Ten Years, No Coulomb: Schrödinger's Affine Identification, Repriced

Between 1943 and 1951 Erwin Schrödinger built the most determined version of an old dream: a unified field theory with nothing in it but geometry. His single fundamental field was a general affine connection — the rule for comparing directions at neighbouring points, with no metric assumed beneath it. From the connection he built its Ricci tensor, took his Lagrangian as the square root of that tensor's determinant, and then made the move this paper prices. The Ricci tensor of a general connection is not symmetric. Its symmetric part, ten components, he identified with gravitation. Its antisymmetric part, six components, he identified with the electromagnetic field. Neither identification is derived anywhere in the programme. Both are postulates — the second resting on exactly one piece of positive evidence, a count: the antisymmetric part has six components, and so does the electromagnetic field. But the same connection supplies at least four different antisymmetric tensors with six components each; a count that fits four candidates selects none of them. This paper prices the identification step against the scholarly record of what the programme actually produced: of seven deliverables the postulate promised — gravitation recovered, Maxwell's homogeneous equations, Maxwell's equations with real charges and currents, Coulomb's law, a force law for charges, the meson field announced at the start, and a model of the electron — two were delivered, one of them only formally, and five never arrived at all. The author's own audit, in his 1954/55 report from Dublin, is the sharpest line in the file: "It is a disconcerting situation that ten years endeavour of competent theorists has not yielded even a plausible glimpse of Coulomb's law." What the affine programme actually produced was general relativity in affine dress, plus an antisymmetric tensor with electromagnetism's name written on it. What the postulate promised was electromagnetism. The distance between those two sentences is the price. Grade: TWO IDENTIFICATIONS POSTULATED, ZERO DERIVED; TWO OF SEVEN DELIVERED — PRICED. This paper stands outside my work on the vacuum catastrophe; quantum gravity stands not solved in my books, and nothing here moves it. Keywords: Schrödinger; affine geometry; unified field theory; electromagnetism; postulate; census.