Vacuum Polarization: the Running Coupling of QED

Quantum electrodynamics predicts that the vacuum around a charged particle is filled with virtual electron–positron pairs that constantly appear and vanish under the Heisenberg energy–time uncertainty relation. A real charge polarizes this cloud — attracting the opposite virtual charge and repelling the like one — which screens part of the bare charge from anything probing it at long range. This simulator renders that polarization cloud in 3D around a central charge, lets you slide a probe from far outside the cloud down to well inside the electron's Compton wavelength, and recomputes the one-loop QED formula for the running effective coupling α(r) live, showing exactly how and why the "constant" fine-structure constant isn't constant at all.