Turning Without Touching: The Casimir Torque Between Birefringent Plates and Its Angular Scale

Two birefringent plates held parallel, with their crystal axes misaligned, experience a torque from the vacuum between them that tries to rotate them into alignment. This paper sizes the effect with a stated anisotropy model: the peak torque per unit area at a hundred nanometres is 2.167e-08 in the units computed by the script, falling as the inverse cube of the separation, so that a square millimetre of plate at that gap feels a torque of order 10^-12 newton-metres. Torsion balances of the kind used in short-range gravity tests resolve such torques, and a first measurement of the effect in a liquid-filled geometry has been reported. The torque is a useful member of the laboratory vacuum family because it is purely orientational: it vanishes for isotropic plates at every separation, so its detection isolates the vacuum's polarisation structure with no competing classical background of the same symmetry. Computed from a stated model, not measured.