Why nothing travels faster than light — and what happens when you try
In 1905, Einstein proposed something radical: the speed of light in vacuum, c = 299,792,458 m/s, is the same for all observers regardless of their motion. This single postulate, combined with the principle of relativity, overturns our everyday intuitions about space and time.
Time slows down for moving objects. Lengths contract. And nothing with mass can ever reach the speed of light. These aren't just theoretical predictions — they're experimentally verified facts that GPS satellites must account for every day.
Imagine a clock that ticks by bouncing a photon between two mirrors. When the clock is stationary, the photon travels straight up and down. But when the clock moves, the photon must travel a longer diagonal path — yet light speed is constant. The only resolution: time itself slows down for the moving clock.
Try it: Drag the velocity slider and watch the photon's path stretch. The moving clock ticks slower by a factor of γ = 1/√(1 - v²/c²). At 86.6% of light speed, the clock runs at half the rate.
In everyday life, velocities simply add: if you walk at 5 km/h on a train moving at 100 km/h, you move at 105 km/h relative to the ground. But Einstein showed that the true formula is v = (v₁ + v₂) / (1 + v₁v₂/c²). No matter how you combine velocities, the result never exceeds c.
While distances and time intervals change between reference frames, the spacetime interval ds² = -c²dt² + dx² + dy² + dz² is invariant — all observers agree on its value. It classifies pairs of events as timelike (causally connected), spacelike (causally disconnected), or lightlike (connected by light).
Key insight: The spacetime interval replaces the Euclidean distance formula of everyday geometry. Its minus sign in front of the time term is what makes spacetime fundamentally different from ordinary 4D space.
Muons are subatomic particles created when cosmic rays hit the upper atmosphere. They have a half-life of just 1.56 μs — at nearly the speed of light, they should only travel ~660 m before decaying. Yet we detect them at sea level, 15 km below their creation point. The explanation: time dilation stretches their lifetime by a factor of ~22.
Classical prediction: Muons have a mean lifetime of 2.2µs. At v = 0.998c they travel ~660m before decaying. The atmosphere is ~15 km thick, so very few muons should reach the ground.