  A phenomenological model is proposed to explain the recent observed
cosmological variation of the fine structure constant as an effect of the
quantum vacuum, assuming a flat universe with cosmological constant $\Lambda$
in the cases ($\Omega_M, \Omega_\Lambda$) equal to (0.3,0.7) and (1,0). Because
of the fourth Heisenberg relation, the lifetime of the virtual pairs of the
zero-point radiation must depend on the gravitational potential, so that the
quantum vacuum changes its density and acquires a relative permittivity
different from one. Since the matter was more concentrated in the past, the
gravitational potential of all the universe was stronger and the optical
density of the vacuum higher, the electron charge being then more renormalized
and smaller than now. The model is based on a first order Newtonian
approximation that is valid for the range of the observations, but not for very
high redshift, its prediction being that $\Delta \alpha /\alpha$ is
proportional to $\Omega_M[a(t)^{-1}-1]-2\Omega_\Lambda [a(t)^2-1]$, $a(t)$
being the scale factor. This agrees with the observations.
