Saturday, January 28, 2017

The Significance of the BGV Theorem

Let's continue to explore the question of whether or not our universe had an actual beginning.  In two previous posts I have said that (1) if our universe had a beginning, then the cause of the universe must be transcendent, a characteristic of the Christian God, and (2) we may never have any observational or theoretical evidence about what happened in the first 10-35 seconds of the universe.

However, there have still been a lot of ideas from theoretical physicists about what may have happened to bring the universe into being and what we can surmise from the equations and laws that we know describe our universe.  One of the most often discussed papers dealing with our past was published by Arvind Borde, Alan H. Guth, and Alexander Vilenkin in 20031 and called the BGV theorem after the three authors.  In this paper, the authors show that any universe which is on average expanding has a timeline that cannot be infinite into the past, it must have had a beginning when it started to expand.  Since our universe is known to be expanding this theorem seems to require that it had a beginning.  (There are some technicalities to this conclusion like, for instance, the difference between "expanding" and "on average expanding" but, in general, what is known about our universe corresponds with the requirements of the BGV theorem.)

The BGV theorem has been used extensively by theists such as William Lane Craig to argue that the universe had a beginning which then points to a transcendent cause like God.  Opponents of that view provide an alternative scenario by citing some technical aspects of the BGV theorem, or other theoretical ideas which either contradict the BGV theorem or provide special circumstances where it may not be applicable.  For instance, although the BGV theorem has very few assumptions, it is formulated in a classical space-time which may not give valid conclusions during the first 10-35 seconds of the universe when quantum gravity would have been in effect as described in the previous post already mentioned.  I will discuss some of the challenges to the BGV theorem and alternative ideas like those proposed by Anthony Aguirre and Steven Gratton2 in later posts as we explore this topic even further.  But a good synopsis of how the BGV theorem has been received is given by Vilenkin himself when he says "The validity of the BGV theorem is not in question, but its interpretation has generated some controversy."3

As an experimental physicist I tend to draw conclusions based on what is known observationally and experimentally rather than on conjecture or speculation.  So what are the facts about the origin of our universe? The equations of general relativity suggest that the universe had an actual beginning of space, time, matter, and energy and the BGV theorem along with the expansion of the universe would require that this universe had an actual beginning of the expansion.   Other ideas about the origin of the universe like those proposed by Lawrence Krauss4 or Sean Carroll5 do not have real scientific evidence to back them up.  They are conjecture.  (Still I'll talk about them in more detail in future posts.)

I have had the "privilege" to sit on a few juries during my life.  Any jury is supposed to determine a verdict based on the evidence beyond a reasonable doubt.  As with scientific conclusions, a jury knows there is no certainty or proof, but there is evidence.  The conjecture or speculations made by many theoretical physicists in order to avoid a beginning to this universe would not be admitted as evidence since they are not based on observable or demonstrable phenomena.  Considering only the factual evidence for an origin of the universe, I'm confident a jury would come to the conclusion that our universe had a beginning.  Alexander Vilenkin, with co-author Audrey Mithani, come to a similar conclusion in a paper titled, "Did the universe have a beginning?"  Their answer is, "At this point, it seems the answer to this question is probably yes."6  Any other conclusion draws not on what we know, but on what we don't know.

1Borde, Guth, Vilenkin, "Inflationary spacetimes are not past-complete," Phys. Rev. Lett. 90 (2003) 151301.
2Aguirre, Gratton, "Inflation without a beginning, a null boundary proposal," Phys. Rev. D 67 (2003) 083515.
3Vilenkin, "Arrows of time and the beginning of the universe," Phys. Rev. D 88 (2013) 043516.
4Krauss, Lawrence, "A Universe From Nothing," Simon and Schuster, New York, 2012.
5Carroll, "What if Time Really Exists," arXiv:0811.3722 [gr-qc] (2008).
6Mithani, Vilenkin, "Did the universe have a beginning," arXiv:1204.4658 [hep-th] (2012).


  1. Dr. Strauss, thank you for posting this. I look forward to your analyses of Sean Carroll's and Lawrence Krauss' proposed models.

  2. Excellent work! Love reading about your work!

  3. Yes thank you! You make incredibly complex ideas very accessible to people like me who don't share your genius. Thank you very much.

  4. "Audrey Mithani, come to a similar conclusion in a paper titled, "Did the universe have a beginning?" Their answer is, "At this point, it seems the answer to this question is probably yes."6 Any other conclusion draws not on what we know, but on what we don't know."
    Awesome article. I'm a software engineer, so don't know anything about physics or cosmology really. All I know is in today's age, I'll need answers for everything atheists peddle when my young kids are older.
    To learn this subject, I have been watching many of William Lane Craig's debates. All the atheists in the comments always insist that Craig simply doesn't understand cosmology or physics.
    I was certain that the people he was debating were merely arguing from what "could be" rather than anything with any observational support. It is great to hear an expert in the field verify this..

