Can the Variational Principle Explain the Laws of Nature for Classic Fields?

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SUMMARY

The discussion centers on the application of the variational principle to classical fields, emphasizing its role in deriving Newton's laws and the Euler-Lagrange equation. Participants explore the foundational nature of the variational principle, questioning whether it is a fundamental law of nature or merely a derived concept. The conversation highlights the philosophical implications of the principle, suggesting that it reflects a tendency towards minimal action in the universe. Recommendations for further reading on the topic are also sought.

PREREQUISITES
  • Understanding of the variational principle in physics
  • Familiarity with classical mechanics, specifically Newton's laws
  • Knowledge of the Euler-Lagrange equation
  • Basic concepts of field theory
NEXT STEPS
  • Research the derivation of Newton's laws from the variational principle
  • Study the Euler-Lagrange equation in detail
  • Explore classical field theory and its applications
  • Read foundational texts on the variational principle, such as "The Calculus of Variations" by Gelfand and Fomin
USEFUL FOR

Physicists, students of classical mechanics, and anyone interested in the philosophical implications of physical laws and the variational principle.

Phymath
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I'm trying to understand why you can get away with using the variational principle on classic fields at all. The variational principle says minimize some value of a function the action. This idea is for point particles and is also motivated by the fact that Newton's laws can be derived via the action principle also be used to prove the validity of the Euler-Lagrange function, and also vice versa Newtons laws can be used to derive the Euler-Lagrange equation for classic particles. So how is it at all possible that variation of a field in a local area gives the correct formulation of the laws of nature, is there any reason this works and any motivations that this should work?

Is this just a law of nature that can not be derived similar to Newtons laws being simply stated and unprovable without experimentation. Any book suggestions would also be useful
 
Physics news on Phys.org
a posteriori justification aint so bad
 
I took the variational principle to simply mean the universe, and everything in it, is as lazy as possible. This is in agreement with my personal experience since I am as lazy as possible as well.
 

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