Static magnetic field vacuum birefringence measured at the QED value
In plain words
A strong magnet should make the vacuum very slightly birefringent, by an amount far too small for any experiment so far. The question is whether any optical cavity experiment can reach the predicted value.
Precise statement
For a static field $B \ll B_S = m^2 c^3/(e\hbar) \sim 4.4e13\,\mathrm{G}$, QED predicts $\Delta n = n_{\mathrm{par}} - n_{\mathrm{perp}} = (\alpha/(30\pi))(B/B_S)^2$, about $4e-24$ at $B = 1e4\,\mathrm{G}$. Determine whether a Fabry-Perot ellipsometer with rotating or modulated fields of $1e4-1e5\,\mathrm{G}$ can reach this value with $\text{signal-to-noise} > 5$, by identifying and suppressing the excess low-frequency noise that limited previous experiments, and measure $\Delta n$ to within 10%.
What would settle it
An ellipsometric measurement of $\Delta n/B^2$ consistent with the QED value at $5\sigma$, with the field-dependence verified.
Status in the literature
PVLAS ended in 2020 with $\Delta n = (12 \pm 17)e-23$ at $B = 2.5e4\,\mathrm{G}$, a $1\,\sigma$ uncertainty about 7 times the QED value $2.5e-23$ (Ejlli et al., Physics Reports 2020).