  5. "I was certain that the people he was debating were merely arguing from what "could be" rather than anything with any observational support. It is great to hear an expert in the field verify this..

    Since WLC is in exactly the same boat, do you have a point?

    WLC does NOT know about the subject.

    Basically this article is saying we don't know therefor the BGV stands even though the authors of it says its not relevant to the universe we do live in as it IS based on purely classical physics. It was just an intellectual exercise that does not tell us anything about the beginning of our universe. WLC has had BLEEP fits over that FACT.

  6. Does it really make sense to say the universe had a "beginning" or are we really talking about whether time is finite or not? To say that "time had a beginning" seems nonsensical to me. A finite timeline makes enough sense, and they intuitively seem like the same thing, but they aren't, are they?

    1. The spacetime theorems of general relativity indicate that time as we know it came into existence just as space came into existence. Since we are so confined to space and time we don't understand experientially what that means but that is what the math says. The BGV theorem says that the universe is not infinite in the past, which seems to indicate the timeline we know is finite and had a beginning. I don't think it makes common sense because we can't comprehend existence without space or time but it does make mathematical sense.

  7. Hello,

    I have found a way to avoid the beginning of the universe.

    What if we devise an unknown stable quantum system (eternal cosmic egg) that exists since eternity and is generating space-time bubbles/singularities from the eternity past and our universe is one such bubble?

    Note that this quantum system resides in a different dimension of space and time which is distinct from the dimensions of our cosmic space and time and the universe bubbles generated by it have different dimensions of space-time which are distinct from the space-time dimensions of this quantum system. I know a little difficult to follow.

    The idea of a quantum system of space-time dimensions-A giving birth to a mini-universe with space-time dimensions-B may seem very difficult to grasp but it is not impossible as the idea of God giving birth to the universe ex nihilo is also very difficult to grasp. I know that this model is highly speculative and cannot be empirically tested in any way whatsoever but the idea of God is also extremely speculative and impossible to verify empirically.

    This is not a multiverse theory and the proponent of this model is not claiming that our universe came from nothing. He is just trying to make his own mechanical god to avoid God.

    This system avoids any possible problem with its mechanics that one can propose:

     Since this quantum system is stable, the quantum fluctuations will not push it to expand or contract.

     This quantum system is constantly generating space-time bubbles since eternity and hence the need for a personal agent evaporates. It is not like it does nothing forever and then suddenly start producing universes.

     This quantum system is stable and hence it would endure for an indefinite time in the past and the problem of either producing universes from eternity past or not-at-all evaporates.

     The problem of time coming into existence as itself a temporal process resolves because this system has a different dimension of time which is distinct from our cosmic time.

     Since this system resides in a different dimension of space which is distinct from our space, it would be wrong to say that the term ‘spaceless void’ is self-refuting.

     The universe bubbles generated by this quantum system don’t delve inside it, as they have different dimensions of space and time which are distinct from that of the system itself; rather they exist outside of this system having different space dimensions. Thus, given infinite past time as these universe bubbles expand, they will not collide and coalesce with one another.

    We can refute this speculation from a philosophical perspective by simply claiming that this quantum system has been generating bubbles since eternity, which means there has been an actually infinite number of changes(each generation is a change), but an infinite regress of changes is not possible regardless of which dimension of time we are talking about.

    But can we refute this from a scientific perspective?

    Please help me!

    1. This approach has been explored. The problem is that all such bubbles are unstable and cannot endure for an indefinite time. They have to have a very limited lifetime which makes this idea unacceptable to solve the problem.

    2. Hello Sir

      This QM system generates universe bubbles purposelessly and randomly. So given infinite amount of time, it is possible that one such bubble (out of other infinite bubbles) experienced a very aggressive inflationary expansion (by chance) and avoided the problem of collapsing.

      In order to refute this "Mechanical God", you will have to prove that this entire QM System itself cannot survive for an infinite time.

      So that even if the universe bubbles produced by this Quantum System make it through inflation then still their Mother Quantum System would have to had a beginning.

    3. As I said, this has been explored and hs problems. Have you looked at the papers on this idea to see what has already been published and the reasons for the limited lifetime of the system?

    4. Yes! I have read some papers.

      1. They argue that such a system would need incomprehensible amount of fine tuning for such a system to exist for indefinite time in the past which raises the problem of cosmic design.

      2. They also argue that such systems are quantum mechanically unstable and hence will collapse by quantum tunneling to zero radius. So initially even if this universe is perfectly fine-tuned, it will be destabilized by quantum fluctuations and will either start inflating or collapse to a singularity. I read this from a paper by Alex. Vilenkin

      I think that the instability is due to the uncertainty principle which is the core of Quantum Mechanics, so we cannot have, at least given our current understanding, an eternal stable QM system.

      But if I am wrong anywhere please correct me. And I would love it if you could cite some papers regarding this approach.

    5. if I am wrong anywhere please correct me. And I would love it if you could cite some papers regarding this approach.