Two national laboratories compare optical clocks over an optical-fibre link
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
Two national laboratories compare optical clocks over an optical-fibre link. Laboratory A stands 120 m above sea level and laboratory B stands 1590 m above sea level. Both clocks are at rest on the ground. Take g=9.81ms−2 as uniform over this range of heights, c=2.998×108ms−1, and work to first order in gΔh/c2; ignore the Earth's rotation and any difference in the local mass distribution.
((a)) Find the fractional difference in rate between the two clocks, and say which runs faster.
((b)) How long must the comparison run before the two clocks' readings differ by 1.00 ns?
((c)) Each clock is accurate to a fractional rate of 1.0×10−18. What vertical displacement of one clock would produce a rate change just equal to that accuracy? (This is why such clocks are used as altimeters.)