Special Relativity Explorer
Drag the velocity slider to see how time, length, and mass transform at relativistic speeds.
Lorentz coordinate transforms and spacetime invariants 🖖
Special relativity states that the laws of physics are invariant in all inertial frames, and the speed of light c is constant. This requires replacing Galilean transformations with Lorentz transformations, leading to time dilation t' = t / sqrt(1 - v²/c²) and length contraction. Spacetime is unified into a four-dimensional manifold where the interval ds² = c²dt² - dx² - dy² - dz² is invariant under rotation and boost.
Why the Lorentz factor γ runs everything 🖖
The whole tool orbits one number: the Lorentz factor γ = 1/√(1−β²), where β = v/c. At walking speed γ ≈ 1, so relativity stays hidden; as v nears the speed of light c, γ climbs without limit. At v = 0.87c, γ = 2 — moving clocks tick half as fast and lengths halve. Because reaching c would demand γ = ∞, no massive object ever gets there: the price is infinite energy.
A speeding object looks rotated, not shrunk 🖖
Length contraction is what you measure, not what you see. Because light from an object's far side leaves earlier than light from its near side, a photograph of a body rushing past captures it apparently rotated rather than flattened — a sphere still shows a round outline. This Terrell–Penrose rotation went unnoticed for 54 years, until James Terrell and Roger Penrose spotted it independently in 1959.
Example problems
- Muon (0.9c) - Muon at 0.9c: γ=2.29, time slows
- GPS satellite - GPS satellite: tiny but measurable dilation
- Half c - Half light speed: γ=1.155
- 0.99c - 0.99c: γ=7.09, dramatic effects