Equations (1661)-(1663) can be regarded as giving the resultant, , of two velocities, and , and are therefore usually referred to as the relativistic velocity addition formulae. The following relation between the magnitudes and of the velocities is easily demonstrated:
According to Equation (1664), if then , no matter what value takes: that is, the speed of light is invariant between different inertial frames. Note that the Lorentz transform only allows one such invariant speed [i.e., the speed that appears in Equations (1643)-(1646)]. Einstein's relativity principle tells us that any disturbance that propagates through a vacuum must appear to propagate at the same speed in all inertial frames. It is now evident that all such disturbances must propagate at the speed . It follows immediately that all electromagnetic waves must propagate through the vacuum with this speed, irrespective of their wavelength. In other words, it is impossible for there to be any dispersion of electromagnetic waves propagating through a vacuum. Furthermore, gravity waves must also propagate at the speed .
The Lorentz transformation implies that the propagation speeds of all physical effects are limited by in deterministic physics. Consider a general process by which an event causes an event at a velocity in some frame . In other words, information about the event appears to propagate to the event with a superluminal velocity. Let us choose coordinates such that these two events occur on the -axis with (finite) time and distance separations and , respectively. The time separation in some other inertial frame is given by [see Equation (1646)]