Definition
Special relativity is Einstein's 1905 theory of space, time, and motion, built on two postulates:
- The laws of physics take the same form in every inertial (non-accelerating) reference frame.
- The speed of light in vacuum, c, is the same in every inertial frame, independent of the motion of the source or observer.
From these two assumptions follow time dilation, length contraction, relativity of simultaneity, the relativistic addition of velocities, and the equivalence of mass and energy.
Why it matters
How it works
The starting puzzle was electromagnetism. Maxwell's equations predict electromagnetic waves travelling at speed c, but they do not specify a preferred rest frame. Either Maxwell's equations are wrong, the principle of relativity is wrong, or our intuitions about adding velocities are wrong. The 1887 Michelson–Morley experiment failed to detect Earth's motion through any "luminiferous ether," ruling out the simplest preferred-frame solutions.
Einstein chose the third option. If c is the same in every inertial frame, then the Galilean transformation (t' = t, x' = x − vt) cannot be right — it would give different values of c to different observers. The correct transformation must mix time and space. The result is the Lorentz transformation:
t' = γ (t − vx/c²)
x' = γ (x − v t)
γ = 1 / √(1 − v²/c²)
The factor γ approaches 1 at low speeds (Newtonian limit) and diverges as v → c. From it follow the textbook consequences:
- Time dilation: a clock moving with velocity v ticks slower by a factor γ relative to a stationary clock. Confirmed in muon lifetimes, atomic-clock flights (Hafele–Keating, 1971), and routinely in GPS satellites.
- Length contraction: a moving rod is shorter along its direction of motion by a factor 1/γ.
- Relativity of simultaneity: two events that occur at the same time in one frame generally do not in another, unless they occur at the same location.
- Mass–energy equivalence: a body has rest energy
E₀ = mc²; total relativistic energy isE = γmc².
Special relativity is special because it is restricted to inertial frames — no acceleration, no gravity. Generalising it to include those was the work of the next decade, culminating in the 1915 general theory of relativity.