A laser at the foot of a m tower sends light vertically up to a detector at the top

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

A laser at the foot of a

35.0

m tower sends light vertically up to a detector at the top. Both ends of the tower are at rest on the ground, the gravitational field is taken as uniform with

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

over this height, and

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

. Work to first order in

gh/c^2

. ((a)) Find the fractional frequency shift

\Delta\nu/\nu = (\nu_{\rm rec} - \nu_{\rm em})/\nu_{\rm em}

of the light on arrival at the top. ((b)) Two identical atomic clocks are placed at the two ends of the tower. By how much does the clock at the top get ahead of the clock at the bottom in one year, taken as

3.156 \times 10^7

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