Recently, it was predicted that extraordinary light waves in hyperbolic metamaterials may exhibit two-time physics behavior. We report experimental observation of this effect via investigation of gravity-like nonlinear optics of iron/cobalt-based ferrofluid hyperbolic metamaterials. In addition to conventional temporal coordinates, the spatial coordinate oriented along the optical axis of the metamaterial also exhibits timelike character, which leads to very unusual two-time physics behavior in these systems on small scales.