Borde, Guth, and Vilenkin’s Past-Finite Universe
Whenever William Lane Craig is forced to retreat from his use of the Standard Big Bang model, he will often cite a paper by Arvind Borde, Alan Guth, and Alexander Vilenkin:
…three leading cosmologists, Arvin Borde, Alan Guth, and Alexander Vilenkin, were able to prove that any universe which has, on average, been expanding throughout its history cannot be infinite in the past but must have a past space-time boundary.
-W.L Craig “Contemporary Cosmology and the Beginning of the Universe”
The 2003 Borde-Guth-Vilenkin paper (pdf) shows that “almost all” inflationary models of the universe (as opposed to Dr. Craig’s “any universe”) will reach a boundary in the past – meaning our universe probably doesn’t exist infinitely into the past.
Dr. Craig seems to interpret this information as “the universe definitely began to exist” although that is a bit presumptuous. For example, this theorem doesn’t rule out Stephen Hawking’s no-boundary proposal which states that time may be finite without any real boundary (just like a sphere is finite in surface area while it has no “beginning”).
Furthermore, the author of the Arizona Atheist blog asked Vilenkin if his theorem with Guth and Borde proves that the universe had a beginning, and Vilenkin responded:
[I]f someone asks me whether or not the theorem I proved with Borde and Guth implies that the universe had a beginning, I would say that the short answer is “yes”. If you are willing to get into subtleties, then the answer is “No, but…” So, there are ways to get around having a beginning, but then you are forced to have something nearly as special as a beginning.
However, Craig’s main problem is that a beginning of the universe can still be described in scientific terms. Nothing in the Borde-Guth-Vilenkin paper suggests a beginning from “absolute nothingness” (as Craig often claims). In fact, the opposite is true. The authors write,
What can lie beyond the 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.
This “quantum nucleation event” refers to a paper Vilenkin wrote in 1982 (pdf) which discusses the universe coming into being through quantum mechanics. Interestingly, many theists use Vilenkin’s paper as evidence that the universe came from “literally nothing” but Craig has already criticized this work.
Oddly, I’ve been unable to find any article of Craig’s (scholarly or otherwise) which actually quotes from the 2003 Borde-Guth-Vilenkin paper. Instead he almost exclusively quotes a paragraph from Vilenkin’s 2006 book Many Worlds in One (amazon) which discusses the 2003 paper:
It is said that an argument is what convinces reasonable men and a proof is what it takes to convince even an unreasonable man. 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 (pg. 176).
Now that’s a pretty straight forward quote which at least seems to favor Craig’s argument, but on the very same page Vilenkin writes,
Theologians have often welcomed any evidence for the beginning of the universe, regarding it as evidence for the existence of God … So what do we make of a proof that the beginning is unavoidable? Is it a proof of the existence of God? This view would be far too simplistic. Anyone who attempts to understand the origin of the universe should be prepared to address its logical paradoxes. In this regard, the theorem that I proved with my colleagues does not give much of an advantage to the theologian over the scientist.
Vilenkin then concludes this statement by suggesting that cosmic origins could be described in “purely scientific terms” – a task which he attempts in the chapter which follows.
two interesting comments and a paper.
sean carroll says in comment 100 ” Hi George — That’s a good idea, I’ll try to do it some time when I’m less busy. I’ve described my favorite model before, e.g. here. I should also mention that the Borde/Guth/Vilenkin theorem is (1) completely classical, not quantum, of course, and (2) a little less definitive than you make it sound, as they assume an “averaged expansion condition” which certainly may be violated along some geodesics. But it’s a good theorem, no question.” @ http://blogs.discovermagazine.com/cosmicvariance/2006/10/29/the-god-conundrum/
anthony aguirre says in comment 2 “A couple of brief comments, hopefully more later. First, Borde, Guth & Vilenkin did *not* prove that eternal inflation has singularities to the past. As you know, most singularity theorems prove geodesic incompleteness, and this is the case here. What all of their theorems do are (a) write out a set of conditions which they consider to correspond to eternal inflation, then (b) show that the region in which these conditions hold is geodesically incomplete. This would indeed be consistent with eternal inflation “emerging from a primordial singularity”, but it is also consistent with eternal inflation just being grafted onto some spacetime region that is not eternally inflating by their definition. This is exactly what Steven & I did in various ways in our paper; and in most cases we argued that the ‘extra’ region was indeed eternally inflating, just not in accord with their criteria for eternal inflation.” @ http://blogs.discovermagazine.com/cosmicvariance/2007/04/27/how-did-the-universe-start/
anthony paper is @ http://arxiv.org/abs/gr-qc/0301042
Science is provisional–so of course the Borde, Guth, and Vilenkin theorem doesn’t prove that the universe had a beginning, but it does show that it’s more plausible than our universe having no beginning.
I agree–science can’t prove anything 100 percent; so not sure how Craig is debunked. This is a case of what is most plausible, assent to the incoherence of an infite regress, and a basic understanding of the entrophy associate with thermodynamics seems to underpin a significant failure of the multi-universe theory, no matter how you construct your model. The entire mutli-universe seems to be used as a very small possibility, simpley to avoid a creator. It makes more sense to me that matter is a result of an infite mind, rather than the mind developing from matter. Science is permeated with assumptions that cannot be scientifically accounted for: intial conditions found in physics, purpose, self, asthetics, mathematics & logic–even science itself cannot be proven by science.
