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[4] viXra:2608.0086 [pdf] submitted on 2026-08-26 20:21:59
Authors: Yonglin Tong
Comments: 6 Pages. (Note by viXra Admin: Please cite listed scientific reference and submit article written with AI assistance to ai.viXra.org)
We report a universal geometric identity for charged particles: the product of the classical electron radius r_e and the Schwarzschild radius r_s is fixed by the Planck length and the fine-structure constant: r_e r_s = 2 alpha l_P^2. The mass m completely cancels, indicating that this constraint is independent of the specific particle mass and represents a universal relation between charged matter and spacetime geometry. Two independent paths provide cross-validation: (1) an algebraic path—direct multiplication of the classical definitions; and (2) a dynamical path—Dekker (2014) derived the characteristic radius r_c = l_P sqrt(alpha) from exact solutions of the Einstein—Maxwell equations, which is algebraically equivalent to the identity above. From this identity, a natural length scale r_res = l_P / sqrt(2 alpha) is defined, corresponding to the Compton energy E_res = sqrt(2 alpha) E_P approx 1.47 x 10^18 GeV, which contains no free parameters and lies within a potentially testable window of ultra-high-energy cosmic-ray physics. We also propose an S^3 x R^3 fiber-bundle geometry as a heuristic framework providing a geometric picture for the resonance scale.
Category: History and Philosophy of Physics
[3] viXra:2608.0085 [pdf] submitted on 2026-08-25 12:46:38
Authors: Peter Cameron
Comments: 9 Pages.
This essay explores a historical question: did twentieth-century physics gain extraordinary predictive power at the cost of losing a unified geometric language? It traces the development of Grassmann's exterior algebra and Clifford's geometric algebra, their eclipse during the rise of vector analysis, and the subsequent evolution of relativity, quantum mechanics, and gauge theory. This change in mathematical language also changed the direction in which theoretical physics sought explanation—from beginning with geometry and asking how physical law emerges, to beginning with physical law and deriving wavefunctions as solutions of field equations. It concludes by suggesting that recovering the geometric representation of the vacuum wavefunction may reopen a complementary bottom-up tradition in theoretical physics.
Category: History and Philosophy of Physics
[2] viXra:2608.0070 [pdf] submitted on 2026-08-17 22:55:18
Authors: Mnoz Pathibharaman
Comments: 23 Pages.
A derivation, once completed, is typically treated as settling the question it was undertaken to answer. This paper argues that this is not generally true, and that the gap between a completed derivation and a settled physical question is easy to overlook precisely because it has no name and leaves no formal trace once crossed. We develop the point through a case in which the gap is unusually visible: a citation, in Hawking’s canonical 1976 physics paper, offered as the source of an extension the citing paper needs but does not itself derive, which turns out oninspection to point to two unsupported sentences in an earlier paper. We use this case not toadjudicate the underlying physical claim, but to isolate two distinct achievements that citationpractice, and derivation itself, can silently conflate: extending a mathematical formalism to abroader domain, and showing that the extended formalism answers a question about a physicalsystem, in the operational sense that connects a model’s terms to what an observer would measure. We argue, drawing on Bridgman’s operational analysis and the model/target-system distinction in philosophy of science, that even a fully executed derivation closing the citation gap we identify would establish the first achievement without thereby establishing the second: a frequency-resolved extension of Hawking’s formalism cannot characterize the polarization structure of the emitted state, and so cannot by itself be used to evaluate the unitarity question the citation is invoked to support, whatever that question’s true answer turns out to be. The dependency this creates is not merely evidentiary but constitutive of Hawking’s own 1976 formal apparatus: that paper’s superscattering operator is built from Hilbert spaces the paper does not construct for the higher-spin sectors, so its own formal question, for those sectors, remains a construction the citation was invoked to supply and does not. We do not argue that this precise structure recurs throughout physics; doing so responsibly would require the same case-by-case verification this paper insists on. We do argue that the case examined here is nota bibliographic curiosity but an instance of a general and underappreciated distinction in whatclosing a derivation can and cannot be shown to achieve.
Category: History and Philosophy of Physics
[1] viXra:2608.0027 [pdf] submitted on 2026-08-07 14:04:51
Authors: Martin Kraus
Comments: 10 Pages.
Physicists have been searching for a vibrational interpretation of the Schrödinger equation for a century; so far with limited success. This work presents a speculative vibrational interpretation in the special case of the Schrödinger equation for a hydrogen-like atom. Solutions of this equation are interpreted as high-frequency stationary vibrations of the atom’s electromagnetic field driven by de Broglie’s internal clock of the atom’s electron, which is assumed to orbit around the atom’s nucleus. The proposed vibrational interpretation challenges existing interpretations of the Schrödinger equation in various ways, which pose interesting research questions for future work.
Category: History and Philosophy of Physics
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