Gravitational Time Dilation

Gravitational time dilation is the phenomenon predicted by general relativity — and most dramatically exhibited by the Schwarzschild metric — in which the passage of time slows in the presence of a gravitational field. A clock closer to a massive object runs slower than an identical clock farther away. This is not an optical illusion or a mechanical effect on clocks; it is a genuine difference in the rate at which time itself flows at different points in the geometry of spacetime.

The effect is measured routinely by the Global Positioning System, whose satellites orbit at an altitude where gravitational time dilation runs faster than clocks on Earth's surface. Without relativistic correction, GPS would accumulate errors of kilometers per day. The effect has been confirmed in laboratories using atomic clocks at different heights, with precision reaching fractions of a picosecond.

Gravitational time dilation is often described as a consequence of the equivalence principle — that gravity and acceleration are locally indistinguishable — but this is only half the story. The deeper structure is geometric: the Schwarzschild metric's time component g_tt = -(1 - R_s/r) explicitly shows that the coordinate time interval between two events depends on the radial distance from the mass. Time is not a universal backdrop. It is a local property of the metric, and the metric varies with position.

At the event horizon of a black hole, where r = R_s, the time dilation factor diverges: a distant observer sees an infalling object slow to a halt and never cross the horizon. This is not a physical freezing but a coordinate effect — the observer's clock and the infalling object's clock disagree, and the disagreement is unbounded. The horizon is where the geometry of time itself becomes pathological from the outside perspective.

Gravitational time dilation is not a distortion of clocks. It is a revelation that time itself is a local variable, and the universe has no central clock. Every point in spacetime keeps its own time, and the differences between them are not errors but geometry.