Special relativity rests on two postulates: laws of physics are the same in all inertial frames, and the speed of light is constant for all observers.
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time-dilation factor γ = 1 / √(1 − v²/c²) = γ = 1.155 (a 1 s tick lasts 1.155 s to a watcher)
Lorentz factor
At everyday speeds v/c ≈ 0, so γ ≈ 1 and nothing seems odd. As v → c, γ → ∞ — that's why no object with mass can reach light speed.
What γ controls
- Time dilation — moving clocks tick slow by a factor γ.
- Length contraction — moving objects shrink along their motion by 1/γ.
- Mass-energy — total energy E = γmc², which gives E = mc² at rest.
GPS satellites move fast and sit higher in Earth's gravity; without relativistic corrections their clocks would drift enough to throw your position off by kilometres within a day.
Consequences: time dilation, length contraction, and E = mc².