Looking for clarification on something. Take the metric in this form ds^2 = dt^2 - dx^2 Brian Green likes to say a null path is one where motion through space is shared equally with motion through time, or (ds=0). Motion through space is not allowed that is "faster" than motion through time because that would make the root of ds negative. (i.e. the Lorentzian signature of the metric does not allow motion through space faster than c.) However, seems like this is the more popular convention ds^2 = -dt^2 + dx^2 which throws all that out the window, doesn't it? Or was it incomplete/wrong reasoning in the first place? Thanks.