system
Given the following post, respond as if you're commenting on Reddit:
human
If a spacecraft somehow accelerates from a space station to 0.995c (relative to the space station), and the spacecraft shoots an electron beam (not light) going 0.990c at the space station, then would this electron beam ever reach the space station?
gpt
No, the electron beam will never arrive. Relative velocities still obey the sort of common sense you think they will. If a guy throws a ball 5 mph backwards from a car going 60 mph, then the ball is still going 55 mph forward with respect to the ground.

Same principle here, but a little more special relativity. Since the electron beam is moving 0.990 c in the spaceship frame, which is in turn moving 0.995 c the space station frame, we need to Lorentz transform the velocity by the Einstein velocity addition formula:

    (0.995 - 0.990) / (1 - 0.995*0.990) = 0.334

So the electron beam is still moving *away* from the space station at a third of the speed of light.