The Collision Time, Priced: Drude's Assumed Scattering, the Lorenz Number It Returns by Cancellation, and the Heat Capacity It Misses by Sixty
Year: 2026
Type: preprint
Abstract: Census pricing (row CC-109, Scout Batch 7) of the founding step of Drude's 'Zur Elektronentheorie der Metalle,' Ann. Phys. 306, 566-613 (1900), against a fixed bench (postulated / derived / numeric return / reach). The step: the metal's electrons are a classical ideal gas flying freely between instantaneous randomising collisions with immobile ion cores, the whole scattering physics carried by one mean collision time tau that is fitted, not computed. Verified in the notebook (7 checks, exit 0) for copper from named constants plus labelled measured inputs (never spent as derived): carrier density n = 8.4912e28 m^-3 at the model's own assumed one free electron per atom; tau = 2.4876e-14 s extracted backwards from the measured resistivity (an extraction, exhibited as such); mean free path 2.871 nm = 7.95 lattice constants at the model's classical rms speed, against its own collision picture. The Lorenz number priced three ways: Drude's published form 3(k_B/e)^2 = 2.2278e-8 W Ohm/K^2 (ratio 0.9990 to the measured input 2.23e-8) earned by the cancellation of two ~100x errors; the consistent classical form (3/2)(k_B/e)^2 = 1.1139e-8 (ratio 0.4995); Sommerfeld's 2.4430e-8 as closure-by-replacement comparison only. Where nothing cancels, the classical electronic heat capacity (3/2)R = 12.472 J/(mol K) exceeds the measured electronic term gamma*T = 0.2036 J/(mol K) by a factor 61.2. Hall coefficient -7.3505e-11 vs measured input approx. -5.5e-11 m^3/C. Scout-grade verification disclosed on the manuscript's face (CC-91 form). EXTENSION. Vacuum catastrophe NOT SOLVED; quantum gravity NOT SOLVED.
Author: Aldred, William Alexander
Language: English
Subfield: Mechanical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225269939
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