Time dilation at near light speeds?

This is the twin paradox. The solution basically boils down to saying that the person in the rocket is not in an inertial frame because he has to slow down, stop and speed up again in order to turn around and come back to Earth. He experiences forces when slowing down and speeding up which means he knows he's not stationary and so can't use his own frame as a frame of reference (in contrast to travelling at constant speed where you only know you're moving if you look out of the window, so you can take your own position to be a fixed point and calculate time dilation for everyone else who is travelling "fast").