One caesium clock sits in a valley station at m above sea level and an identical one…

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · The equivalence principle and gravity as geometry · The equivalence principle and gravity as geometry

Relativity and Gravitation, Ch Gravity as curved spacetime: redshift and local inertial frames

Problem

One caesium clock sits in a valley station at

250

m above sea level and an identical one on a plateau at

1650

m above sea level. Both are at rest on the ground and the Earth's rotation is ignored. Take the field as uniform with

g = 9.81\ \mathrm{m\,s^{-2}}

between the two heights and

c = 2.998 \times 10^8\ \mathrm{m\,s^{-1}}

, and work to first order in

gh/c^2

. ((a)) By what fraction does the rate of the plateau clock exceed that of the valley clock? ((b)) The two clocks are compared after

30

days (

2.592 \times 10^6

s) of running. What time difference has built up between them?

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