Fifth-Coordinate Consequences for Laboratory Clocks: Drift Bounds from Optical Clock Comparisons

In Einstein-Cartan spin-torsion gravity the Aldred Limit gives a fractional density correction rho/rho_A that is undetectable by optical clocks through the density channel (short by about 35.5 orders of magnitude at osmium). This paper treats a separate channel: an additional compact dimension (the fifth coordinate) whose local value couples to clock rates, with coupling nu(chi) = nu_0[1 + kappa_5(chi - chi_0)], where kappa_5 has dimensions of inverse length and is a free parameter not fixed by the frame. Two clocks differ fractionally by kappa_5 times their fifth-coordinate separation, or by kappa_5 gamma L over a spatial baseline L with gradient gamma. Null results from published optical-clock comparisons (Al+, Yb, Sr) at the 10^-18 level bound |kappa_5 Delta chi| < 10^-18, |kappa_5| < 10^-18 per metre at a 1 m separation, and |kappa_5 gamma| < 10^-18 per metre over 1 m (10^-21 per metre over 1 km). The 1 m bound lies 52.8 orders of magnitude below the inverse Planck length; at a Planck-scale coupling the permitted fifth-coordinate separation is 1.62e-53 m. AI-use disclosure: an AI assistant, Dave, assisted in the preparation of this work, including computation and drafting, under the direction of the author.