Suppose a particle orbit as a function of time (t) is given in an inertial frame K and the integral dt r(t) is evaluated. Using the invariance of the space-time interval, show that if the same calculation is done in a frame K'moving uniformly with respect to K, then t' = T. In other words, the proper time r along a particle orbit is a Lorentz invariant quantity.

Suppose a particle orbit as a function of time (t) is given in an inertial frame K and the integral dt r(t) is evaluated. Using the invariance of the space-time interval, show that if the same calculation is done in a frame K'moving uniformly with respect to K, then t' = T. In other words, the proper time r along a particle orbit is a Lorentz invariant quantity.

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