A beginner's question:
I have always understood that (four-dimensional) Minkowski spacetime can be recovered up to a constant factor—i.e. 'up to a dilation' or 'up to global scale'—from its causal structure. That is to say, I understand that whereas the symmetry group of Minkowski spacetime is the Poincaré group, the symmetries of its causal structure are the Poincaré group + dilations.
Recently, I was told that Minkowski geometry can only be recovered up to local scale from its causal structure. And elsewhere, I have now read that Minkowski geometry can be recovered up to a conformal factor from its causal structure.
Which is it, and how significant is the difference between a global constant factor, a local constant factor, and a conformal factor?