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Title: Casimir torque between two solid birefringent plates across vacuum
Plain: 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: 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.
Settled by: A torsional measurement of the angle- and gap-dependent torque between two solid birefringent plates in vacuum.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: partially-resolved
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.
Posed since: (empty)