JohnDenker
commented
8 years ago For the next level of detail on "law" and the various synonyms, see https://www.av8n.com/physics/scientific-methods.htm#main-rule-law
For a discussion of the word "theory" and its various meanings, see https://www.av8n.com/physics/scientific-methods.htm#main-theory and https://www.av8n.com/physics/scientific-methods.htm#sec-kyrio
From @JohnDenker: Also from page 2 of the book: Currently it says: "A law tells us /what/ happens [....]
A theory tells us /why/ something happens [....]"
If somebody asks me the difference between law and theory, the short answer is "nobody knows and nobody cares. In this course we focus on things that are actually important, and that ain't one of them."
-- Newton's theory of gravity does not explain "why" F=GmM/r^2 any more than Newton's laws explain "why" F=ma. -- The theory of special relativity does not explain "why" E=mc^2, whereas the law of unintended consequences explains a lot.
As for "why": Galileo is recognized as the father of modern science because he made it clear that science is supposed to say /what/ happens. It may or may not explain /how/ it happens, and the fundamental laws and theories almost never explain /why/ it happens. This is what separates physics from metaphysics, philosophy, and religion.
If somebody wants a longer answer, I point out that in practice, there are at least a dozen words in this family: Gauss’s law. Newton’s method. Cramer’s rule. Euler’s identity. Parseval’s theorem. Maxwell’s equations. Pascal’s principle. Watzlawick’s axioms. The Lorentz transformation. The Euclidean algorithm. The Tolman relation. The Kutta condition. The Cauchy criterion. The quadratic formula. The big-bang model.
It is a fool's errand to attempt to draw distinctions here. For example, there is absolutely no basis -- other than historical accident -- why the Maxwell equations and the Maxwell relations have those names and not vice versa.
There is a lot more I could say about this, but I'll stop here.