{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"7b44f13622982a90d1f7ee5741cd5a44cc1281e4bc5edb79799145b61bbde3ba","created":"2026-10-03T07:17:53Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"5af128d2e57734a87dffc9faf05b2984acf34333367629f06864163890e6465b","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":"1","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 $1e-4\\,\\mathrm{cm}$, agreeing with theory using measured permittivity tensors.","problem_ref":null,"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":"55304ca08284e7e9dcef4619089d0254a5b2c4ea521d0ef72f8036eb785a7e96"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"ddcb2b53db85e1b84cd790cf92df97991fad320cdd492f52746005bfb0ad5d86","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"ec629d16d95652714d9e339e62ed7e3477235b8b08498ce4be007919a6a172d1","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"vPWqh_kDbogEFMIJC0n7gMQQZGlAYcuU38NpN_FqwkLlZXsXP76Ca8bA-3D7mn-oUCA380uRsNxFWVYSLDreDg"},"schema":"pubphys.envelope/1"},"record_hash":"ddcb2b53db85e1b84cd790cf92df97991fad320cdd492f52746005bfb0ad5d86","leaf_index":378}