Concerning the BGV theorem Craig is correct in saying that the result holds for any geodesic observer with a non-comoving congruence of time-like geodesic test particles which is on average over the past expanding in a generalized sense, within general relativity , in the sense that such an observer geodesic is necessarily past-incomplete. That is not what he says, of course, but to my ears his statement of this is as good as one can expect. That does not imply a creation event. What it does mean is that if e. I am fairly certain that this is not an in any way controversial result. Ultimately, both the BGV theorem and the quoted paper on the generalized second law may be interpreted as supporting the idea of some sort of "creation event," in the sense that they do not conradict it and serves to narrow down other possibilities.

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When someone produces a private, unpublished statement from a person contradicting what that person has consistently said in his published work, you can bet something is fishy.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. 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. 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,. 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. The first paragraph hardly merits boldfacing. It is a truism that any theorem is only as good as its assumptions. 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.

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. 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. 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. For special relativistic spacetime, for example, also is a classical picture of spacetime.

Quantum gravity theories that do feature a linear temporal ordering fall under the theorem and so will not be past-eternal. To my delight Vilenkin furnished the unabridged version of his letter to Krauss. 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.

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. Alex Whoa! Because it was too technical?

Is this the transparency, honesty, and forthrightness that Krauss extols? And why delete the remark that such a model is usually assumed to be incorrect? 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. 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. 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. How are these statements compatible? The 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. Yours, Bill On September 6, , Vilenkin responded. 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 have known him for a long time, and he has always been an honest and straightforward fellow. 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. 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. In particular, the beginning of the universe could be a natural event, described by quantum cosmology.

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. Best regards, Alex As you can imagine, the receipt of this response was most gratifying.

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. 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. This suggests that any such model should be given at best an instrumentalist or anti-realist interpretation. Reproduced here by permission of Alex Vilenkin.


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All of these however do not contend with the sweeping BGV theorem in the long run. Assuming an "always positive" expansion rate is simply violated by "bouncing scenarios including LQC" according to Ashtekar. Oscillating Also called the Big Crunch. Under an oscillating model of the universe the current expansion we currently observe is just one part of a cycle, and one cycle of infinite cycles. There have been many cycles of expansion and when traced back in time it contracts then expands out again into a past or future trajectory.


Borde-Guth-Vilenkin singularity theorem

I posted about the " My Good Friend meme " — so named by thoughtful reader Ryan — employed in origins debates by materialist advocates. That means, guys like Dr. Carroll and Prothero, Krauss, Ward, etc. Yesterday, Coyne posted videos of Craig-Carroll as well as Craig-Krauss , neither of which, he says, he has actually watched. Now Ryan writes in with a good correction to what I said earlier. In the encounter with Dr.


Borde–Guth–Vilenkin theorem



Alexander Vilenkin


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