The matter-wave floor on postquantum-classical gravity after the 2026 sodium-cluster experiment
Year: 2026
Type: preprint
Abstract: In postquantum-classical gravity, matter-wave coherence sets a lower bound on the diffusion of the Newtonian potential, and gravitational-wave and torsion data set upper bounds. The most recent summary of these bounds (Oppenheim and Sajjad, arXiv:2605.05375) quotes a matter-wave floor D2 >= 1e-71, taken from a 2011 interferometer with 430-atom molecules, and an open window of about 5.1 orders of magnitude for the scalar channel under full positivity. We recompute the floor with the formula and volume convention those authors use, but with the inputs of the 2026 experiment of Pedalino et al. (Nature 649, 866) on sodium clusters of 143 to 197 kDa. The floor rises to (3.1 to 8.3) x 1e-68, a factor of about 5 x 10^3. Applying the floor directly to the scalar diffusion, as that summary does, the full-positivity window becomes 1.4 orders of magnitude with the uniform-prior LVK ceiling and 0.9 with the log-uniform one. In our reading of the authors' two-coupling relations, the interferometer bounds the scalar decoherence coefficient, so the scalar floor is 2f(x) >= 25/9 times larger; the window is then at most 0.9 and 0.4 orders (ranges 0.7 to 1.2 and 0.2 to 0.6 over the quoted masses and velocities). A further factor of 8 (uniform) or 2.5 (log) in N^(2/3) M^2 tau / d^3 closes the full-positivity branch in that reading; at the present mass this means velocities near 20 or 65 m/s. The prospect the experimenters describe, MDa clusters at about 25 m/s, would overshoot by about two orders. The transverse-positivity branch stays open by about 12 orders up to the LISA Pathfinder ceiling. The result depends on the volume convention and on the delocalisation length: with d = 80 nm, the lower bound the experimenters state, the log-prior window closes. We also note that the coherence time used for the 2011 floor is not supported by the velocities reported in that experiment.
Author: Nguyen, Dat
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225661057