Cavity-Size Dependent Excess Heat from Hydrogen Isotopes: A Zero-Parameter Hypothesis

Kitamura et al. (2009) reported excess heat from hydrogen and deuterium absorbed into pal-ladium nanoparticles at three characterized grain sizes (100, 30, and 10.7 nm), with energy peratom increasing sharply as particle size decreases. No nuclear products were detected. The sizedependence has not been explained. We propose a hypothesis: the vacuum permittivity ε0 is en-tirely emergent from the electromagnetic vacuum mode spectrum. The observed non-dispersion ofthe vacuum then requires each mode to contribute equally. A metallic nanocavity excludes modesbelow a size-dependent cutoff, modifying ε0 locally. The hydrogen ground state—modelled as a 2Dspherical current shell (Mills, 2018)—shifts in energy by ∆E = 13.6(1/f 2 − 1) eV, where f 2 is thesurviving mode fraction computed from standard cavity electrodynamics. This formula has zero freeparameters and is consistent with all six Kitamura measurements (three sizes × two isotopes) andwith four decades of cavity QED showing no level shifts above ∼1 µm. If correct, the hypothesisidentifies metallic cavity dimension as the controlling variable for anomalous heat from hydrogen onmetals, and predicts a specific ∆E(d) curve testable by systematic particle-size sweeps.