Lesson 2

      Now comes the benefit of using Minkowski spacetime instead of other forms of introductory special relativity.  Suppose now that observer B accelerates along a general path.  Let us refer to the path by coordinate functions x(u),y(u),z(u),t(u) (although usually t(u) is taken as just t = u ).  Then the length of the path followed by B between points u = a and u = b is given by

And since the length of the path through spacetime is related to the proper time, T =  S / c is the time experienced by observer B.  Similarly, the time experienced by observer A is the integral of dt/du over the interval (a,b).