(BTW: "et. al." is not correct, "et al." stands for "et alii", so "et" is already the complete Latin word; for reference, "et" = "and" and "alii" = "others", so "et al." = "and others" or "and the rest")

Nope, Vilenkin is definitely a subscriber to the common lore. Vilenkin gave his paper a nice spin, and it's a clever idea, but it'sfarfrom a reliable, case-closed argument. Let's not rely on Craig's summary; let's read what Professor Vilenkin has to say to WLC (Note that I've bolded the salient points; I've inserted full names for clarity):

Vilenkin's Response Letter to WLC

"Dear Bill[i.e.William Lane Craig],

"I’m troubled that Lawrence Krauss in some respects misrepresented your views [on your work on the BVG theorem] in our dialogue in Sydney. In an attempt to rebut the evidence for a beginning of the universe, he showed a powerpoint of your letter with the last two sentences of the second paragraph deleted."

My letter was in response to Lawrence’s email asking whether or not I thought the BGV theorem *definitively* rules out a universe with no beginning. The gist of my answer was that there is no such thing as "definitive ruling out" in science.I would say the theorem makes a plausible case that there was a beginning. But there are always caveats."

Pause. A rhetorical point: Knowing my argument, do you care to guess what those caveats are?

I'm going to skip ahead to WLC's question and Vilenkin's response, but you can get the full text here. Here, WLC asks Vilenkin:

[i.e. Alexander Vilenkin]""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."

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.

Butif the fluctuations are not so wild as to invalidate classical spacetime, the BGV theorem is immune to any possible modifications of Einstein's equations which may be caused by quantum effects.

Best regards,

Alex

In other words: Assuming (without any reason specified) that quantum physics doesn't matter very much, then the BVG theorem does apply. Assuming then they are large, the BVG theorem doesn't apply.It's worth noting that WLC had actually noticed Vilenkin conceding my exact point to Lawrence Krauss and bothered to make an e-mail asking him to clarify; Vilenkin concedes, clarifies, and explains that the point about quantum effects --which I've been saying here since my initial post-- is correct. Next, I move to the following question:

Are Vilenkin's Assumptions Good Ones?

Vilenkin's paper is good; he's just making one assumption and following the logical conclusions from it. However, and he should really be more clear about this in his e-mail to WLC,there's no reason to suspect that the quantum fluctuations won't become incredibly strong and there's no reason to believe that quantum gravity will (and there's really only evidence to the contrary) preserve the notion of a classical spacetime.We only have three* (currently mediocre) successful ideas about quantum gravity:

1.) The noteworthy example of String theory.

2.) The less noteworthy example of "loop quantum gravity"

3.) The even less noteworthy idea of "causal dynamical triangulation".

Every single one of them dispenses with the normal idea of a classical spacetime and in each of them we also know that extremely strong quantum gravity effects are present.In other words, if we want to talk about "evidence" in terms of theories that can at least potentially work, thenwe have 0 for 3 models where the BVG theorem applies. In other words, while we don't have a "satisfactory" model of quantum gravity, we still don't even have a theory of quantum gravity that satisfies the prerequisites of the BVG theorem. And while Squatch is fond of saying "We don't have a model where there are effects that lead to an infinite past", I can make the much stronger statement and say "Sure, but we equally don't have a model where the BVG theorem applies, either, so the only evidence that we have right now is that it won't apply to quantum gravity". This means that there's no good reason to discuss this theorem as though it's the most relevant piece of information. If you can show meanyquantum gravity model which obeys the BVG theorem --and thus has a singularity-- then we could at least compare evidence. But you'd need 4 models before the evidence became 'stronger' that quantum theories of gravity seem to obey the BVG theorem. Because right now, we have no evidence they do and only evidence to the contrary. At this point, even if one of these models had a past singularity, it wouldn't be because the BVG theorem held; this continues to reenforce the fact that the BVG theorem is not the relevant fact to be discussing.

* There's also a fourth attempt which tries to use the "non-perturbative RG running" of GR to go a "UV fixed point", but it's pretty much just speculation in pure GR; however, even there, too, there's not really a coherent picture of a classical spacetime because the quantum effects completely overwhelm the classical picture, which is why it has to use the "non-perturbative" RG flow. This technically makes it 0 for 4 models, but it is my understanding that this isn't any where near as fleshed out as the other three, so I don't feel like it is worth including.

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