So it appears that the signature of spacetime is something that is not knowable a priori, and must be determined by experiment. When a thing is supposed to be experimentally observable, general relati...So it appears that the signature of spacetime is something that is not knowable a priori, and must be determined by experiment. When a thing is supposed to be experimentally observable, general relativity tells us that it had better be coordinate-independent. Is this so? A proposition from linear algebra called Sylvester’s law of inertia encourages us to believe that it is.
