How do we expect that our dynamical equations will allow us to propagate across kin an unambiguous way? I am supposing that in the remote future of the earlier aeon, Einstein's equations hold, all sources being massless and propagating according to well-defined deterministic conformally invariant classical equations. We may suppose that these are Maxwell's equations, the Yang-Mills equations without mass, and things like the Dirac-Weyl equation Vaa'^>a=0 (the Dirac equation in the zero-mass limit), some such particles acting as sources for the gauge fields, all these taken in the limit when rest-mass is treated as having reached zero, in accordance with §3.2. The coupling of these to the gravitational field is expressed in the equation Tab=Tab[H], where H is the phantom field. We know that Tab[H] should be finite on k, despite Q becoming infinite there, because Tab ought itself to be finite at k, the propagation of the fields involved in Tab being conform-ally invariant and therefore not particularly concerned with the location of k within V. The proposal of CCC is that, until the situation becomes more complicated, perhaps through ordinary gravitational sources beginning to acquire rest-mass, etc. via the Higgs mechanism, or whatever alternative proposal might perhaps eventually turn out to be more accurate, these same conformally invariant equations for the matter sources must continue into the post-big-bang region Vv. We shall see, however, that even with the spare situation envisaged here, we are not able to escape the appearance of rest-mass in some form, soon after k has been crossed (see B11).
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