Two light-clocks race side by side, and the moving one ticks slow. Drag the speed slider (β = v/c) and watch the Lorentz factor γ stretch a 10-second trip and shrink a 100-metre ship, all from γ = 1/sqrt(1 - β2).
Special relativity stops being abstract the moment you watch a clock built from light. This simulator runs twin light-clocks: one at rest, one gliding past at a speed you set with the beta slider (β = v/c, from 0.00 to 0.99). Press Start to let the pulses bounce, and watch the moving clock's pulse trace a longer diagonal path. Because light travels at the same speed c for every observer, that longer path takes more time, so each tick stretches. That diagonal is the physical reason a moving clock runs slow.
Every readout follows from one quantity, the Lorentz factor γ = 1 / sqrt(1 - β2). It equals 1 at rest and climbs toward infinity as β approaches 1; at β = 0.6 it is exactly 1.25. The dilated time readout multiplies a 10.0 s proper-time interval on the moving clock by γ, so the stationary observer records γ times 10 = 12.5 s at β = 0.6. The contracted length readout divides a 100.0 m proper-length ship by γ, giving 80 m at that same speed. Only the dimension along the motion shrinks; transverse widths never change.
Notice that both effects vanish at everyday speeds and grow only as v nears c, which no massive object can ever reach. To put numbers on a specific journey, open the Time Dilation calculator; to explore why c is the universal limit, try the Speed of Light Simulator; or browse the full collection of interactive physics labs.
A moving clock runs slow. A time interval measured on a clock moving at speed v is stretched by the Lorentz factor gamma when read by a stationary observer: dilated time = gamma times the proper time.
gamma = 1 / sqrt(1 - v^2/c^2). It equals 1 when at rest and grows without limit as the speed approaches the speed of light. At v = 0.6c it is exactly 1.25.
A moving object is measured shorter along its direction of motion by the factor gamma: contracted length = proper length / gamma. A 100 m ship at 0.6c measures 80 m. Lengths across the motion are unchanged.
Because the Lorentz factor gamma heads to infinity as v approaches c, so it would take infinite energy to accelerate a massive object to light speed. Only massless things, like light itself, travel at c.