time dilation

A clock moving steadily past you ticks more slowly than your own, as you measure it. The faster it moves, the larger the gap. At everyday speeds the effect is far too tiny to notice, but it grows without limit as the clock approaches the speed of light. This is not the clock breaking down; the very flow of time, as you reckon it for that clock, has slowed.

The slowdown follows the Lorentz factor gamma: a moving clock's elapsed time is stretched out by that factor in your frame. Strangely, the effect is fully symmetric. Each observer sees the OTHER clock running slow, with neither being wrong, because they disagree about which distant events are simultaneous. The apparent contradiction dissolves once you remember that 'at the same time' is itself frame-dependent.

A clear way to picture it is a 'light clock': a pulse bouncing straight up and down between two mirrors, one tick per round trip. If that clock glides past you, the pulse must travel a longer zig-zag path to keep up with the moving mirrors, yet light still crawls at the same speed c. A longer path at fixed speed means a longer tick, so the moving clock runs slow exactly by gamma.

This is measured fact, not philosophy. Muons created high in the atmosphere are so short-lived they ought to decay long before reaching the ground, yet crowds of them arrive because their internal clocks run slow at near-light speed. Atomic clocks flown around the world on aircraft return measurably behind their stay-at-home twins, by just the amount the Lorentz factor predicts.