#336

September 23, 2013

# “Honesty, Transparency, Full Disclosure” and the Borde-Guth-Vilenkin Theorem

Dear Dr Craig,

During your recent dialogue in Sydney Professor Krauss presented personal E-mail correspondence with cosmologist Alexander Vilenkin concerning the application of the Borde-Guth-Vilenkin theorem to the beginning of the universe. According to Vilenkin's E-mail, in the case of a quantum theory of gravity "all bets are off."

I was wondering if you have seen this correspondence and whether you could comment on the claims in it.

And thank you for the way you very graciously handled Professor Krauss' attempts to malign you. Sadly, it became obvious that he wasn't interested in seriously engaging with the issues at these dialogues. The example you set for how Christians should engage with this sort of antagonism was admirable.

Kind regards,

Dan

Australia

Thank you, Dan! When someone produces a private, unpublished statement from a person contradicting what that person has consistently said in his published work, you can bet something is fishy. That was what I immediately suspected here. If you’ll listen to our Melbourne dialogue, you’ll find that I confront Prof. Krauss regarding this email.

Here is the email as Krauss reproduced it (taken from his Sydney powerpoint slide):

Hi Lawrence,

Any theorem is only as good as its assumptions. The BGV theorem says that if the universe is on average expanding along a given worldline, this worldline cannot be infinite to the past.

A possible loophole is that there might be an epoch of contraction prior to the expansion. Models of this sort have been discussed by Aguirre & Gratton and by Carroll & Chen. . . . . .

. . . Jaume Garriga and I are now exploring a picture of the multiverse where the BGV theorem may not apply. In bubbles of negative vacuum energy, expansion is followed by contraction. . . However, it is conceivable (and many people think likely) that singularities will be resolved in the theory of quantum gravity, so the internal collapse of the bubbles will be followed by an expansion. In this scenario, . . . it is not at all clear that the BGV assumption (expansion on average) will be satisfied.

. . . of course there is no such thing as absolute certainty in science, especially in matters like the creation of the universe. Note for example that 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.

Alex

The boldface was added by Krauss. Let’s now look at this letter paragraph by paragraph.

The first paragraph hardly merits boldfacing. It is a truism that any theorem is only as good as its assumptions. What’s remarkable about the BGV theorem is that it makes only one assumption: that the universe is, on average, expanding throughout its history. The theorem won’t apply to models where that isn’t true.

In the next paragraph one realizes that something doesn’t smell right. For the two models mentioned (Aguirre-Gratton and Carroll-Chen) were specifically addressed by name by Vilenkin in the paper from the Cambridge conference which I quoted in my opening speech. These models were comprised in Vilenkin’s conclusion, “None of these scenarios can actually be past-eternal.” So when Vilenkin says that they afford a “possible loophole,” the idea must be that because they deny the single assumption of the theorem, maybe that’s a way to avoid the beginning of the universe. But in his paper Vilenkin proceeds to close this loophole by showing that these models cannot be past-eternal for other reasons. This led me to wonder if Krauss had even read the relevant paper by Vilenkin—yes, the one he accuses me of not understanding—because he was evidently unfamiliar with its contents.

Then I noticed the ellipsis points in Krauss’ quotation of Vilenkin’s email. Something in the original had evidently been deleted by Krauss. What was it? My mind went back to a similar letter Vilenkin wrote to Victor Stenger a few years ago, in which he said,

You can evade the theorem by postulating that the universe was contracting prior to some time. . . . This sounds as if there is nothing wrong with having contraction prior to expansion. But the problem is that a contracting universe is highly unstable. Small perturbations would cause it to develop all sorts of messy singularities, so it would never make it to the expanding phase. (A Vilenkin to V Stenger, cited by http://arizonaatheist.blogspot.com/2010/05/william-lane-craigs-arguments-for-god.html)

Could Krauss have deleted a qualifying comment like the above? In the Melbourne dialogue Krauss said he had deleted just “technical material.”

In the third paragraph of his email Vilenkin mentions a model he is exploring to try to evade the theorem. This is unremarkable. Such an undertaking merely represents a procedure Krauss described well in our dialogues: a theorist will try to falsify his own theory. If the theory repeatedly survives attempts at its falsification, then the theory receives what philosopher of science Karl Popper called corroboration. A corroborated theory is far more secure than an untested theory. So Vilenkin is engaged in just that activity which has the potential to strengthen the theorem even more. Again, we notice all the ellipsis points. Was the original just too long to quote, or were important qualifiers omitted?

