A Constant Promoted by Postulate: Jordan's Variable G, Priced Against the Modern Bounds

In 1955 Pascual Jordan published the mature form of a theory he had built over the preceding decade: take the five-dimensional geometry of Kaluza and Klein, let its fifth metric component be a genuine field instead of a fixed constant, and that field plays the role of a gravitational "constant" that is not constant at all. The promotion was the postulate. Dirac's large-number coincidence suggested that G might vary; Jordan's projective machinery gave the suggestion a home; nothing in the work derived that G varies, fixed the field's coupling, or computed a rate. In his original construction Jordan added a second coupling that let matter itself be created over time — the variability and the creation were both put in by hand, following Dirac's ideas. I priced the postulate against the modern record, fetched for this count. The rate the Dirac law that motivated the whole construction demands today — Ġ/G of order the Hubble rate, about 7×10⁻¹¹ per year — is excluded by lunar laser ranging, which measures Ġ/G = (7.1 ± 7.6)×10⁻¹⁴ per year: the motivating law overshoots the allowed band by a factor of roughly five hundred to a thousand. Run backwards, the same law would make G some 36,000 times larger at recombination and some 10¹⁵ times larger at nucleosynthesis; the microwave background and the light-element abundances instead pin G at those epochs to within a few percent of today's value. And the theory's living form — conformally the same scalar-tensor theory Brans and Dicke published in 1961 — is fenced by the Cassini measurement into the same corner as theirs: its coupling must exceed about 40,000, the corner where the scalar does almost nothing. The deficit is two assumed steps and zero selection equations. Jordan built the structure variable G lives in. He did not derive that anything lives there.