Relativistic kinematics with Caianiello's maximal proper acceleration

The maximal acceleration proposed by Caianiello (1981) is introduced into the equations of relativistic kinematics, passing from a Minkowsky four-dimensional space-time to an eight-dimensional space (incorporating four coordinates proportional to the four-velocity) in order to derive transformations which leave the eight-dimensional distance invariant. A number of simple cases are analyzed, and the relationships between time and length measurements and velocity and acceleration, and among the energy, momentum, and rest mass of a particle are explored.