A set of parallel mirrors were launched into space and set in motion in the direction parallel to the planes of the mirrors. Light bouncing between the mirrors at constant light speed takes a longer time interval between bounce as the mirrors move at higher velocity. The motion of the mirrors adds a displacement component along its direction of travel. Light instead of just bouncing perpendicularly between the mirrors has to travel along this direction of motion also.
This has nothing to do with gravity! The setup might as well be on earth and the result is the same. There was no need to go into outer space.
The time interval taken as light bounce between the mirrors was used to "measure" time. It was said that since this interval increases as the mirrors speed up, time itself slows down. And the astronaut with the mirrors aged slowly.
Light bouncing off mirrors has nothing to do with the astronaut aging unless the astronaut is also bouncing off the mirrors and each time he hits a mirror he dies a little. In this case, the longer it takes between consecutive bounce the less he aged. Ouch..., Ouch..., Ouch... compared to Ouch, Ouch, Ouch.
In a gravity field, without the action of any force, as an object increases in velocity in space (KE for PE), its speed in time decreases.
\(v^2_t+v^2_s=c^2\) --- (*)
where \(v_t\) is the object velocity in time, \(v_s\) is its velocity in space and \(c\) is a constant.
Energy across the time and space dimensions is conserved. In this way, time as experienced by the object slows. The gravity field here is incidental, the object could be likewise accelerating in a temperature field or an electric field without the action of an applied contact force.
If there is an applied force from an engine, is energy still conserved? No. Does time speed slow? No, (*) does not apply.
And life goes on, Ouch...
