One dimensional Brownian rotation of magnetic microspheres

Many experimental observations of 3D random rotations of particles have been interpreted using Einstein's 1D Gaussian solution. However, in contrast to 1D, 3D rotations are non-commutative, and cannot rigorously be described by Einstein's model. To test the potential discrepancy between theory and experiment, we monitor a particle rotating freely around a single fixed axis, subsequently comparing it with the particle's 3D Brownian rotation. To carry out these observations, we use a fluorescent ferromagnetic microsphere that has one hemisphere coated with an opaque metal (aluminum), while the other is left intact. In rotating, the particle undergoes intensity fluctuations which are observed in a fluorescent microscope. Restraining the rotation by aligning the ferromagnetic particles with an external magnetic field, allows us to see, for the first time, Brownian rotation of a sphere around a fixed axis.