One Medium, Two Constants: The Plenum Density, the Permittivity of Free Space, and the Magnetic Bridge

The Info-Magneto-Electrostatic (IME) cosmos models space as a real medium, the plenum, and assigns it a density 0=8.85410−12 kg m−3, numerically equal in SI units to the permittivity of free space 0. The literal equality depends on units, since replacing the kilogram by the gram moves the ratio by a factor of a million. This paper asks what survives. It separates scaling dimensions, which change with units, from label dimensions such as charge, flux and cell number. The dimensional gap between 0 and 0 is exactly a squared magnetic field. The charge label of 0 cancels against the flux label of B2, and the identity reduces to a relation between two pure counts, cells per unit volume and flux quanta per unit area. Standard electrodynamics supplies the mechanism: a charge-bearing body moving through a magnetic field carries field momentum 0B2 per unit volume per unit velocity, and a body that grips an isotropic field band acquires inertia 0⟨B2⟩ per unit volume. The plenum density is therefore the permittivity weighted by the mean square field that the electron cloud grips, and the SI coincidence is equivalent to a gripped field of one tesla. Through the f-sum rule, with each electron’s self-mass subtracted, that field corresponds to a valence plasma energy of 16.4 eV, typical of ordinary solids. The permittivity, and with it the density, is local, altered near a body by its mass and magnetic dipole. It predicts an Eötvös ratio of −2.3910−15 for titanium and platinum, within one standard deviation of MICROSCOPE.