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) | Gamma | 1 Earth year = ship time |
|---|---|---|
| 0.1c | 1.005 | 11.9 months (barely noticeable) |
| 0.5c | 1.155 | 10.4 months |
| 0.8c | 1.667 | 7.2 months |
| 0.9c | 2.294 | 5.2 months |
| 0.95c | 3.203 | 3.7 months |
| 0.99c | 7.089 | 1.7 months |
| 0.999c | 22.37 | 16 days |
| 0.9999c | 70.71 | 5.2 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