minkowski spacetime

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OK so moving on with my special relativity odyssey. The book I am reading states that S=CT2 - X2 which leads to a hyperbolic curve on which the distance in spacetime sits relative to the observer. This equation allows for different values for CT2 and X2 but the distance S remains the same for all observers. Except the way I look at it the distance changes because S can sit anywhere on the curve depending upon the observers relative position. I understand that if I know a different observers position relative to the event then I can work out the spacetime distance, but I thought the whole point was to make S absolute. Again can some patient person set me straight.

Oops I Think I have bee incredibly dense Space time is not Euclidean therefore any point on the hyperbolic curve is the same distance to all observers. Yes?

Sorry, I was going to reply to you but I've been busy lately. Minkowski space-time conforms to hyperbolic geometry rather than Euclidean geometry, so the "distance" between two space-time points is s^2 = (ct)^2 - x^2 - y^2 - z^2 or s^2 = -(ct)^2 +x^2 + z^2, depending on your sign convention rather than the distance given by the Pythagoras theorem for Euclidean space. You can think of it as a "Pythagoras theorem" for hyperbolic geometry, the only difference is that we actually use S = s^2 to define space-time separation, hence why S = (ct)^2 - x^2 in your example, because there are some squared "distances" that are negative.