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# #733 Misrepresenting the Borde-Guth-Vilenkin Theorem

May 23, 2021Hello Dr. Craig

I hope you can help me to umderstand the observation an atheist guy who studies cosmology said about the beginning of the universe and the.very fact, that christian apologists misrepresent what the BVG theorem:

"I don't think you've done much research on the BVG theorem. It seems more like you're parroting talking points from Reasonable Faith. Let me just cite from the paper itself:

“What can lie beyond this boundary? Several possibilities have been discussed, one being that the boundary of the inflating region corresponds to the beginning of the Universe in a quantum nucleation event [12]. The boundary is then a closed spacelike hypersurface which can be determined from the appropriate instanton. Whatever the possibilities for the boundary, it is clear that unless the averaged expansion condition can somehow be avoided for all past-directed geodesics, inflation alone is not sufficient to provide a complete description of the Universe, and some new physics is necessary in order to determine the correct conditions at the boundary [20].” – (https://arxiv.org/abs/gr-qc/0110012)

Also, from Alexander Vilenkin himself:

“Mr. Stenger asked Mr. Vilenkin the following question, Does your theorem prove that the universe must have had a beginning? Vilenkin replied, No. But it proves that the expansion of the universe must have had a beginning. You can evade the theorem by postulating that the universe was contracting prior to some time.”

Also, the article I posted is from Ethan Siegel, a Ph.D theoretical cosmologist; I can certainly trust him, especially given what he says is in line with what the BVG theorem also says. It's also not true that I misrepresented his article, as evidenced by the quote directly from it confirming what I said. I study cosmology extensively. I can assure you I understand the subject well. It's also worth noting that Dr. Vilenkin has stated numerous times (such as in the quote I've provided above) that the theorem he worked on with Arvind Borde and Alan Guth does not prove that the Universe has a beginning. In fact, it makes no statements about the beginning of the Universe because the BVG theorem does not describe the earliest moments in the Universe's history. It's applicability does not go beyond the geodesic boundary, and nowhere in the original paper is it stated that said boundary is or must be an absolute beginning. In fact, the paper explicitly states that one can go beyond the boundary but must utilize an extension of inflationary physics.

“Whatever the possibilities for the boundary, it is clear that unless the averaged expansion condition can somehow be avoided for all past-directed geodesics, inflation alone is not sufficient to provide a complete description of the Universe, and some new physics is necessary in order to determine the correct conditions at the boundary [20].” – (https://arxiv.org/abs/gr-qc/0110012)

Alan Guth has also stated that through models like eternal inflation, one can easily extend physics beyond the geodesic boundary. I'm fact, Alan Guth himself has stated that he believes the Universe is likely eternal. Also, Arvind Borde has developed models of infinite universes as well as models of Universe's with defined physics beyond the geodesic boundary. Literally none of the three original authors themselves believes that their theorem proves that the Universe has a beginning, because it doesn't. It shows that the *expansion* of the Universe has a beginning, not the entirety of the Universe itself.

Also, Leonard Susskind, a distinguished professor of physics at Stanford University, the co-founding director of the Stanford Institute for Theoretical Physics, and one of the co-founders of string theory has also expressed that the BVG theorem does not prove that the Universe has a beginning (but its expansion does), and that there are viable scenarios in which the theorem does not hold.

Sean Carroll, a Ph.D theoretical astrophysicist and cosmologist has also expressed exactly the same; the BVG theorem does not prove that the Universe has a beginning, only that its expansion did. He has also developed viable cosmogonic models in which the BVG theorem doesn't hold. (https://www.preposterousuniverse.com/blog/2012/09/25/let-the-universe-be-the-universe/)

