  Even though the usual form of relativistic mechanics does not allow
superluminal particle velocities and nonlocal interactions, these features are
not forbidden by relativity itself. To understand this on a deeper level, we
study a generalized form of relativistic mechanics in which the particle is
influenced not only by the usual tensor (gravitational) and vector
(electromagnetic) potentials, but also by the scalar potential. The scalar
potential promotes the mass squared M^2 to a dynamical quantity. Negative
values of M^2, which lead to superluminal velocities, are allowed. The
generalization to the many-particle case allows a nonlocal scalar potential,
which makes nonlocal interactions compatible with relativity. Particle
trajectories are parameterized by a scalar parameter analogous to the Newton
absolute time. An example in which all these general features are explicitly
realized is provided by relativistic Bohmian mechanics.
