If you're like me, you might find astronomical tests of general relativity a bit well, impersonal, (no offense to the astronomers and cosmologists out there). If that's the case, you'll be happy to know that there was a series of laboratory/benchtop tests of general relativity tests performed in the early 1960s. While they receive far less publicity and class time than their solar eclipse/mercury perihelion counterparts, these experiments proved the gravitational Doppler shift of gamma ray frequencies using fairly compact and very self-contained laboratory apparatus.
The discovery that enabled these experiments was the Mössbauer effect. Mössbauer found that very pure crystals could absorb and emit a highly specific frequency of gamma radiation. If the frequency of the incident gamma rays was changed by a tiny amount, (say the amount that might be caused by general relativistic effects in the laboratory), then the crystal would simply absorb the gamma ray without re-emitting it. This allowed other researchers to look for and detect effects that modified the frequency of gamma rays by minuscule amounts.
The experiment that gets the most attention was performed by Pound and Rebka in 1960. To provide the change in gravitational potential, they actually separated their gamma source and their detector at opposite ends of a 74 foot high tower at Jefferson Laboratory. Their apparatus is shown below and the experiment is summarized on the APS web site.
My favorite version of the experiment, however, is the one done by Hay, Schiffer, Cranshaw, and Egelstaff which scooped Pound and Rebka by two months. Hay and associates took Einstein's principle of equivalence at face value, (a gravitational acceleration is indistinguishable from any other kind in the accelerating frame). Rather than utilizing a tower to provide the gravitational potential difference, they built their apparatus on a rotating disc. The source near the center of the disc experiences a different centripetal force than the detector at its edge. Their much smaller apparatus is shown below.
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