Expanding quasars and the expansion of the universe

Thirty-two compact radio sources have both a redshift z and an internal proper motion, μ, measured with VLBI. These two observables are anticorrelated. There is a rough upper limit to μ(z) which falls much faster than (1 + z)^-1^, the function which describes the limiting proper motion in a simple model in which quasars are all at the same distance, and their various values of z reflect their peculiar velocities. Thus redshift is a measure of distance, unless there is a strong anticorrelation between z and the linear velocity of the VLBI components. Friedmann cosmology describes the upper limit, and a relativistic beam model gives γ ~ 9-18 for the Lorentz factor of the moving components, for H_0_ = 100-50 km s^-1^ Mpc^-1^. In this model most of the sources are aimed close to the line of sight, and Doppler boosting is probably responsible for this selection effect. Relativistic shells expanding into dipole fields do not match the data, unless the Hubble constant is allowed to assume extreme values. Chronometric cosmology does not appear to describe the upper limit to the observed proper motions.