For a Kaluza-Klein modified gravitational potential, the gravitational Aharonov-Bohm phase produces energy-level shifts that are dominated by an assumed constant correction to Newton's constant, while the claimed new quantum-number splitting is a higher-order sideband artifact.
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Signatures of modified gravity from the gravitational Aharonov-Bohm effect
For a Kaluza-Klein modified gravitational potential, the gravitational Aharonov-Bohm phase produces energy-level shifts that are dominated by an assumed constant correction to Newton's constant, while the claimed new quantum-number splitting is a higher-order sideband artifact.