Gravitational Time Dilation

Gravitational time dilation arises from the principle that the rate at which time passes is influenced by the curvature of spacetime. In a region of stronger gravity, the ‘flow’ of time itself is slower relative to a region of weaker gravity. This is not a mechanical effect on clocks but an actual difference in the passage of time. For example, a clock at sea level runs slightly slower than an identical clock on a mountain. The formula for this effect for a non-rotating, spherically symmetric mass is \(t_f = t_0 \\sqrt{1 – \\frac{2GM}{rc^2}}\), where \(t_f\) is the time for the distant observer and \(t_0\) is the time in the gravitational field.

This effect was first confirmed experimentally by the Pound-Rebka experiment in 1959, which measured the gravitational redshift of photons (a related phenomenon). The most significant real-world application is the Global Positioning System (GPS). The atomic clocks on GPS satellites are in a weaker gravitational field than clocks on Earth’s surface, so they run faster by about 45 microseconds per day. They also experience special relativistic time dilation due to their high velocity, making them run slower by about 7 microseconds per day. The net effect is that GPS satellite clocks run faster by about 38 microseconds daily. Without correcting for this, GPS navigation errors would accumulate at about 10 kilometers per day, rendering the system useless.