In an Evolving Block Universe (http://arxiv.org/abs/0912.0808, http://arxiv.org/abs/1407.7243) the future does not exist. The present moment is the bounding edge of the universe in the time dimension. As the present moment advances it leaves an eternal block universe of the past behind it.
GR tells us that photons do not experience time and that would suggest that photons only exist in the advancing present moment (a 3d surface precisely as we experience the universe). This would suggest that photons are moving at the same rate as the bounding edge of the universe (at least in the time dimension).
Does this not suggest that C gives us the rate of growth of the universe, or more importantly, that the rate of growth of the universe gives us C? This seems like a really profound result.
I wonder if this also means that the value of C is not constant but has followed a sigmoid curve i.e. inflation.
This would also seem to suggest that if you could visit the past (rather than just rewind time) that it would be cold and dark - the ashes of the present.