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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?

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  • $\begingroup$ 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. $\endgroup$ – Jon Custer Jul 1 '14 at 18:34
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The quote continues: "He knows that they are all equivalent, and that nobody is ever going to be able to decide which one is right..."

So I don't think classical gravitation versus generally relativity is a good example, because they can be distinguished experimentally.

Perhaps the Schrodinger versus Heisenberg formulations of quantum mechanics.

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  • $\begingroup$ True, good point. $\endgroup$ – Basti Jul 1 '14 at 19:50
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I think you are just being a bit too broad in your categories. Take for example classical mechanics. Yes there is a broad split between newtonian and analytical mechanics, but within each of those there is a range of pictures you can use to understand a situation. On the analytic side there is the Lagrangian and Hamiltonian formulation. On the Newtonian side you can think about the problem in terms of force, energy, angular momentum, etc. Yes there is a certain amount of overlap but I would say that for most problems I could tell you about what is going on in terms of most of those concepts individually (though it would not necessarily be very concise or insightful)

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