Hi there.
I will revisit this again, however to quickly respond. Vilenkin, though not taking this to be proof of any theistic conclusion, clearly states in his 2006 work that “past-eternal inflation without a beginning is impossible” p-175. Craig doesn’t need to engage what Vilenkin thinks this may or may not prove. He he simply getting the scientific information as to support his philosophical argument.
Also, by his own admission in “A Brief History of Time”, Hawking’s model only works in an anti-realist construal of metaphysics as the theory would not work without the use of imaginary numbers, which unfortunately do not translate to real space and time.
Though we clearly disagree on issues and William Lane Craig’s work itself, I appreciate the blog and the discussion of the issues.
Take care!
“The conclusion that Borde and collaborators had proved that the universe had to have a beginning was disputed the same year by University of California-Santa Cruz physicist Anthony Aquirre and Cambridge astronomer Steven Gratton in a paper that Craig ignores.”
“I contacted Vilenkin…I first asked Vilenkin if Craig’s statement is accurate. Vilenkin replied:
“I would say this is basically correct, except the words “absolute beginning” do raise some red flags….[details of BGV Theorem following]”
“I sent this to Aquirre who commented that the “infinitely rare” particles have worldlines [trajectories in space-time] that extend intdefinitely into “the past,” and can prevent there being a “time” as which the universe is not expanding/inflating.”
“I then asked Vilenkin, “Does your theorem prove the universe must have had a beginning.” He immediately replied:
“No. But it proves that the expansion of the universe must have had a beginning. You can evade the theorem by postulating the universe was prior to some time.”
“I also checked with Caltech cosmologiss Sean Carroll…here was his response:
“I think my answer would be fairly concise: no result derived on the basis of classical spacetime can be used to derive anything truly fundamental, since classical general relativity isn’t right. You need to quantize gravity. The BGV [Borde, Guth, Vilenkin] singularity theorem is certainly interesting and important, because it helps us understand where classical GR breaks down, but it doesn’t help us decide what to do when it breaks down.”
Source: Victor J. Stenger, The Fallacy of Fine-Tuning, 2011.
Now, on Sean’s point- Anthony Aqurrie made a few corrections on Carroll’s point on the BGV Theorem.
“Anthony A. Says:
Sean,
A very nice post on a very interesting question. The part where you sort out “big-bang” (well-tested evolution of an expanding homogeneous hot patch) from “big-bang” (an initial singularity) is important, as the two are often conflated even by people who know better.
A couple of brief comments, hopefully more later. First, Borde, Guth & Vilenkin did *not* prove that eternal inflation has singularities to the past. As you know, most singularity theorems prove geodesic incompleteness, and this is the case here. What all of their theorems do are (a) write out a set of conditions which they consider to correspond to eternal inflation, then (b) show that the region in which these conditions hold is geodesically incomplete. This would indeed be consistent with eternal inflation “emerging from a primordial singularity”, but it is also consistent with eternal inflation just being grafted onto some spacetime region that is not eternally inflating by their definition. This is exactly what Steven & I did in various ways in our paper; and in most cases we argued that the ‘extra’ region was indeed eternally inflating, just not in accord with their criteria for eternal inflation.”
Sean later replied:
“Sean Says:
Anthony, thanks for the clarification about the BGV results.”
Source: Sean Carroll’s blog, website: http://blogs.discovermagazine.com/cosmicvariance/2007/04/27/how-did-the-universe-start/
(You must see the comments section below!)
“It should first be pointed out that imaginary numbers aren’t any more “imaginary” than most real numbers. As mathematicians John Conway and Richard Guy write, imaginary numbers “turn out to be invaluable in many applications of mathematics to engineering, physics, and almost every other science. Moreover, these numbers obey all the rules which you already know for ‘real’ numbers” (The Book of Numbers, pg. 212).”
So, can imaginary numbers be used to describe the concept of time in the very early universe? Luckily, this is discussed at length in A Brief History of Time (pg. 139). ”If the universe really is in such a quantum state, there would be no singularities in the history of the universe in imaginary time. … In real time, the universe has a beginning and end at singularities that form a boundary to space-time and at which the laws of science break down. But in imaginary time, there are no singularities or boundaries. So maybe what we call imaginary time is really more basic, and what we call real time is just an idea that we invent to help us describe what we think the universe is like.” Hawking then suggests that asking the question “which is real” might be irrelevant, “It is simply a matter of which is the more useful description.””
Source: Andy Burke, Tuseday Afternoon (Blog), William Lane Craig vs. Stephen Hawking.
Before Craig can use this “information” to build his case for his philosophical argument, he might want to make sure he has fact-checked his interpretations of the theorem. This is the same problem Dr. Stenger had written about in his previous books on Craig’s use of the Hawking-Penrose singularity theorems. He used them to make his case for the universe’s beginnings, but overlooked the flaws Hawking and Penrose themselves admitted within their theorem… they failed to consider quantum mechanics!