The Imported Drag Law: Einstein's Stokes Mobility, Priced
Year: 2026
Type: preprint
Abstract: In 1905, A. Einstein derived the diffusion constant of a suspended particle as its mobility times the thermal energy, D = μkT — the fluctuation–dissipation structure that made the molecular hypothesis measurable, and a derivation I credit at full strength: given the mobility, it is exact, and my bench verifies that it returns its diffusion constant digit for digit. What I evaluate is the mobility's content. To turn the structure into a number, the paper imports Stokes's drag law for a macroscopic sphere in a continuum fluid, μ = 1/(6πηa), with stick boundary conditions, and uses it on particles in a liquid whose molecular granularity is the paper's own subject. The import carries its value on its face, and my bench prints it twice. First, the import's own internal band: the same law read with slip boundary conditions (4π in place of 6π) returns a diffusion constant larger by a factor of exactly 1.500000 at every radius — at a = 1.000000 nm, 3.680597e-10 m²/s against the stick reading's 2.453731e-10 m²/s — and no 1905 step derives the selection. Second, the import's domain: against the solvent's own molecular diameter (0.275000 nm, declared), the used sizes run down to a/d = 1.000000, where the continuum the law presupposes is the very granularity the paper was written to prove. Counted plainly: 1 imported drag law carrying the continuum assumption it rides on, against 0 derivations in 1905 of the drag law at the molecular scale, of either boundary condition, or of the continuum's reach. Grade for this census entry, printed at full size: REASON FOUND / STILL TURNING — PREMISE-ONLY, explicitly not a kill and not a falsification. The program headline stands unmoved: vacuum catastrophe NOT SOLVED / PARTIAL, producing-count 0. Keywords: Einstein 1905; Brownian motion; Stokes–Einstein relation; Stokes drag; mobility; continuum assumption; boundary conditions.
Author: Aldred, William Alexander
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225404553