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It has been measured with a liquid crystal on a solid crystal, but not between two solid plates across empty space.","posed_since":"","precise":"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 $10^{-4}\\,\\mathrm{cm}$, agreeing with theory using measured permittivity tensors.","problem_ref":"ddcb2b53db85e1b84cd790cf92df97991fad320cdd492f52746005bfb0ad5d86","references":"","settled_by":"A torsional measurement of the angle- and gap-dependent torque between two solid birefringent plates in vacuum.","status_note":"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.","title":"Casimir torque between two solid birefringent plates across 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