Relativistic Brownian Motion in 3+1 Dimensions

We solve the problem of formulating Brownian motion in a relativistically covariant framework in 3+1 dimensions. We obtain covariant Fokker-Planck equations with (for the isotropic case) a differential operator of d'Alembert form. Treating the spacelike and timelike fluctuations separately in order to maintain the covariance property, we show that it is essential to take into account the analytic continuation of "unphysical" fluctuations. We discuss the notion of locality in this framework and possible implications for entangled states.