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Experimental tests of general relativity starting from the Schrödinger equation: the Pound-Rebka experiment

Jayson Vavrek

Doctoral Candidate
Laboratory for Nuclear Security and Policy

The Pound-Rebka experiment (1959) was one of the first precision tests of Einstein's general relativity. General relativity predicts that a photon's energy will be red- or blue-shifted by a gravitational field, but the magnitude of the effect is exceedingly small over typical laboratory distances and under terrestrial gravity. However, these small energy shifts can be detected in high-precision spectroscopy experiments using the Mössbauer effect, as was done by Pound and Rebka at Harvard, providing a link between physics on cosmological and quantum scales.

Starting from the Schrödinger equation, I will show how the finite potential well gives rise to the Breit-Wigner resonance cross section under a first-order Taylor expansion. I will then discuss the Breit-Wigner behaviour of nuclear resonance fluorescence and its special case, the Mössbauer effect. Next, I will show how the Mössbauer effect can be used for high-precision (ΔE/E ~ 10-15) measurements of photon energies. Finally, I will derive the competing photon redshift predictions from both special and general relativity and cover how the observed net redshift was confirmed by Pound and Rebka to closely match the theoretical result.