Inside a laboratory on Earth’s surface the effects of spacetime curvature are so small that current technology cannot measure them. Therefore, experiments performed in the laboratory can be analyzed using special relativity. 

(a) Explain why the space time metric in the proper reference frame of the laboratory’s floor has the form

plus terms due to the slow rotation of the laboratory walls, which we neglect in this exercise. Here g is the acceleration of gravity measured on the floor.

(b) An electromagnetic wave is emitted from the floor, where it is measured to have wavelength λ_o, and is received at the ceiling. Using the metric (24.75), show that, as measured in the proper reference frame of an observer on the ceiling, the received wave has wavelength λ_r = λ_o(1+ gh), where h is the height of the ceiling above the floor (i.e., the light is gravitationally redshifted by △λ/λ_o = gh).

The first high-precision experiments to test this prediction were by Robert Pou 2nd and his student Glen Rebka and postdoc Joseph Snider, in a tower at Harvard University in the 1950s and 1960s. They achieved 1% accuracy. 

Transcribed Image Text:

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