# Different equivalent representations for same physics

I want to expand my understanding of physics and just watched a Feynman lecture where he said "every theoretical physicist who is any good knows six or seven different theoretical representations for exactly the same physics".

Trying to think of such different representations, I can see mechanics which can be approached from Newton's laws or the Lagrangian way. For gravity there would be the classical gravitation law and the general relativity way. But that's about where it ends for me. What other alternative ways of looking at physics are there?

• Perhaps think smaller. For a given classical mechanics problem, how many different ways are there to set up the Lagrangian? Picking a different set of independent variables yields a different Lagrangian, but solves the exact same problem. Some formulations will be much easier to solve than others, yet they all describe the same physical system. Sometimes I think that the development of 'physical insight' is driven by a distaste for long ugly equation crunching - identify the right way of looking at the problem and it is easy. – Jon Custer Jul 1 '14 at 18:34