for relativistic relative velocity in any frame, where the speed of light is set to unity so that and agree. It this expression, and are velocities of two objects in any one given frame. The quantity is the speed of one or the other object relative to the other object as seen in the given frame. The expression is Lorentz invariant, i.e. independent of which frame is the given frame, but the quantity it calculates is not. For instance, if the given frame is the rest frame of object one, then . The line element is found by putting or equivalently , with and the usual spherical angle coordinates for taken in the -direction. Now introduce through and the line element on rapidity space becomes Relativistic particle collisions In scattering experiments the primary objective is to measure the invariant scattering cross section. This enters the formula for scattering of two particle types into a final state assumed to have two or more particles, or, in most textbooks, where is spacetime volume. It is an invariant under Lorentz transformations. is the total number of reactions resulting in final state in spacetime volume . Being a number, it is invariant when the same spacetime volume is considered. is the number of reactions resulting in final state per unit spacetime, or reaction rate. This is invariant. is called the incident flux. This is required to be invariant, but isn't in the most general setting. is the scattering cross section. It is required to be invariant. are the particle densities in the incident beams. These are not invariant as is clear due to length contraction. is the relative speed of the two incident beams. This cannot be invariant since is required to be so. The objective is to find a correct expression for relativistic relative speed and an invariant expression for the incident flux. Non-relativistically, one has for relative speed . If the system in which velocities are measured is the rest frame of particle type , it is required that Setting the speed of light , the expression for follows immediately from the formula for the norm (second formula) in the general configuration as The formula reduces in the classical limit to as it should, and gives the correct result in the rest frames of the particles. The relative velocity is incorrectly given in most, perhaps all books on particle physics and quantum