Question

Problem 4-5: Denote by E the event on the ct-axis of a spacetime diagram that is a proper time cr from the origin. What is the locus of all events on the spacetime diagram that are separated from the origin by the same proper time? The answer should be a hyperbola that asymptotes to the line ct - x but which is horizontal on the spacetime diagram right at E.

Answer 1

"I = (Detla x)_mu (Delta x)^mu = -(Delta x^0)^2 + (Delta x^1)^2 + (Delta x^2)^2 + (Delta x^3)^2 = -c^2 t^2 + d^2 I > 0 for space like interval when interval is space like it is a ""hyperboloid of one sheet"" I = x^1 - c^2 t^2 = 0 x = ct "

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