Light Scattering From Light: The Vacuum Box Diagram From Optical Energies to Collider Detection

Photons are electrically neutral and, in classical electrodynamics, pass through one another without interacting. In quantum electrodynamics they scatter, through a virtual electron-positron loop, with a cross section that at optical energies is 7.265e-70 square metres, a value so small that the effect hid from experiment for eighty years. This paper follows the sixth-power energy growth of the low-energy cross section from one electronvolt to ten kiloelectronvolts and explains, in rate terms, why the first observation required colliding lead nuclei: gigaelectronvolt photons, supplied coherently by charges of eighty-two, raised the rate by dozens of orders of magnitude. The vacuum box diagram is the purest of the laboratory vacuum effects, involving no matter and no bound states, only the polarisable vacuum itself. All cross sections here are computed from the stated low-energy formula, not measured.