A Halfway Bridge Between Classical and Quantum Physics: A Parameter-Free Photoelectric Law for 40 Metals and a Classical Test of Quantum Mechanics' Founding Experiments

Abstract The photoelectric threshold frequency of 15 elemental metals follows a classical law set by lattice geometry, ν₀ ≈ 0.70 × f_orbit(r), to within 16.5% in leave-one-out tests. Here f_orbit is the classical orbital frequency of an electron about a unit charge at half the nearest-neighbour distance r; the law contains no Planck constant. We arrive at it from a semiclassical mechanism: a classical light wave pushes a charge confined by its surroundings, frequency rather than intensity decides the push, and the charge leaves when the exchange exceeds its binding. Each swing exchanges a fixed action h with the wave, treated here as a constant of nature, as in classical electrodynamics with zero-point radiation. The orbit law beats a quantum-confinement formula (25% error) but trails a simple electrostatic energy law, φ ≈ 0.40 e²/(4πε₀r) (14%), which is close to known image-charge models. At three scales, characteristic frequencies are fixed fractions of a classical frequency: metal photoemission thresholds, inner-shell X-ray lines (1.0% rms across eight elements with relativity), and nuclear thresholds and resonances. With h as a constant, the picture reproduces the energy-exchange experiments listed in Section 5, among them blackbody radiation, Compton scattering and X-ray lines, several to within 1%. Bell tests, antibunching, spin and Pauli exclusion still require quantum mechanics. We propose a strain test that separates classical from quantum scaling.