Quantum fluctuations of the electromagnetic field give rise to a zero-point energy that persists even in the absence of electromagnetic sources. One striking consequence of the zero-point energy is manifested in the Casimir force, which causes two electrically neutral metallic plates to attract in order to reduce the zero-point energy. A second, less well-known, effect is a torque that arises between two birefringent materials with in-plane optical anisotropy as a result of the zero-point energy. In this paper, we discuss the influence of Brownian motion on two birefringent plates undergoing quantum electrodynamical ( QED) rotation as a result of the system's zero-point energy. Direct calculations for the torque are presented, and preliminary experiments are discussed.