The body of work cited above has demonstrated that essentially all of the open-universe models are "future-transparent", i.e., that these models lack the absorption necessary to account for all of the present emission of neutrinos and electromagnetic radiation in the context of generalized Wheeler-Feynman absorber theory. However, there is also another problem which arises in considering the backward extrapolation of advanced waves to the T=0 point or "origin" of a Big Bang model.
Let us imagine an advanced wave function which has just been produced in the emission of a very low energy neutrino, and which now propagates backward in time toward the Big Bang. Assume that the medium is transparent enough to permit the wave to penetrate the region of high density and energy just after the "origin". What happens when it reaches the T=0 singularity? Clearly, no matter how penetrating and non-interacting such a wave is, it seems unreasonable that it should extend to a time before the T=0 origin. If it does not, then it must terminate at (or after) the T=0 point.
Let us, then, adopt a boundary condition model for the T=0 Big Bang
by assuming that all waves extending backward in time to the T=0 point must
terminate there without a transfer of energy, i.e., that
(T)=0 and
E=0
for T<0. This is effectively a reflection boundary condition analogous to
that employed in electrical circuit theory to describe the interaction of an
electrical impulse travelling in a transmission line with a "shorted"
termination of the transmission line. However, while the latter boundary
condition requires cancellation of the impulse only at a boundary point in
the "space" of the one dimensional transmission line, the T=0 boundary
condition stated above requires an analogous cancellation of a four-vector at
a locus in space-time which includes all four-vector world lines. Such a
condition produces cancellation not only at that locus, but also elsewhere
along the four-vector.
It is implicit in the W-F description of the emission process that
there is an advanced-to-retarded "phase flip" at the event-point of emission on
the lightlike world line which contains the pair of emitted waves. It should
be emphasized that in the T=0 reflection as described above there is no such
advanced-to-retarded "phase flip" across the T=0 boundary point. The
reflected wave is not a retarded wave (E>0) but an advanced wave (E<0) which
"mirrors" the incident advanced wave. Thus no energy is exchanged with the
T=0 boundary point, as required by the
E=0 condition stated above.
Let us consider this boundary condition in the context of the "open-ended" emission of a low energy neutrino as described above, which sends a retarded neutrino wave function into the future and at the same time sends an advanced neutrino wave function in the negative time direction until it encounters the T=0 Big Bang. The result of the T=0 boundary condition described above is the production of a "reflected" advanced neutrino wave function which is identical to, lies on the same world-line with, and is 180o out of phase with the incident advanced neutrino wave function. This produces a cancellation of the incident wave not only at the T=0 event but at every point along the world line back to the point of emission. At that point the reflected advanced wave becomes in phase with the emitted retarded wave and the two reinforce. To an external observer, this process involves no advanced waves at all, but only the "open-ended" emission of a retarded wave. This process is illustrated in Fig. 2.
Unlike the other absorber theory transactions, this process has no time-reversed analog, for the T=0 Big Bang in an open universe model exists only on the "past" time direction, not in the "future" direction. This, then, accounts for the electromagnetic direction of time and for the analogous "weak" arrow of time associated with neutrino emission. It is also consistent with the general argument given by Gold[21], showing that where all detailed physical theories are time symmetric, the arrow of time must ultimately be associated with the large-scale properties of the universe.
The arguments given above must be modified to some extent because it is unlikely that waves travelling in the negative time direction could actually reach the T=0 point without being scattered or absorbed. The issue, however, is not the complete absence of interaction but whether the wave and its precursors retain their serial identity, or whether they lose that identity and reach a condition of thermodynamic equilibrium before the T=0 point. Davies[22] has argued that such an equilibrium is more difficult than it might seem because the blue shift in the negative time direction scales all energies together, so that the time-reversed wave is always orders of magnitude "hotter" than its environment and can retain its identity.
Nevertheless, there is a serious problem with this point of view at the extremely high densities, energies, and temperatures (1027 K) near the T=0 point. In such a domain there should be a complete breakdown of the spontaneous symmetry breakings which distinguish the strong interaction from the electromagnetic interaction and the electromagnetic interaction from the weak interaction. When such a breakdown occurs we lose the distinguishability of bosons vs. fermions, hadrons vs. leptons vs. photons, etc. The propagation of an advanced wave (or chain of advanced waves) through this "soup" to the T=0 boundary must be considered problematic at best. In fact, a detailed analysis of the likelihood of such an event is well beyond the scope of our present theoretical understanding because of the incredibly high densities and temperatures involved.
However, we may approach this problem from a slightly different perspective. Consider entities (we do not need to specify whether they are hadrons, leptons, or photons) which are produced a very short time after T=0. According to the generalized Wheeler-Feynman protocol, advanced and retarded wave functions for these entities will be produced in pairs. The advanced waves will then immediately propagate backward through the short time interval to T=0 where they will be "reflected" and cancelled. Thus, from the start the universe will have an established predominance of retarded waves, and according to the arguments given by Hogarth this will establish a time direction which is irreversible and will persist into our epoch.
It should be emphasized that, in the generalized version of Wheeler-Feynman absorber theory presented here, the T=0 reflections are only a "transaction of last resort" for radiation which is too weakly absorbed to interact with a future absorber according to the emitter-absorber protocol described above and in AT1. In the more usual emitter-absorber transactions the advanced waves from the emitter are cancelled by those of the absorber so that the T=0 boundary condition plays no role in the transaction. Only when there is no future absorber does the effect of the T=0 boundary condition appear.
It can be argued that the T=0 boundary condition model presented here, while plausible, is no better and no less ad hoc than any other boundary condition model, and, in particular, is no improvement over the "causality" boundary condition model (CBC) usually applied to electrodynamics. The latter asserts as a boundary condition to the solution of the wave equation that the advanced fields and potentials do not exist because they would violate the principle of Causality (i.e., the cause always precedes the effect in time sequence). There are several arguments which can be made against this point of view, which we will enumerate here:
(1) The T=0 boundary condition describes a plausible property of a physical boundary (the T=0 point) in the interaction of that boundary with advanced waves. The CBC, on the other hand, is not a boundary condition in the strict sense of the term, in that it seeks to directly establish a correspondence with observation rather that stating a property of a physical boundary. The CBC is reminiscent of the Aristotelian boundary condition that "Nature abhors a Vacuum".
(2) The T=0 boundary condition, unlike the CBC, establishes a definite connection between the direction of electromagnetic time (the "retarded" direction) and the direction of cosmological time (the time direction in which the universe expands). Further, the T=0 boundary condition is specific, in that, unlike the CBC, it "works" only in an open universe, and is incompatible (without special assumptions) with closed and cyclic universe models.
(3) The goal of the present work is to find a way of reconciling generalized absorber theory with the experimental fact of the dominance of retarded radiation in the universe. The motivation for attempting this synthesis is that generalized absorber theory has been found to provide a solution to quantum mechanical paradoxes (see AT1). The CBC precludes absorber-emitter transactions and therefore cannot achieve the desired synthesis. As was discussed in the preceding section, previous attempts to connect the electromagnetic and cosmological arrows of time using an absorption boundary condition have ultimately led to the conclusion that the electromagnetic arrow should be directed in the opposite direction.
(4) The CBC, given the dominance of retarded radiation, has no discernible consequences which lead to experimental tests. The T=0 model has at least one consequence which is, in principle, subject to experimental verification, i.e., the requirement of an open universe. As will be discussed in the next section, there may also be other consequences of the model which can be subjected to experimental tests.