I am a teacher trying to design multi-disciplinary unit around the Ender's Game series. I would like to know, is there any scientific basis for the difference between subjective time for light-speed travelers and "real" stationary time? If so, what sort of formula could one use for calculating subjective time at light speed?
The time-dilation effect is a well-known theoretical result of Einsteinian relativity. In practical terms, of course, the energy required to move a starship at the speed you must be traveling in order to observe time-dilation (i.e., very nearly the speed of light) is so vast that it cannot be done by any method now known.
As for the mathematical formulae, I have never attempted anything that precise. You would have to ask a physicist.