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I'm a computer science student with a limited physics background and was recently introduced to special relativity. I have a question I haven’t been able to answer, and I would appreciate your help.

Assume a spacecraft travels at a constant speed close to the speed of light and has a basic computer and clock onboard. On Earth, the computer takes $T$ units of time (measured by the same type of clock) to perform a specific computation C. Now, if the clock onboard the spacecraft shows 2 p.m. when the computation starts, will the clock read (2 p.m. + $T$) when the computation is finished, or does relativity affect the clock's time in this situation?

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In the reference frame of anyone within the same ship, the computer will take a time $T$ to perform the computations, just as it would in Earth. So, to them, it would be 2 pm + $T%$. But to an observer looking into the ship from Earth, they would observe that the computation time is now $T'=\gamma T$, where $\gamma = 1/\sqrt{1-(v/c)^2}$ is the Lorentz factor.

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