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?
 
Physics news on Phys.org
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.
 
  • Like
Likes   Reactions: atyy and Delta2
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.
 
  • Informative
  • Like
Likes   Reactions: fresh_42 and Delta2
As we all know...Physics is where the action is!
 
  • Like
Likes   Reactions: hutchphd
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?
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
4K
  • · Replies 19 ·
Replies
19
Views
5K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 31 ·
2
Replies
31
Views
7K
  • · Replies 0 ·
Replies
0
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 19 ·
Replies
19
Views
2K