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wedrifid comments on The Graviton as Aether - Less Wrong
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Is there a single example of this that you can think of? There are the different ways of computing classical mechanics (Newtonian, Lagrangian, Hamiltonian), but these were known to be just different ways of doing the same math at the time of discovery.
No, it's just a theoretical property of the 'A, B, X' abstraction that you mention. In fact, it would not surprise me if the general problem of proving whether or not two theories are exactly equivalent is intractable in a similar way to the halting problem.