Finally, we come to the fourth paragraph, the one about which you asked and about which Krauss made a fuss. Again, it’s a truism that there is no certainty in science. Rather the really interesting statement in this paragraph is the following: “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.” This is puzzling because Vilenkin has said in his published work that the BGV theorem has only one condition and doesn't even presuppose that gravity is described by Einstein's equations, so that if those equations need to be modified the theorem should still hold.

I wrote to Don Page, an eminent cosmologist, to ask him about Vilenkin’s remark. Here’s the interpretation I proposed to Page:

How are these statements to be reconciled? Here's my best attempt: A ‘classical picture of spacetime’ should not be equated with general relativistic spacetime. For special relativistic spacetime, for example, also is a classical picture of spacetime. So the theorem does not presuppose general relativistic spacetime but simply a spacetime that is classical in the sense that it is linearly ordered temporally and so can be said to be expanding in the ‘later than’ direction. In any such spacetime a universe that is, on average, in a state of expansion can’t be past-eternal. But in a quantum gravity regime, if the linear ordering of time is abolished, then it is impossible to speak of expanding, and so the theorem’s one condition isn’t met. The question, then, is not one’s gravitational theory, but whether time exists in one’s model. Quantum gravity theories that do feature a linear temporal ordering fall under the theorem and so will not be past-eternal.

Page replied: “I think this is indeed one possible interpretation of what Alex wrote, but I'm not quite sure what he really meant.” Page then wrote to Vilenkin and, at my request, also asked for the full text of the email Vilenkin had sent to Krauss.

To my delight Vilenkin furnished the unabridged version of his letter to Krauss.1 I have put Krauss’ deletions in boldface:

Hi Lawrence,

Any theorem is only as good as its assumptions. The BGV theorem says that if the universe is on average expanding along a given worldline, this worldline cannot be infinite to the past.

A possible loophole is that there might be an epoch of contraction prior to the expansion. Models of this sort have been discussed by Aguirre & Gratton and by Carroll & Chen. They had to assume though that the minimum of entropy was reached at the bounce and offered no mechanism to enforce this condition. It seems to me that it is essentially equivalent to a beginning.

On the other hand, Jaume Garriga and I are now exploring a picture of the multiverse where the BGV theorem may not apply. In bubbles of negative vacuum energy, expansion is followed by cocntraction, and it is usually assumed that this ends in a big crunch singularity. However, it is conceivable (and many people think likely) that singularities will be resolved in the theory of quantum gravity, so the internal collapse of the bubbles will be followed by an expansion. In this scenario, a typical worldline will go through a succession of expanding and contracting regions, and it is not at all clear that the BGV assumption (expansion on average) will be satisfied.

I suspect that the theorem can be extended to this case, maybe with some additional assumptions. But of course there is no such thing as absolute certainty in science, especially in matters like the creation of the universe. Note for example that 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.

Alex

Whoa! That puts a very different face on the matter, doesn’t it? Why didn’t Krauss read the sentence, “It seems to me that it is essentially equivalent to a beginning”? Because it was too technical? Is this the transparency, honesty, and forthrightness that Krauss extols? (By the way, Vilenkin’s criticism of these models is the same one that Vilenkin makes in his Cambridge paper: far from showing an eternal past, these models actually feature a universe with a common beginning point for two arrows of time.)

And why did Krauss delete Vilenkin’s caveat that the BGV theorem can, in his estimation, be extended to cover the case of an expanding and contracting model such as Garriga and Vilenkin are exploring? And why delete the remark that such a model is usually assumed to be incorrect? It’s evident that Vilenkin’s email was selectively edited to give it the spin Krauss wanted.

Buoyed by Vilenkin’s response to Page, I wrote to Vilenkin myself, both to express my concern about Krauss’ use of his email and also to ask for clarification about the question you posed to see if my interpretation was correct. Here is the text of my letter:

Dear Prof. Vilenkin,

Thanks so much for your response! You may recall that we once met, as we were both participants in a sort of roundtable conference in Berkeley on science and religion sponsored by the Center for Theology and Natural Science. I’ve appreciated your work over the years.

I’m troubled that Lawrence Krauss in some respects misrepresented your views 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. That gave the audience the impression that contracting models, in particular the two mentioned, were realistic possibilities for evading the beginning of the universe. The last sentence of the second paragraph would have been devastating for Krauss.

Having read two of your recent papers in which you show why the Aguirre-Gratton model and the Carroll-Chen model do not succeed in restoring a past-eternal universe, I knew that Krauss was misconstruing you. You meant “possible” in the sense that they violate the one condition of the BGV theorem, not “possible” in the sense of providing a realistic model of a past-eternal universe.

