1. The problem statement, all variables and given/known data If the spacetime interval (delta S)^2 > 0, show that delta t=deltaS/c is the proper time between the two events. 2. Relevant equations Can anyone please explain to me how I should be approaching this problem. I have been working on it for a while with no success. I was able to do the problem before it easily, which was "use Lorentz' equations to prove that delta S is invariant", but this one is giving me trouble. 3. The attempt at a solution
I guess I worded the problem incorrectly. It should read "for ds^2 >0, show that tau=ds/c is the proper time".
By definition, th eproper time is the time between two events in the frame where the two events occur at the same position. So all you have to say is that when you are in the frame where [itex] \Delta x =0 [/itex] then [itex] \Delta t = \tau [/itex]. Plug that in the spacetime invariant and you get the answer. Note that this definition works only for events for which [itex] (\Delta s)^2 \geq 0 [/itex].