Time Dilation

At speeds approaching light, time slows down for the traveler relative to a stationary observer. This is not science fiction — it’s measured fact with real implications for interstellar travel.

The Physics

From Einstein’s special relativity, a clock moving at velocity v ticks slower by the Lorentz factor:

gamma = 1 / sqrt(1 - v²/c²)

Ship time = Earth time / gamma

Speed (fraction of c)Gamma1 Earth year = ship time
0.1c1.00511.9 months (barely noticeable)
0.5c1.15510.4 months
0.8c1.6677.2 months
0.9c2.2945.2 months
0.95c3.2033.7 months
0.99c7.0891.7 months
0.999c22.3716 days
0.9999c70.715.2 days

What This Means for Travel

The Good News

A crew traveling at 0.9c to dest-proxima-centauri (4.24 ly) experiences only ~1.85 years of subjective time, even though 4.7 years pass on Earth. To dest-trappist-1 at 0.99c, the crew experiences ~5.6 years while 39.9 years pass on Earth.

The Bad News

  • You still need the energy to accelerate to those speeds. Time dilation is free, but the speed isn’t — and energy requirements grow exponentially as you approach c (see concept-relativistic-travel).
  • Deceleration doubles the problem. You must slow down at the destination, requiring either equal fuel or pre-positioned infrastructure.
  • The twin paradox is real. Return travelers find everyone they knew has aged or died. A round trip to Proxima at 0.9c: crew ages ~4 years, Earth ages ~10 years. A round trip to TRAPPIST-1 at 0.99c: crew ages ~11 years, Earth ages ~80 years.
  • It doesn’t help for galaxies. Even at 0.9999c, a trip to dest-andromeda takes 35,900 ship-years.

The Communication Problem

A traveler at 0.9c to TRAPPIST-1 experiences 19 years of travel. But messages sent from Earth take 39.5 years to arrive at the destination. The crew will be increasingly isolated — by the time they arrive, decades of history have passed at home.

Proven by Experiment

  • Muon decay: Cosmic ray muons reach Earth’s surface because time dilation extends their lifespan
  • Hafele-Keating experiment (1971): Atomic clocks flown on jets gained/lost nanoseconds vs ground clocks, matching predictions
  • GPS satellites: Clocks run ~38 microseconds/day fast compared to ground; GPS software corrects for this

See Also