The specific tech that we were thinking magic/science could unlock is the Alcubierre Drive, also known as Warp Drive (though amusingly somewhat less magical than how Warp was commonly depicted in Star Trek).
All of it is theoretically possible, but would take an amount of energy we are currently incapable of producing. Essentially, the theory essentially involves creating a "bubble" in space, by creating negative gravity behind a ship with positive gravity in front. The gravity thus creates a wave that the ship sits on,
but is actually more like the universe moving the ship. Thus, technically, the ship doesn't move at all: it moves the universe around it. That's a weird way of saying that it gets avoids the light speed "speed limit" by not actually moving or accelerating at all. It also wouldn't experience relativistic time dilation.
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