There have been a number of attempts in the literature to apply the W-F approach to cosmology and to deduce from this the observed predominance of retarded radiation over advanced radiation. In their original paper[1], Wheeler and Feynman attempted to derive this predominance from the thermodynamic properties of the absorbing medium in a static euclidian universe, attributing the electromagnetic Arrow of Time to the thermodynamic Arrow of Time implicit in the Second Law. Later authors have tended to reject this approach because of its incompatibility with reasonable models of the universe.
Hogarth demonstrated[9] that the application of the W-F approach to a system with many interconnected electromagnetic interactions involving radiation and absorption and a high absorption probability in one or both time directions leads to only two stable equlibrium conditions: the system is either completely dominated by advanced radiation or by retarded radiation, depending on differences in the probability of absorption in the past and in the future. Hogarth then attempted to connect the electromagnetic arrow of time to the cosmological expansion of the universe. Hoyle and Narlikar[5] later adopted a similar approach in relation to their "C-field" cosmological model based on an expanding universe with the continuous creation of particles. They argued that the C-field model alone is consistent with the dominance of retarded radiation and took this as evidence in support of their model. Roe[10] and Burman[11,12] have also employed absorber theory and the observed dominance of retarded radiation as tools for investigating cosmological models.
Unfortunately, none of the treatments which "explain" the dominance of retarded radiation has been able to withstand close scrutiny. Davies[13] has shown quite convincingly that any ever-expanding cosmology (in the absence of a special postulate such as continuous creation of matter) will be transparent (i.e., deficient in future absorption) if R(T) grows faster than T1/3, where R(T) is the time-dependent scale factor of the model, e.g., the radius of the universe. This means that there will always be more absorption in the past, where the absorber density is large because R is small, than in the "transparent" future.
Given the observed dominance of retarded radiation, this argument excludes all open-universe models except the Dirac model (Np1/2 = mpT) and some of the C-field models of Hoyle and Narlikar. Moreover, Davies has also been able to show that the C-field models are not able to explain the dominance of retarded radiation for other reasons. In the context of absorber theory, this leads to the conclusion that the electromagnetic arrow of time should point in the opposite direction from that of the cosmological expansion of the universe, in clear contradiction to observation.
Closed universe models such as the oscillating Friedmann models are not subject to this criticism because they become opaque during their collapsing phase if R collapses faster than T1/3, which is normally the case. However, because they collapse in both time directions, such models are intrinsically time symmetric and cannot explain the dominance of retarded over advanced radiation (in the absence of additional special postulates). Treatments which assume that thermodynamic processes also have time symmetry in such a model[10] therefore imply the necessity for a mixture of advanced and retarded radiation, in contradiction to observation.
If we generalize the ideas of absorber theory beyond their application to classical electromagnetic radiation, as was done in AT1 and elsewhere, by assuming that the emitter-absorber transaction also applies to the emission and absorption of neutrinos, then models of the universe can also be examined as they apply to neutrino processes. This has been done by Narlikar[14], by Csonka[15], and by Burman[16,17, 18]. We note that the evidence for the complete dominance of retarded neutrino radiation is less compelling than is the case for the dominance of retarded electromagnetic radiation, but it is still fairly strong. In particular, experimental searches for post-endpoint electrons in beta decay processes (which would imply negative-energy, i.e., advanced neutrinos) have in effect set very low upper limits on the emission of advanced neutrinos with negative energies of less than -60 eV[19].
The treatment of Burman in investigating the transparency of cosmological models to neutrinos follows that of Davies[13] discussed above, and concludes that open-universe models are transparent to neutrinos if R grows faster than T1/3. This, then, is the same result which Davies obtained for electromagnetic radiation. However, in deriving this result Burman employed the assumption, based on the current-current model without weak neutral currents (which was the standard weak interaction model at the time the calculations were performed), that the effective neutrino cross section is independent of energy even at low energies. The neutral current model of weak interactions would imply that the latter assumption is correct at higher energies, but that as their energy E goes to zero the neutrinos should gain transparency. It predicts[20] that at low energies the neutrino absorption cross section vanishes and the neutrino scattering cross section becomes proportional to E2. The effect will become important for red-shifted neutrinos travelling cosmological distances in an open universe, and implies that such a universe is transparent to neutrinos if R grows faster that T1/5. This revision of Burman's calculation then excludes the Dirac model mentioned above.
The conclusion of this body of work is that no reasonable model of the universe, either open or closed, is consistent with the observed predominance of retarded radiation in the context of Wheeler-Feynman absorber theory, at least in the way in which the latter has been used in these calculations. This, then, would appear to place W-F absorber theory in direct conflict with contemporary cosmology. If no way can be found around this difficulty, it is a very serious criticism of the whole absorber theory approach.