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The Casimir force acts on nearby surfaces due to zero-point fluctuations of the quantum electromagnetic field. In the nonretarded limit, the interaction is also known as the van der Waals force. When the electromagnetic response of the surfaces is anisotropic, a torque may act on the surfaces. Here, we review the literature and recent developments on the Casimir torque. The theory of the Casimir torque is discussed in an explicit example for uniaxial birefringent plates. Recent theoretical predictions for the Casimir torque in various configurations are presented. A particular emphasis is made on experimental setups for measuring the Casimir torque.

We investigate the torque on two rotating particles and two rotating plates due to the thermal fluctuation and vacuum fluctuation. A general formula has been developed including the temperature difference on each plate and vacuum, and the different angular velocity on each plate. We show that the Casimir torque in absorbing material occurs whenever there is a difference in temperature or a relative angular velocity between the plates and the vacuum.

The effect of roughness and correlation on the Casimir torque is studied. The plates are assumed to be perfect conductors. This is a good approximation when the separation between plates is not too small. The pairwise summation (PWS) method is used, which is a good approximation when the correlation length is much larger than the distance between the plates. Torque components both parallel and perpendicular to the plates are obtained. It is seen that the component parallel to the plates is nonvanishing even if the plates are smooth, but there are contributions due to roughness and correlation as well, and the contribution of the correlation is an increasing function of both the roughness exponent and the correlation length. The component perpendicular to the plates, however, is nonvanishing only if the plates are rough and correlated to each other. As the roughness exponent increases, this component increases, reaches a peak and then decreases.

The Casimir force acts on nearby surfaces due to zero-point fluctuations of the quantum electromagnetic field. In the nonretarded limit, the interaction is also known as the van der Waals force. When the electromagnetic response of the surfaces is anisotropic, a torque may act on the surfaces. Here, we review the literature and recent developments on the Casimir torque. The theory of the Casimir torque is discussed in an explicit example for uniaxial birefringent plates. Recent theoretical predictions for the Casimir torque in various configurations are presented. A particular emphasis is made on experimental setups for measuring the Casimir torque.