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

In summary, the variational principle can be used on classic fields because it is based on the concept of minimizing a function known as the action. This principle is derived from Newton's laws and the Euler-Lagrange equation, which can both be used to prove each other's validity. It is not fully understood why this works, but it is similar to the unprovable nature of Newton's laws without experimentation. Some suggest that the universe and everything in it is inherently lazy, which aligns with the variational principle.
  • #1
Phymath
184
0
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
 
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  • #2
a posteriori justification aint so bad
 
  • #3
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.
 

What is Field Theory Justification?

Field Theory Justification is the process of validating a theoretical framework, known as a field theory, by confirming its predictions through empirical evidence.

Why is Field Theory Justification important?

Field Theory Justification is important because it allows scientists to demonstrate the validity and usefulness of their theories, which can then be applied to make predictions and inform further research.

What are the steps involved in Field Theory Justification?

The steps involved in Field Theory Justification typically include formulating a hypothesis based on the field theory, designing and conducting experiments or studies to test the hypothesis, analyzing the data collected, and drawing conclusions about the validity of the field theory.

What types of evidence can be used in Field Theory Justification?

Evidence used in Field Theory Justification can include experimental data, observational data, and computational simulations. Additionally, evidence from multiple sources and studies can be combined to strengthen the justification.

Can Field Theory Justification be applied to all fields of science?

Yes, Field Theory Justification can be applied to all fields of science that use theoretical frameworks to explain phenomena and make predictions. This includes fields such as physics, biology, psychology, and sociology.

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