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The Different Theories of Hamiltonian Mechanics
I think that it is impossible to imagine a case where tomorrow we will do an experiment that says one is right and the other one is wrong. I mean, in the case of Hamiltonian mechanics versus Lagrangian mechanics, you can literally start from the equations of one and derive the equations of the other. There's no improvement of one over the other. The reason why you think there's an improvement is because you often have incomplete information. One way of thinking about those skeptical scenarios is that they're trying to describe a way things could be observationally equivalent for us but the underpinnings of reality be radically different.