- #106
member 11137
The experiment for the actual discussion here is the Morley and Michelson experiment.Fredrik said:How am I "already imposing linearity"? I'm starting with "takes straight lines to straight lines", because that is the obvious property of inertial coordinate transformations, and then I'm using the theorem to prove that (when spacetime is ℝ4) an inertial coordinate transformation is the composition of a linear map and a translation. I don't think linearity is obvious. It's just an algebraic condition with no obvious connection to the concept of inertial coordinate transformations.
Right, if we add that to our assumptions, we can eliminate the Galilean group as a possibility. But I would prefer to just say this: These are the two theories that are consistent with a) the idea that ℝ4 is the underlying set of "spacetime", and b) our interpretation of the principle of relativity as a set of mathematically precise statements about transformations between global inertial coordinate systems. Now that we have two theories, we can use experiments to determine which one of them makes the better predictions.
Intuitively (I am not a specialist) this means that that isomorphism holds true only locally (on short distances around the observer). There is not really a global inertial coordinate system (except on the paper, in theory). And (as far I understand the generalized version of the theory) this is a crucial point. Among others things, this was forcing us (Weyl's work) to introduce the concept of parallel transport and of connection.How is that a correction? It seems like an unrelated statement.