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I'm trying to understand the nature of coordinate transformations in physics. In classical mechanics, we can transform to a different coordinate frame by means of a Galilean transformation. In special relativity, this is replaced by a Lorentz transformation. I am now wondering whether there exists a general notion of coordinate change. More specifically, say we have a function from some manifold M to itself, is there a general set of conditions for this function to qualify as a 'coordinate change'?
(I have encountered the notion of diffeomorphism in the context of general relativity, but I want to confirm whether this is truly the concept I am looking for here.)
(I have encountered the notion of diffeomorphism in the context of general relativity, but I want to confirm whether this is truly the concept I am looking for here.)