A clock sits at sea level and an identical clock sits at the summit of a mountain of…
PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · The equivalence principle and gravity as geometry · The equivalence principle and gravity as geometry
The Geometry of Gravity, Ch Redshift, local inertial frames and the failure of flat spacetime
Problem
A clock sits at sea level and an identical clock sits at the summit of a mountain of height ℓ=8849 m. Both clocks are at rest in the Earth's weak, static field, over a height range small enough that Φ=g⊕ℓ with g⊕=9.81ms−2.
((a)) Find the fractional rate difference Δν/ν between the summit clock and the sea-level clock.
((b)) State which clock runs faster.