Thanks, that sounds like the explanations I've seen too, and that I hope to understand some day. Atm I'm at the point where I gladly accept that time may seem to dilate, but not that it actually does. Maybe I just need to dive deeper into it than I've been willing to do so far.
You may want to investigate how GPS works. They have to incorporate the effects of time dilation to get accurate positioning data. I don't know if this is the correct direction to get the answer for which you are searching but it is a concrete example with the maths worked out.
http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps....