Moreover, I had a copy of your letter to Victor Stenger in which you explained the messy singularities such contracting models would face, so that it would never come to a new expansion. I surmised that your letter to Krauss also contained some such qualification.

You should be aware that your work has entered into popular culture, where it has become the subject of heated debate. Certain staunchly secular thinkers want to avoid the beginning of the universe because to them it smacks of theism, and so they are bent on reconstruing the significance of your work. That is why you are receiving letters from people like Stenger, Krauss, *et al*. I hope to have understood and represented you accurately. If not, I want to be corrected.

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.

Yours,

Bill

On September 6, 2013, Vilenkin responded. In the following email, he intersperses his replies to my comments, which are marked with”>”.2

Dear Bill,

> I’m troubled that Lawrence Krauss in some respects misrepresented your views

> 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.

I did not hear your debate in Sydney, but I don’t think Lawrence would intentionally misinterpret my views. I have known him for a long time, and he has always been an honest and straightforward fellow.

> Having read two of your recent papers in which you show why the

> Aguirre-Gratton model and the Carroll-Chen model do not succeed in restoring

> a past-eternal universe, I knew that Krauss was misconstruing you. You

> meant “possible” in the sense that they violate the one condition of the BGV

> theorem, not “possible” in the sense of providing a realistic model of a

> past-eternal universe.

> Moreover, I had a copy of your letter to Victor Stenger in which you

> explained the messy singularities such contracting models would face, so

> that it would never come to a new expansion. I surmised that your letter to

> Krauss also contained some such qualification.

The Aguirre-Gratton model can avoide singularities by postulating a small "initial" closed universe and then allowing it to evolve in both directions of time. I put "initial" in quotation marks, because Aguirre and Gratton do not think of it that way. But this model requires that a very special condition is enforced at some moment in the history of the universe. At that moment, the universe should be very small and have very low entropy. Aguirre and Gratton do not specify a physical mechanism that could enforce such a condition.

Carroll and Chen claim that the universe did not have to be small at that special moment. But in my recent paper I show that in this case singularities are unavoidable.

> You should be aware that your work has entered into popular culture, where

> it has become the subject of heated debate. Certain staunchly secular

> thinkers want to avoid the beginning of the universe because to them it

> smacks of theism, and so they are bent on reconstruing the significance of

> your work. That is why you are receiving letters from people like Stenger,

> Krauss, et al. I hope to have understood and represented you accurately.

> If not, I want to be corrected.

I think you represented what I wrote about the BGV theorem in my papers and to you personally very accurately. This is not to say that you represented my views as to what this implies regarding the existence of God. Which is OK, since I have no special expertise to issue such judgements. 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.

> 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.

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.

But if 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

As you can imagine, the receipt of this response was most gratifying. In Vilenkin’s first remark, we discover how prejudicially Krauss had framed the issue by asking about “definitive” proof, when those who know my work realize that I claim merely that the premises of the cosmological argument are more plausible than not. You'll recall that Krauss himself admitted in our first dialogue that it is more plausible than not that the universe began to exist.

In Vilenkin’s second paragraph we see Vilenkin’s graciousness, which is in such marked contrast with Krauss’ tendency in our Brisbane dialogue to rush to judgement.

In the third and fourth paragraphs Vilenkin reinforces his case against the past-eternality of the two models in question.

The fifth paragraph is especially gratifying personally. As for Vilenkin’s theological views, while I would never rejoice that someone is not a Christian, I find his agnosticism to be helpful in that no one can accuse him of having a theological axe to grind in his defense of the universe’s beginning. As for his proffered natural explanation of the universe’s beginning, I interact with it in *Reasonable Faith*, pp. 115-16, and in the *Blackwell Companion to Natural Theology*, pp. 183-4 (with Jim Sinclair).

Finally, in his closing paragraphs we can see that Vilenkin affirms the interpretation I gave to his words. The issue is not quantum gravity but the reality of time and causation. This raises very fundamental questions about the nature of time, whether time is identical to the operationally defined quantities in physics or whether those quantities are, as I maintain, but measures of time, which exists independently of them. So long as the universe is expanding over time in the quantum gravity regime, the BGV theorem holds. Indeed, it is questionable whether it is even coherent to speak of classical spacetime's "emerging" from a timeless condition, since that state cannot be said to be before or earlier than classical spacetime. This suggests that any such model should be given at best an instrumentalist or anti-realist interpretation.

1Reproduced here by permission of Alex Vilenkin.

2Reproduced here by permission of Alex Vilenkin.