In short, I'd recommend actually reading the 2003 paper, but I'd also recommend understanding what a null or time-like geodesic is, as well as what geodesic incompleteness is. These concepts do not imply that the Universe has a beginning, they imply that physics only takes us back so far before it fails to provide physical descriptions of reality; to go beyond the geodesic boundary, we need better physics that we don't yet have. I also wanted to specify that singularities are not physical objects. Singularities are mathematical concepts which arise when the function becomes non-differentiable along some asymptote, or where the limit of a function becomes undefined. Wd get singularities in general relativity and in the BVG theorem because these models are incapable of propely describing the physics of the early Universe, but singularities are not physical objects. So, when you actually understand the cosmology, and when you actually ask real cosmologists (I've cited three beyond the authors of the BVG paper), you can see that theistic apologists exclusively misrepresent the BVG theorem, and that the consensus of professionals (including all three of its authors) is that the BVG theorem does not state that the Universe has a beginning, but rather that specifically the *expansion* of classical spacetime cannot be extended indefinitely into the past.

Rebecca

Italy

## Dr. craig’s response

A

Thanks for forwarding this post, Rebecca! Despite its confident--indeed, we have to say, smug--tone, this atheist’s post is riddled with errors, exposing his claim to have studied cosmology “*extensively*” and to “*understand the subject well*” as just so much empty posturing. You needn’t be intimidated by his condescending assertions that “*when you actually understand the cosmology, and when you actually ask real cosmologists. . . , you can see that theistic apologists exclusively misrepresent the BVG theorem.*” You may be assured that I and my collaborator James Sinclair have discussed these issues personally (and carried on extensive correspondence) with not only Vilenkin, but also such prominent cosmologists as George Ellis, Christopher Isham, Donald Page, James Hartle, Robert Brout, and many others in order to ensure the accuracy of our work.[1]

Some of your friend’s mistakes are just amusing, some more serious.

For example, on the amusing end, if one is going to opine about the BGV theorem, then don’t you think one should at least get the name of the theorem right? -- the BGV theorem (for Borde-Guth-Vilenkin, in alphabetical order), not the BVG theorem. And one should cite one’s sources correctly, don’t you think? I was amazed to see an anonymous quotation (which is, in fact, from a blogger named Arizona atheist[2]) in which your friend misrepresents what Vilenkin had said to Victor Stenger about cyclic models. In my debate with Peter Millican, who (innocently) also uses this quotation, I explained that in context Vilenkin says that such cyclic models fail for *other* reasons to evade the beginning of the universe implied by the BGV theorem (a fact omitted by your atheist friend).[3]

More seriously, concerning the central claim from the 2003 BGV paper, as I explain in my debate with Sean Carroll and in my article “Big Bang Cosmology,”

The BGV theorem proves that classical spacetime, under a single, very general condition, cannot be extended to past infinity but must reach a boundary at some time in the finite past. Now either there was something on the other side of that boundary or not. If not, then that boundary is the beginning of the universe. If there was something on the other side, then it will be a non-classical region described by the yet to be discovered theory of quantum gravity. In that case, Vilenkin says,

itwill be the beginning of the universe.[4]

Either way, the universe began to exist.

Therefore, your atheist friend is just misinformed when he says, “*Vilenkin has stated numerous times (such as in the quote I've provided above *[NB the one from Arizona atheist!]*) that the theorem he worked on with Arvind Borde and Alan Guth does not prove that the Universe has a beginning*.” Hmm! Here are Vilenkin’s reflections on the significance of that theorem in 2006:

The theorem proved in that paper is amazingly simple. Its proof does not go beyond high school mathematics. But its implications for the beginning of the universe are very profound. . . . With the proof now in place, cosmologists can no longer hide behind the possibility of a past-eternal universe. There is no escape: they have to face the problem of a cosmic beginning.[5]

Neither Susskind nor Guth nor Carroll has been able to craft a tenable model of a beginningless universe. In fact, the Carroll-Chen model advocated by Guth to evade the BGV theorem’s implications features a reversal of time’s arrow in the past, which is not merely non-physical, but implies the very beginning of the universe that Guth wanted to avoid, and Vilenkin takes him to task for it.[6]

