the wave function converts this field into the total advanced field $$\sum F_{{\rm adv}\,\mu\nu}=F^{(i)}_{{\rm adv}\,\mu\nu}+\sum_{j\not=i}
F^{(j)}_{{\rm adv}\,\mu\nu}.$$

If we wish to believe in our absorber wave function collapse scenario, then we have the observational cosmological constraint on the model that the universe should be transparent to light on the future null cone. This is a severe constraint on a cosmological model. It was first shown by Hogarth[@Hogarth] that if the universe is an ideal (perfect) or quasi-ideal absorber along the future light cone, and is non-ideal along the past light cone, then the effective electromagnetic field acting on a particle at the apex of the light cone is a retarded field: $F^{(i)}_{\rm rad}=1/2(F^{(i)}_{\rm ret}-F^{(i)}_{\rm adv}), F^{(i)}_{\rm eff}=
F^{(i)}_{\rm ret}$ observed in local measurements. For the opposite case, the field is the advanced electromagnetic field plus radiation: $F^{(i)}_{\rm rad}=-1/2(F^{(i)}_{\rm ret}-F^{(i)}_{\rm adv}),
F^{(i)}_{\rm eff}=F^{(i)}_{\rm adv}$.

By considering thermodynamic properties of cosmological models, Davies[@Davies1; @Davies2] has derived concise conditions to be satisfied by opaque and transparent universes. Let us consider a single photon. The probability that a photon will be absorbed in time $dt$ while passing through objects of density $\rho$ and cross section $\sigma$ is $$1-\exp(-\rho\sigma dt)\sim \rho\sigma dt.$$ If the integral 