  We propose a quantum model for the vacuum filled of virtual particle pairs.
The main originality of this model is to define a density and a life-time of
the virtual particles. Compared to the usual QED $(p,E)$ framework, we add here
the $(x,t)$ space time parameters. We show how $\epsilon_0$ and $\mu_0$
originate from the polarization and the magnetization of these virtual pairs
when the vacuum is stressed by an electrostatic or magnetostatic field
respectively. We obtain numerical values very close to the measured values. The
exact equalities constraint the free parameters of our vacuum model. Then we
show that if we simply model the propagation of a photon in vacuum as a
succession of transient captures with virtual pairs, we can derive a finite
velocity of the photon with a magnitude close to the measured speed of light
$c$. Again this is the occasion to adjust better our vacuum model. Since the
transit time of a photon is a statistical process we expect it to be
fluctuating and this translates into a fluctuation of $c$ which, if measured,
would bring another piece of information on the vacuum.
  When submitted to a stress the vacuum may change and this will induce a
variation in the electromagnetic constants. We show this to be the case around
a gravitational mass. It gives a physical interpretation of a varying vacuum
refractive index equivalent to the curved space-time in General Relativity. The
known measurements of the deflection of light by a mass, the Shapiro delay and
the gravitational redshift do bring constraints on the way inertial masses
should depend upon the vacuum.
  At last some experimental predictions are proposed.
