[PTTG]

Light-speed travel is invented in 2045. It functions by "cycling" kinetic energy from the future to the present, accellerating the ship to near-light-speed. The ship travels the distance and then deaccellerates by dumping its excess kinetic energy into the past, when it needed it.

The time looping effect works because the ship itself experiences nearly no time during the jump; as a result, it's a fairly managable trick to have all the atoms shuffle the energy around briefly.

This all allows ships to effectively move at light speed (Well, within 10^-10 % of light speed). Protecting a ship from light-speed collisions with space dust is dealt with by a special arrangement. I recommend taking a basic course on relativity at your local university to fully appreciate the consequences.

Departing Earth orbit and arriving at Alpha Centauri takes no time at all from your perspective and more than four years from the perspective of someone at either star. Aside from everything else, the future is always two jumps away.