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Gravitational time dilation
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Clocks run slower in stronger gravity.
Δt = Δt₀/√(1−2GM/rc²)Clocks run slower deeper in a gravitational potential: Δt = Δt₀/√(1 − 2GM/rc²). On Earth's surface vs high altitude it's a few parts in 10¹⁶ per metre.
GPS clocks gain 45 μs/day from weaker gravity.
Seen with atomic clocks separated by 1 m.
In more detail
Clocks run more slowly in stronger gravitational fields, so a clock at sea level ticks slower than one on a mountain. This gravitational time dilation is confirmed by experiments.
Real-world uses
- GPS satellites correct for gravitational time dilation.
- Precision clock comparisons have measured the effect over height differences.
- GPS engineers correct satellite clocks for gravitational time dilation, since they run faster at high altitude.
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Frequently asked questions
How big is the effect?
On Earth it is tiny, but measurable with atomic clocks at different heights.
Why does it matter for GPS?
Without correction, the errors would accumulate to kilometres per day.
Do clocks run faster or slower in weaker gravity?
Clocks run faster where gravity is weaker, such as higher up, and slower near massive bodies.
Related topics in Relativity
Relativistic electromagnetism · Tachyons · Equivalence principle · Gravitational redshift · GPS and relativity · Curved spacetime