Vacuum Birefringence in Laboratory Magnets: The Ellipticity Budget From the Euler-Heisenberg Term to Present Limits

Quantum electrodynamics predicts that a magnetic field makes the vacuum slightly birefringent, with an index difference of 3.974e-24 at one tesla, rising as the square of the field. This paper budgets the effect for laboratory configurations from one tesla over one metre to thirteen tesla over an effective hundred metres, computing the ellipticity an optical polarimeter must resolve in each case. Even the strongest configuration yields a single-pass ellipticity of order 10^-16 radians, which is why real experiments fold the optical path through the field tens of thousands of times with a Fabry-Perot cavity. The calculation also fixes the scale comparison that matters for gravitational accounting: birefringence samples virtual electron-positron pairs at the electron rest energy, half a megaelectronvolt, eleven orders of magnitude above the milli-electronvolt scale of the surviving vacuum density, so a detection would certify the high-energy vacuum while saying nothing direct about the remainder. Computed from stated assumptions, not measured.