Gravitational time dilation within a single-atom spatial superposition
In plain words
A clock held higher runs faster, so an atom whose internal ticking is split between two heights at once should carry two different ages that later interfere. This quantum version of gravitational time dilation has been proposed but not measured.
Precise statement
In an atom interferometer whose arms are separated vertically by $\Delta z$ for a time T, with atoms in a superposition of two clock states, general relativity predicts a proper-time difference of order $g\Delta z T/c^{2}$ between the arms, which shifts the clock phase and reduces the clock-state visibility through which-path information (Zych et al 2011; Roura, arXiv 1810.06744). Measure this gravitational proper-time effect, separated from laser-phase and light-shift contributions that cancel in ordinary closed-loop geometries, and determine whether it agrees with the general-relativistic prediction.
What would settle it
A clock-state atom interferometer with a verified nonzero gravitational proper-time signal that scales with $\Delta z$ and $T$ as predicted.
Status in the literature
Unverified note
Clock-interferometry schemes, including an optical-tweezer proposal (arXiv 2402.14412, 2024), have been published, but no measurement of a gravitational proper-time difference within a single superposition has been reported as of mid-2026.