[user_7832]

What is the frame of reference, or is there even one, in this case? If you have one spacecraft moving in one direction at 0.5c flying by Earth, is the craft at 0.5c and experiencing "slower" time, or is Earth experiencing slower time? Or do they both experience the same thing as they're not accelerating wrt each other?

[aidenn0]

If they just pass by each other without changing speeds, each sees the other as experiencing slower time. For the case where one leaves and comes back, see the Twin paradox[1] which is resolved by the simple fact that to change speeds one must accelerate (or that the one who returns must have experienced at a minimum two different frames of references; one to leave and one to return).

1: https://en.wikipedia.org/wiki/Twin_paradox

[kijin]

There is no independent frame of reference by which we can tell whose time is slower.

From the spacecraft's frame of reference, Earth's time is slower. From Earth's frame of reference, the spacecraft's time is slower. Both are right.

When we say that time is slower or faster on a spacecraft, the Moon, or an exoplanet of Christopher Nolan's, we are implicitly prefixing the statement with "From Earth's frame of reference..."