The volume in the matter-wave bound on postquantum-classical gravity is set by a smearing length, not the wavepacket
Year: 2026
Type: preprint
Abstract: Lower bounds on the diffusion constant D2 of postquantum-classical gravity come from matter-wave coherence through the formula tau = D2 c^3 V / (2 G^2 N^(2/3) M^2), in which the volume V has been chosen in different ways, moving the bound by many orders of magnitude. For the local decoherence kernel behind this formula, the decoherence rate between two centre-of-mass positions does not depend on the wavepacket within each branch; it is fixed by the body's mass density convolved with the length l over which the theory smears mass, which the theory leaves free. The decoherence term then has the form of the mass-proportional CSL term with rC = l, as noted before, and we translate collapse-model limits into D2 >= 2 G^2 m0^2 / [c^3 lambda_max(l) (4 pi l^2)^(3/2)]. For the 2026 sodium-cluster interferometer (7482 atoms, 133 nm grating period) we compute the floor as a function of l by a pair sum over a bcc cluster. It is 1.3e-66 at l = 0.1 nm, flattens near 1.1e-66, is 0.7e-66 at 1 nm, and then falls as l^-3 and l^-5, while below 0.1 nm it rises as individual nuclei are resolved; the choice V = d^3 used in the latest summary of bounds corresponds to l = 5 nm. On matter-wave data alone, l < 2 nm is excluded against the gravitational-wave ceiling on tensor diffusion, and only l < 0.1 nm, marginally, against the scalar ceiling. If the decoherence is Markovian up to X-ray frequencies, which the theory's authors doubt, the XENONnT limit excludes l < 0.3 to 0.6 um against the tensor and full-positivity scalar ceilings. Otherwise the LISA Pathfinder collapse-model limit, proportional to l^-1, sets the lower edge above 0.14 um. One consistent way to keep the trade-off, used by Tilloy and Diosi, smears the Newtonian coupling at the same l; then short-range gravity tests limit l from above. The viable window is a region in the (D2, l) plane rather than an interval in D2.
Author: Nguyen, Dat
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225633070