{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"dcdde85cad62af27fe182c39b7dde90cd83c1bbcf8a4da1ba67c7d01cf7ae810","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b","ddcb2b53db85e1b84cd790cf92df97991fad320cdd492f52746005bfb0ad5d86"],"salt":"9f1ff080af55870f4cc8b00a8c40a9ff65b96a03f8498f8853d98b38f2d7c6a3","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"amo.casimir-dispersion-forces.casimir-torque","kind":"well-posed","literature_status":"partially-resolved","n":"2","parents":[],"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.","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 vacuum","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"b50b30295d451b258d25179c6bed6abaea4248cdcfa8a1a245381c409e69b63c","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"ada1c985efb934c88726f4eb78702df688677dd0b538cae4583ebee4984f3fcb","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"gfKTpX3Yo8bJXIsOy04e7cKXqLsOTqshwb7m-xKAmR7EVST93AcImL_REi5wHsz_i5OtNokokzXq5aRv68PfCw"},"schema":"pubphys.envelope/1"},"record_hash":"b50b30295d451b258d25179c6bed6abaea4248cdcfa8a1a245381c409e69b63c","leaf_index":2198}