Posted: Mar 05, 2011 8:35 am
hackenslash wrote:Animavore wrote:Oh I will. Especially how he made the leap to a minus figure for Pytagoras' therom. I don't know if my mind wandered and I missed a bit or if this book is a mess.
He does address it, specifically with the example I gave above. Using the plus version violates causality, because it gives a situation in which two events in spacetime the same distance s apart can happen in reverse, even if one of the events is the cause of the other. Think of a bullet fired from a gun and hitting a target. In the plus sign version of the equation, the bullet can hit its target before it's fired from the gun. The jump to the minus sign version protects causality, because it generates a non-Euclidean spacetime, known as Minkowski spacetime.
I got that bit. He doesn't explain why it does or how he gets a circle or why using a minus gives you a hyperbola in the top only that it does.