Casimir torque between two solid birefringent plates across vacuum
In plain words
Two crystals whose optical properties depend on direction should twist toward alignment because of quantum fluctuations, the Casimir torque. It has been measured with a liquid crystal on a solid crystal, but not between two solid plates across empty space.
Precise statement
Two uniaxial birefringent plates (e.g. calcite, quartz, black phosphorus) at gap $d$ across vacuum, with optic axes at relative angle $\theta$: Lifshitz-type theory predicts torque per area $M(\theta, d) \sim A(d) \sin(2\theta)$, with $A(d)$ set by the anisotropic permittivities. An answer is a measurement of A(d) and the $\sin(2\theta)$ dependence at $d$ below about $1e-4\,\mathrm{cm}$, agreeing with theory using measured permittivity tensors.
What would settle it
A torsional measurement of the angle- and gap-dependent torque between two solid birefringent plates in vacuum.
Status in the literature
The torque between a birefringent crystal and a liquid crystal across a thin solid spacer was measured in 2018 (Somers et al., Nature); a solid-solid vacuum measurement has not been reported.