Alexander Vilenkin: Whatever it's worth, my view is that the BGV theorem does not say anything about the existence of God one way or the other. In particular, the beginning of the universe could be a natural event, described by quantum cosmology.
Bill Craig: In that vein, I do have a question about your statement:
the BGV theorem uses a classical picture of spacetime. In the regime where gravity becomes essentially quantum, we may not even know the right questions to ask.
Elsewhere you’ve written:
A remarkable thing about this theorem is its sweeping generality. . . . We did not even assume that gravity is described by Einstein’s equations. So, if Einstein’s gravity requires some modification, our conclusion will still hold. The only assumption that we made was that the expansion rate of the universe never gets below some nonzero value [Vilenkin, 2006, p. 175].
How are these statements compatible? The 2006 statement sounds as if a quantum theory of gravitation would not undo the theorem. But the letter to Krauss sounds as if we are awash in uncertainty.
I have my own idea of how you might understand these statements, but rather than burden you with my surmises, I’d prefer to simply ask you how you understand the situation.
Vilenkin: The question of whether or not the universe had a beginning assumes a classical spacetime, in which the notions of time and causality can be defined. On very small time and length scales, quantum fluctuations in the structure of spacetime could be so large that these classical concepts become totally inapplicable. Then we do not really have a language to describe what is happening, because all our physics concepts are deeply rooted in the concepts of space and time. This is what I mean when I say that we do not even know what the right questions are.