Math Playground
Physics

Relativity (special)

Speed of light is constant — so time and space have to bend.

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.

Try this
0.5
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.