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Constraining Classical Field Models of Self-Generated Particle Structure: Successive No-Go Theorems

Year: 2026
Type: preprint
Abstract: Classical-field models of the electron require a localized field configuration that persists in a linear, source-free field on unbounded space. We show that for linear source-free fields this is excluded by theorem, and we locate where the missing structure must enter. Theorem A, given two independent proofs, states that a finite-energy source-free Maxwell field on unbounded vacuum R3 whose energy density is stationary or time-periodic in some inertial frame is the zero field. Its scalar/Klein–Gordon corollary (Theorem A′ ), stated for constant coefficients on R3 without boundaries or trapping, transports the obstruction to a linear wave carrier: the massless case closes by the transferred strong-Huygens argument, the gapped case by the spectral argument through the Ruelle–Amrein–Georgescu–Enss (RAGE) theorem; spatially varying coefficients or an added trapping potential lie outside the hypotheses, and are where bound states can arise. A zero-net-flux proposition records that every closed surface carries vanishing electric and magnetic flux. The results assemble established tools—local energy decay, RAGE, the co-area formula— under explicitly fenced hypotheses, and use them to place the wave-electron models: each posits persistence at a stratum where one hypothesis fails. What survives names the additional structures through which localization or charge may enter: a time-dependent internal phase, gauge coupling, or topology in the sources or the potential sector; source-free field-line topology alone disperses under Theorem A. Companion paper: "Schrödinger as the Envelope Equation of a Gapped Electromagnetic Carrier", DOI 10.5281/zenodo.21534577 (all versions). The two papers are co-posted and cross-cite by concept DOI. Version 2 (September 2026). Substantially revised. Principal changes since v1: (i) the Beltrami/closure theorem (formerly Theorem B) has been excised in full — the reason of record is that under the monochromatic field pin the Ampère law forces the Beltrami current to vanish, and the printed closure quantity omitted a k^-3 scale factor; the paper now presents Theorem A (two proofs), its constant-coefficient scalar/Klein–Gordon corollary A′, and the zero-net-flux proposition; (ii) the A′ proof is rewritten in the unitary energy representation a± = (Ωφ ± i∂ₜφ)/√2, with the massless case closed by the transferred strong-Huygens argument alone and the gapped case by a RAGE argument through a compact resolvent composition; (iii) the frame-transfer of finite energy (|P| ≤ E/c) is now stated at hypothesis (H1), with the scalar mirror restricted to v = c; (iv) the Wolff and Williamson–van der Mark placements are rebuilt as explicit three-horn trilemmas; (v) linearity is stated as an explicit fenced hypothesis (HS0) for the scalar corollary, with a distributional-regularity remark following the zero-net-flux proposition; (vi) the abstract, keywords, declarations, and the hypothesis language for spatially varying coefficients are rewritten and standardized; (vii) all printed record DOIs now use the Zenodo concept (all-versions) DOIs so citations resolve to the newest version. A complete change ledger (paper0_delta_v1.0_to_v1.18.txt) and a latexdiff of the full revision (paper0-diff-v1.0-v1.18.pdf) accompany this version.
DOI: 10.5281/zenodo.21531712
Language: English
Open Access status: green
OpenAlex ID: W7170688140
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