A possibly paradoxical corollary of the T=0 boundary condition model arises if the same arguments presented above are also applied in the forward time direction to radiation (or particles) encountering a black hole which eventually collapses to a singularity (rather than eventually evaporating through the Hawking process). While black holes are proper absorbers in the Wheeler-Feynman context since advanced waves can escape from them in the negative time direction (the time-reverse of radiation capture by a black hole), a "reflection" of incident retarded waves at the singularity of the black hole, in analogy to the T=0 boundary condition, would produce a cancellation of the incident wave functions. This leads to the curious conclusion that such black holes might create a condition such that light could not be emitted in their direction, i.e., that they might appear as anti-emission loci. In other words, such black holes might be truly black, in that light "would refuse to shine" in their directions.
However, in an open and continually expanding universe, given enough
time all black holes should eventually undergo Hawking evaporation.
Further, there is no particular reason why a
=0 (at singularity and beyond)
boundary condition need be applied to black holes. Moreover, the
thermodynamics of a black hole should be rather different from the
time-reversed Big Bang, in that the ambient temperature of the former would
normally be very much higher that that of incident radiation and thus the
establishment of a thermodynamic equilibrium before reaching the singularity
would be essentially certain. Thus, black holes would not be expected to be
anti-emission loci. It would, nevertheless, be worth testing this point with
a suitable experiment, if one could be designed.
There is also a second experimental effect which might arise from the T=0 boundary condition model presented above. Let us make the plausible (but not completely necessary) ansatz that the probability of "open-ended" emission of a wave in a particular direction depends on the volume of momentum phase space occupied by 4-vectors connecting the emission event with the T=0 point in the reverse space-time direction. If this is the case then the emission probability for such waves will not necessarily be spatially isotropic. Indeed, the anisotropy of this phase space will be a function of the rest-frame of the emission event, and there will be a preferred inertial reference frame which has an isotropic phase space in all spatial directions.
This is analogous to the preferred reference frame defined by the isotropy of 2.7 K black-body radiation from the Big Bang, which is essentially the time-reverse of the phenomenon considered here. It has been demonstrated experimentally that the Earth has a velocity of about 0.1% c with respect to the rest frame defined by the 2.7 K radiation. Thus, it would be expected that "open-ended" emission processes might be slightly anisotropic if the emission occurs in any reference frame in which this phase space were skewed (such as that of the Earth). The anisotropy of the emitted radiation would not necessarily replicate the phase space anisotropy, if only because the rescattering of the advanced waves travelling back to the T=0 point would tend to equilibrate these waves with the momenta of the scattering centers and would therefore tend to average out any such anisotropy. Furthermore, it is not clear that the dependence of the "open-ended" emission probability on the phase space volume is a necessary consequence of the T=0 boundary condition.
Such a dependence would have consequences which could be observed experimentally. For the case of radio waves at frequencies around 10 GHz, two such tests have already been performed, and both experiments have given negative results[23,24]. However, it is not completely clear that radio waves represent a suitable case for "open-ended" emission, since the probability of absorption of such waves by the inverse bremsstrahlung process grows without limit as the waves are red-shifted while travelling cosmological distances in an open universe. Davies[13] has demonstrated that most open universe models are "transparent" to such radiation in the sense that the absorption cross section integrated over all future times is not infinite, but the latter, while finite, might still be very large. In that case, only an infinitesimal fraction of the transmitted flux might be truly "open-ended" emission events.
An alternative test of emission anisotropy involves the emission of neutrinos. Neutrinos cannot be absorbed in the equivalent of the inverse-bremsstrahlung process because they are fermions and have a neutral-weak-current scattering cross section which is inversely proportion to their wavelength at low energies. Such an experiment is now in progress at the University of Washington, and employs the angular correlation between the directions of neutrino and electron emission in a pure Gamow-Teller beta decay to deduce a possible anisotropy in neutrino emission by observing the spatial distribution of emitted electrons, as measured in back-to-back beta scintillation spectrometers. Any anisotropy in neutrino emission would be reflected in a nine times weaker anisotropy in electron (i.e., beta-particle) emission. The phase-space dependence assumption described above would imply that the maximum anisotropy which might be found in the electron emission would be about a part in 104, and it could be much weaker.
The size of the neutrino emission anisotropy, under the phase-space ansatz mentioned above, depends strongly on the velocity of the source. Thus, if the neutrinos are emitted from a source moving at a relativistic velocity, the anisotropy should be greatly magnified. In particular, the spatial anisotropies in neutrinos produced by the decay of a collimated beam of pi mesons should be quite anisotropic, and this anisotropy should be reflected in the distribution of muons resulting from the pion decays. An experiment searching for such an anisotropy in the muon distribution in the pion center-of-mass reference frame has several advantages over the beta decay experiment: (1) it involves mu-neutrinos which are presumably more difficult to absorb than are electron-neutrinos; (2) it involves a two body decay, with a back-to-back angular correlation between the decay products enforced by energy and momentum conservation (instead of the rather weak angular correlation of the beta decay experiment), and therefore there is a one-to-one correspondence between muon and neutrino anisotropies; and (3) since the center-of-mass velocity of the pion beam can be made very large compared to the laboratory rest frame, an effect depending on phase space volume would be greatly magnified over a similar effect measured in the laboratory frame, leading to a greatly enhanced experimental sensitivity.
It should be emphasized, however, that such experiments test the hypothesis that an "open-ended" emission process reflects the phase space of the Big Bang in the negative time direction. This is a far stronger assumption than the T=0 boundary condition model itself. These proposed tests are, therefore not definitive tests of the boundary condition model presented here. In particular, a negative result from such experiments would not serve to eliminate the T=0 boundary condition model but a positive result could be taken as evidence in favor of the model.