Your browser couldn’t start WebGL, so the live starfield can’t run here. The explanation below still works.
Push the throttle. Stars crowd ahead, turn blue and blaze; the sky behind reddens and fades. Every effect is computed from Einstein’s equations.
Drag to look around
Nothing in the flight above is decoration. Each change in the sky follows from two rules: the laws of physics are the same for every steadily moving observer, and light always travels at the same speed, c, for all of them.
This is aberration. Run through vertical rain and it seems to slant toward you; starlight does the same. A star at angle θ from your direction of travel (measured by someone at rest with the stars) appears to you at angle θ′, where
cos θ′ = (cos θ + β) / (1 + β cos θ)
At 0.99c, a star that was directly beside you appears just 8° from straight ahead. Almost the whole sky crowds into a small window at the front.
This is the relativistic Doppler effect. You rush into the light waves coming from ahead, so they arrive with higher frequency (bluer). Waves from behind are stretched out (redder). The factor is
D = γ (1 + β cos θ)
and wavelengths are divided by D. Here each star is a glowing ball of gas with a temperature, and to a moving observer it looks like a ball at temperature D × T. A Sun-like star dead ahead at 0.99c looks like an object of about 82000 K: intensely blue-white.
Light from ahead arrives with more energy per photon and more photons per second, so the energy you receive from a star grows as D². Because aberration also packs stars together, a patch of sky ahead brightens even faster, as D⁴. Behind you, the sky fades toward black.
Switch on Human eye to see a subtle twist. At extreme speeds much of the light from ahead is pushed into the ultraviolet, which eyes can’t see, so stars brighten far less than the total energy would suggest. Behind you, light slides into the invisible infrared.
To someone on Earth, every process aboard your ship (clocks, heartbeats, thoughts) runs slow by the Lorentz factor
γ = 1 / √(1 − β²)
At 0.99c, γ ≈ 7.09: one second for you lasts about 7.09 seconds in Earth’s frame. You don’t feel slow. Your trip just takes less of your time. The Light Clock shows exactly why.
| Speed | γ | Doppler ahead | Doppler behind | Red H-α line (656 nm) ahead → behind | Star at 90° appears at |
|---|---|---|---|---|---|
| 0.5c | 1.15 | ×1.73 | ×0.58 | 379 nm → 1137 nm | 60° |
| 0.9c | 2.29 | ×4.36 | ×0.23 | 151 nm → 2861 nm | 26° |
| 0.99c | 7.09 | ×14.11 | ×0.07 | 47 nm → 9258 nm | 8° |
Each experience is something to play with first and read about second. More are on the way.
Two clocks made of bouncing light. Make one move and watch it fall behind.
Enter experience →One twin stays, one travels. Only one of them turns around, and that settles it.
Enter experience →Measured from outside, a fast-moving ship really is shorter, but only along its direction of travel.
Enter experience →Tilt your “now”. Events that happen at the same time for you don’t for someone moving past.
Coming soonWhy a tiny amount of mass holds a startling amount of energy, and where it shows up.
Coming soonSatellite clocks tick at a different rate from ours. Without the correction, GPS would quickly drift.
Coming soonWhere gravity bends light into rings. A later chapter, beyond special relativity.
Coming soonSpecRel is a growing collection of interactive explanations of Einstein’s special theory of relativity, made by a small independent team. Everything you see is computed from the actual equations, and every page explains the idea in plain English. More about the project.