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Einstein’s geometric theory of gravity was constructed in part to explain why test particles in a gravitational field all follow the same trajectory independent of the mass of the particle. However, it is known that point particles in quantum mechanics must all possess at least two properties: mass and angular momentum. Many have speculated that spin-dependent effects in gravity might exist which are not contained in Einstein’s theory, yet few experimental tests for such a possibility have ever been conducted. We describe an experiment which is very similar to the famous Pound-Rebka experiment, which used the Mössbauer effect to verify for the first time Einstein’s prediction for the curvature of time, but which employs Mossbauer emitters and absorbers with nonzero spin. We present a specific, realistic proposal for such an experiment. We outline the theory for the “normal” effects of general relativity a la Pound-Rebka, the proposed experimental apparatus including spinpolarized emitters and absorbers, the expected sensitivity of the experiment, and potential sources of systematic error.