Quasar Velocity

Quasars have been detected that have recessional velocities greater than the speed of light c based on the cosmological relationship for the redshift z, namely, l + z = exp[v/c]. That is, there are quasars with z > 3, for example. Also, to explain the present state of the universe, the inflationary big bang model requires a faster than light expansion of space in the young universe. Are these examples violations of the special theory of relativity?

Answer

The special theory of relativity says that information cannot be transmitted faster than light. The photons always travel at light speed in the local reference frame, but the space in which the photons travel may be expanding. An analogy would be a 100-meter race with the track lengthening during the race. The elapsed time to reach the 100-meter tape depends on the model for the expansion rate for the runner and for the photons from that distant quasar. Under these expansion conditions, there can be recessional velocities greater than c!