Time runs slower in stronger gravity. A clock on the ground floor ticks slower than a clock on the roof. A clock at sea level ticks slower than a clock on a mountaintop. This is not a measurement error, not a mechanical effect on the clock — time itself passes at different rates depending on gravitational potential.
Every GPS satellite carries atomic clocks. Those clocks are 20,200 km above Earth, where gravity is weaker. General relativity predicts they will tick faster than ground clocks by 45 microseconds per day.
But the satellites are also moving at 14,000 km/h. Special relativity predicts their clocks will tick slower due to velocity by 7 microseconds per day.
Net effect: satellite clocks gain 38 microseconds per day relative to ground clocks. GPS firmware applies this correction continuously.
Without relativistic corrections, GPS position errors would accumulate at roughly 10 kilometers per day. Within a week, GPS would be useless for navigation. Within a month, it would place a receiver in the wrong city. Every GPS fix relies on both special and general relativity being correct to high precision.
The Schwarzschild metric describes the curvature of spacetime around a non-rotating, spherically symmetric mass. It gives the exact formula for gravitational time dilation: clocks tick slower by a factor that depends on the ratio of the Schwarzschild radius to the distance from the center of mass. At Earth’s surface, this ratio is about 1.4 × 10⁻⁹ — tiny, but GPS clocks are precise enough to notice.
Light climbing out of a gravity well loses energy. It does not slow down — light always travels at c — but its frequency decreases and its wavelength increases. It shifts toward the red end of the spectrum.
This is a direct consequence of gravitational time dilation. If time runs slower at the bottom of a gravity well, then a light wave emitted at the bottom has a lower frequency when measured at the top. The wave did not change. The rate of time changed between emission and reception.
In 1959, Pound and Rebka measured gravitational redshift across a 22.5-meter tower at Harvard. Using gamma rays and the Mossbauer effect (which provides extreme frequency precision), they confirmed Einstein’s prediction to within 1%. Gravity measurably changes the frequency of light across the height of a building.
In special relativity, time dilation is symmetric — each observer sees the other’s clock running slow. Gravitational time dilation is different. It is absolute. The clock deeper in the gravity well genuinely runs slower, and both observers agree on this.
Bring two synchronized clocks together at the same altitude. Lower one into a gravity well. Wait. Bring them back together. The lower clock has accumulated less time. This is not perspective — it is a permanent, measurable difference. The Hafele-Keating experiment confirmed this in 1971 using atomic clocks on commercial airline flights.
Gravitational time dilation maps directly to latency variation under load.
Nodes under heavy load process messages slower — their effective “clock rate” decreases. A request entering a heavily-loaded service cluster experiences time dilation: operations that take 5 ms on an idle node take 50 ms on a saturated one. The node is not broken. Its local time is running slower under gravitational load.
Messages leaving a heavily-loaded cluster arrive delayed — they are “redshifted.” A health check that takes 100 ms under normal conditions takes 800 ms from a saturated node. From the outside, the node appears to be running in slow motion. From the node’s perspective, it is processing at normal speed — it just has more work per unit of wall-clock time. This is exactly the structure of gravitational time dilation: local physics is unchanged, but the rate of local time relative to distant observers is different.
Near a black hole, gravitational time dilation becomes extreme. At the event horizon, time (as measured by a distant observer) stops entirely. A clock falling toward a black hole would appear to slow down, redshift, and freeze at the horizon — never quite reaching it from the outside perspective.
From the clock’s own perspective, it crosses the horizon in finite time and continues falling. This disconnect between the infaller’s experience and the distant observer’s view is one of the most counterintuitive consequences of general relativity.
This lesson establishes:
Next: Black Holes