Probing Local Effective Scalar Potentials through Residual Proper Time Deviations in Quantum Dot Systems

The weak-field limit of general relativity (GR) has been tested with increasing precision through modern timekeeping experiments, yet the possibility of small, systematic residuals in quantum-coherent systems remains open. In this work, we introduce an effective scalar potential, denoted as DP, defined operationally as the residual deviation between observed proper time delays and GR predictions. We define the effective scalar potential as DP = (1 / kappa) * (dt_obs - dt_GR), where dt_obs is the measured proper time delay, dt_GR is the corresponding prediction from GR in the weak-field limit, t is the coordinate time interval, and kappa is the standard gravitational coupling constant. This definition relies exclusively on observable quantities and avoids circular assumptions about the origin of the potential. We show that, within linearized gravity, DP reproduces the Newtonian potential as the source of the metric perturbation, while allowing for experimentally accessible residual deviations. As a concrete test case, we propose quantum dot systems coupled to synchronized high-precision atomic clocks as a platform to probe such effects. Under controlled decoherence conditions, the framework predicts reproducible proper-time deviations at the level of 1e-15 to 1e-18, within reach of near-term experimental sensitivity. This approach provides a phenomenological bridge between precision time measurements and potential fine-scale structure of spacetime, offering a systematic way to interpret residual timing anomalies beyond standard GR predictions.