- #1
nomadreid
Gold Member
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I am having problems getting any intuitive idea on the concept of Action (as in the Principle of the Least...) when the Lagrangian is T-V. Every site I visit starts with the mathematical formulation, which is fine, and I understand that not every physical concept comes with an intuitive idea, but most concepts outside of quantum mechanics (and even some of them in quantum physics) have their basis in a historical development that, even if the concepts have evolved into something more abstract, at least gives some conceptual anchor. For example, momentum is an operator and all that, but it began as a more tangible concept ("oomph") that one can at least refer to before heading off into calculations. Energy has always been abstract, but even "caloric fluid" was better than nothing. Time doesn't have an operator as such, but it is like a US Supreme Court judge said: that he couldn't define hard-core porno, but he knew it when he saw it. Often the units give a clue; sometimes a graph or analogy, or occasionally even everyday usage. And so forth. But Action...? It doesn't seem to correspond to the everyday use of the term, and the units of Energy integrated over time, joules-seconds, don't seem to correspond to anything except Planck's constant (which, as a proportionality constant, doesn't give much to cling to) or momentum over distance (also a combination that corresponds to no good intuition), the area under a curve of energy versus time doesn't help, and historically Action seems to have arisen as a purely more convenient method for classical problems (and extended to less classical problems) than the cumbersome contortions of the combination of conservation of energy and momentum. The analogy of the principle of least action with the fact that "lightning follows the path of least resistance" does not seem to be a very good analogy. And so forth. So, can someone forgive my wordiness and supply me with an intuitive idea on which to hang my conceptual hat for Action, without simply stating the equations it works for or how one can use Lagrangian mechanics to derive other (more intuitive) physical principles, or how nice it is in the context of Noether's Theorem, etc.? Thanks.