The problem of the direction of the electromagnetic Arrow of Time is perhaps the most perplexing of the major unsolved problems of contemporary physics, because the usual tools of theoretical physics cannot be used to investigate it. Even the clues provided by the CP violation of the K20 meson, which have lead to profound insights into the dominance of matter over antimatter in the universe, have not shed any light on the problem of origins of the electromagnetic Arrow of Time.
The fundamental reason that the Arrow of Time has proved to be such an intractable problem lies in the conventional treatment of the solutions of the relativistically invariant wave equations describing massive and massless particles. These equations have both retarded (or positive mass-energy) solutions and advanced (or negative mass-energy) solutions which are characteristic of the two possible directions of the Arrow. However, the usual procedure is to invoke a ``Causality'' boundary condition which justifies the elimination of the advanced solutions as unphysical. Once Causality is invoked, an Arrow of Time has been built into the formalism, and it is no longer possible to use the formalism as a tool for the investigation of the origins of the Arrow.
However, there is an alternative approach which, while not in the mainstream of contemporary theory, represents an effective way of preserving the intrinsic time symmetry of the relativistically invariant wave equations and thereby avoiding the ad hoc insertion of an Arrow of Time into the formalism. This is the Wheeler-Feynman (W-F) approach[1], which was anticipated to some extent by the work of Tetrode[2], Fokker[3], and Dirac[4], and which has been given quantum mechanical treatments and generalized by Hoyle and Narlikar[5], Davies[6], and Cramer[7]. The W-F approach is to choose a time-symmetric linear combination of advanced and retarded solutions to the wave equation of interest, and to produce whatever time asymmetries are required to agree with experimental observation through the application of external boundary conditions which do not explicitly involve Causality. The W-F approach will be discussed further below.
While the time symmetric W-F formalism can, in principle, provide a tool for the investigation of the Arrow of Time problem, the previous uses of this tool for that purpose have not been notably successful. In fact, as will be discussed further below, the best work employing W-F theory with various cosmological models would seem to predict an Arrow of Time which points in the wrong direction!
In a previous paper[7] (hereafter referred to as AT1) we employed a generalized form of the W-F approach[1] to provide a solution to a number of ``interpretational'' quantum mechanical paradoxes (The E-P-R paradox[8], The Schrödinger's Cat Paradox, Wheeler's Delayed Choice Experiments, etc.). The basis for this work is the W-F description of an emission-absorption event as an interchange of retarded and advanced waves between the emitter and absorber, respectively. This interchange can be thought of as the emitter sending out a probe wave in various allowed directions, seeking a "transaction" which is verified by the absorber. This transaction concept was shown to provide a mechanistic way of explaining the nonlocality of quantum mechanical processes, and thus to provide a partial solution to the twin problems of Locality and Completeness which have troubled the interpretation of quantum mechanics since its inception.
However, in AT1 the W-F protocol for describing emission processes was found to be inadequate for describing the emission of weakly absorbed radiation. In particular, when the W-F description was applied to the emission of very weakly absorbed particles and waves such as neutrinos and certain frequencies of radio waves, the observed emission of such entities could not be readily reconciled with the less-than-unity probability of their future absorption. This problem is most dramatically illustrated by the case of low energy neutrino emission, where there is a very high probability that there will be no future absorber (or scatterer) to provide the needed verification for the emitted neutrinos.
This problem and the related Arrow of Time problem were identified in AT1 as unsolved problems which represented serious de facto criticisms of the generalized W-F approach. Before embarking on further applications of the W-F approach, we will give a brief review of its formulation.