So in 2012 Vilenkin reported: “There are no models at this time that provide a satisfactory model for a universe without a beginning.”[7] Again, in 2015: “We have no viable models of an eternal universe. The BGV theorem gives reason to believe that such models simply cannot be constructed.”[8] Again, in 2017: “Many people once again hoped that maybe on a far greater scale the universe is indeed eternal--with ancestor bubbles nucleating ad infinitum into the past. Now, however, we know that this is not possible. And once again, the beginning of the universe must be tackled head on.”[9]

Most tellingly, perhaps, Vilenkin has interacted *explicitly* with the *kalām* cosmological argument, and he does not dispute the premiss that *The universe began to exist.* Rather he denies the first premiss, that *Whatever begins to exist has a cause*.[10] I have responded to his argument in my article referenced in note 3.

Finally, your friend doesn’t seem to grasp that the BGV theorem’s implication that the universe began to exist is independent of our ability to describe physically the initial micro-second of the universe. As the cosmologist Charles Misner once remarked to me, “It is as though a tiny window shade were pulled over the first split-second of the existence of the universe. We don’t know what goes on behind the shade, but we know that it doesn’t come out on the other side.” Nor does your friend realize that the truth of the second premiss of the *kalām* cosmological argument does not depend upon the universe’s beginning with a singularity.[11] Non-singular models like the famous Hartle-Hawking model feature a non-singular beginning of the universe.

So your friend has got to do much more if he is to turn back the evidence that the universe began to exist.

[1] See William Lane Craig and James Sinclair, “The *Kalam* Cosmological Argument,” in *The Blackwell Companion to Natural Theology*, ed. Wm. L. Craig and J. P. Moreland (Oxford: Wiley-Blackwell, 2009), pp. 101-201.

[3] https://www.reasonablefaith.org/videos/short-videos/how-atheists-take-alexander-vilenkin-the-bvg-theorem-out-of-context-william/.

[4] William Lane Craig and Sean Carroll, *God and Cosmology*, ed. Robert Stewart (Minneapolis: Fortress Press, 2016); William Lane Craig, “Big Bang Cosmology” https://www.reasonablefaith.org/writings/scholarly-writings/the-existence-of-god/big-bang-cosmology/#_ftn6.

[5] Alex Vilenkin, *Many Worlds in One* (New York: Hill and Wang, 2006), pp.174-76. This statement is cited in our animated video on the *kalām* cosmological argument: https://www.youtube.com/watch?v=6CulBuMCLg0&t=3s.

[6] See my “Creation *Ex Nihilo*: Theology and Science,” in *The Story of the Cosmos*, ed. P. Gould and D. Ray (Eugene, Ore.: Harvest House, 2019), pp. 183-200; Alexander Vilenkin, “Arrows of time and the beginning of the universe,” arXiv:1305.3836v2[hep-th] May29, 2013.

[7] Alexander Vilenkin, “Did the universe have a beginning?” http://www.youtube.com/watch?v=NXCQelhKJ7A. *Cf.* Audrey Mithani and Alexander Vilenkin, “Did the universe have a beginning?” arXiv:1204.4658v1 [hep-th] 20 Apr 2012, p. 1, where they state: “None of these scenarios can actually be past-eternal.”

[8] Alexander Vilenkin, “The Beginning of the Universe,” *Inference: International Review of Science *1/4 (Oct. 23, 2015), http://inference-review.com/article/the-beginning-of-the-universe.

[9] Delia Perlov and Alex Vilenkin, *Cosmology for the Curious* (Cham, Switzerland: Springer, 2017), pp. 330-31; cf. p. 333.

[10] See again his *Inference* article cited in note 7.

[11] See William Lane Craig and James Sinclair, “On Non-Singular Spacetimes and the Beginning of the Universe,” in *Scientific Approaches to the Philosophy of Religion*, ed. Yujin Nagasawa (London: Macmillan, 2012), pp. 95-142.

**- William Lane Craig**