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What is the meaning of the word principle in Physics? For example in the "action principle". Is it an action law, an action equation, or an unproved assumption? (I have an idea what an action is). What confuses me is when I find the expression as in: "...an action principle is defined..." when a Lagrangian is constructed for a system.

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I found this in this Wikipedia link: H.D. Young, R.A. Freedman (2004). University Physics with Modern Physics (11th ed.). Addison Wesley. p. 2. "Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns and principles that relate these phenomena. These patterns are called physical theories or, when they are very well established and of broad use, physical laws or principles." –  Anuar Nov 20 '12 at 18:53
    
Thank you. What confuses me is when I find the expression as in: "...an action principle is defined..." when a Lagrangian is constructed for a system. –  Stefanos Rotas Nov 20 '12 at 19:00
    
why does it it confuse you? When the Lagrangian is constructed or known, you can use the principle of extremal action in a precise manner to understand the behaviour of the system. –  Prathyush Nov 20 '12 at 19:06
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Related: physics.stackexchange.com/q/35660/7924 –  Arnold Neumaier Nov 21 '12 at 10:08

3 Answers 3

That a physical theory/model with an action functional $S[q]= \int \!dt~L $

means by definition that the classical$^1$ equations of motion for the theory are precisely the Euler-Lagrange equations.

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$^1$Here the word classical is used in the sense that Planck's constant $\hbar=0$ is set to zero.

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Thank you. It sounds like achieving a landmark step. And if the Lagarngian becomes covariant then we specify a gauge principle. –  Stefanos Rotas Nov 20 '12 at 19:14

Unfortunately, there is not a standard meaning in physics. Often physicists take the term "principle" with a meaning close to that of "axiom" i.e. as a basic element which applies to any object within the range of applicability of the model/theory. The important difference between mathematicians concept of axiom and physicists concept of principle is that the principles are related to experiments whereas the axioms in math are selected only in basis to formal criteria.

An traditional example of the this meaning of the term "principle" is found in thermodynamics: E.g. first and second principles, although often they are called "laws" of "postulates". Another example is in the common phrase "first-principle computation", which means that you perform a computation in term of basic fundamental properties.

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Thank you for your answer. From the discussion, if I may say, "an action principle is constructed" when a more explicit expression is found that conforms with a group theoretic equivalence. Hence the indefinite article. –  Stefanos Rotas Nov 20 '12 at 19:31

My understanding of physics is that It must order human experience into a logically coherent picture.

The "principle of extremal action" is the logical foundation to understand the behaviour of classical objects. It allows us to single out the correct or experimentally observed description of the object under investigation out of a multitude of possibilities.

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