Two identical optical atomic clocks stand in the same laboratory
PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Atomic, Molecular & Optical Physics · The equivalence principle and gravity as geometry
Relativity and Gravitation, Ch Experimental foundations: free fall, Lorentz invariance and clock tests
Problem
Two identical optical atomic clocks stand in the same laboratory. Each is a single trapped ion whose transition frequency, at rest and far from any other clock, is ν=1.121×1015Hz. One clock is then raised by h=0.330m above the other, and the two are compared through an optical fibre. Take g=9.81ms−2, constant over 0.330m, and c=2.998×108ms−1; both clocks are at rest in the laboratory frame, and the calculation is to first order in gh/c2. The comparison can resolve a fractional frequency difference of 8.0×10−18.
((a)) Which of the three pillars of the Einstein equivalence principle does this comparison test? Say in one sentence why.
((b)) Compute the predicted fractional difference in rate between the raised clock and the lower one, and say which runs faster.
((c)) Compute the predicted difference of the two clock frequencies in Hz, and compare the predicted fractional shift with the resolution quoted.
((d)) State what measured outcome, at this resolution, would falsify the pillar you named in (a), and what would leave it standing.