Wednesday, February 20, 2013

Unstable Universes: guest blog

Guest blog by David Berenstein, Assoc. Prof. in Santa Barbara

It’s a fine day for the Universe to die, and to be new again! Well, maybe not, but the Internet is abuzz with a reincarnation of the unstable universe story. (You can also see it here, or here, the whole thing is trending in Google). In other words, this is known as tunneling between vacua. And if you have followed the news about the Landscape of vacua in string theory, this should be old news (that we may live in a unstable Universe, which we don’t know). For some reason, this wheel gets reinvented again and again with different names. All you need is one paper, or conference, or talk to make it sound exciting, and then it’s Coming attraction: the end of the Universe …. a couple of billion years in the future.

The basic idea is very similar to superheated water, and the formation of water bubbles in the hot water. What you have to imagine is that you are in a situation where you have  a first order phase transition between two phases. Call them phase A and B for lack of a better word (superheated water and water vapor), and you have to assume that the energy density in phase A is larger than the energy density in phase B, and that you happened to get a big chunk of material in the phase A. This can be done in some microwave ovens and you can have  water explosions if you don’t watch out.

Now let us assume that someone happened to nucleate a small (spherical) bubble of phase B inside phase A, and that you want to estimate the energy of the new configuration. You can make the approximation that the wall separating the two phases is thin for simplicity, and that there is an associated wall (surface) tension \(\sigma\) to account for any energy that you need to use to transition between the phases. The energy difference (or difference between free energies) of the configuration with the bubble and the one without the bubble is\[

\Delta E_{tot} = (\rho_B-\rho_A)V + \sigma\Sigma

\] Where \(\rho_{A,B}\) are the energy densities of phase A, phase B, \(V\) is the volume of region B, and \(\Sigma\) is the surface area between the two phases.

If \(\Delta E_{tot}\gt 0\), then the surface term has more energy stored in it than the volume term. In the limit where we shrink the bubble to zero size, we get no energy difference. For big volumes, the volume term wins over the area, and we get a net lowering of the energy, so the system would not have enough energy in it to restore the region filled with phase B with phase A. In between there is a Goldilocks bubble that has the exact same energy of the initial configuration.

Microwave-oven superheated water explodes (boils instantly) when impurities such as sugar are added. Let's hope there is no cosmic sugar, otherwise it could speed up the Armageddon (tunneling).

So if we look carefully, there is an energy barrier between being able to nucleate a large enough Goldilocks bubble so that there is no net change in energy from a situation with no bubble. If the bubbles are too small, they tend to shrink, and if the bubbles are big they start to grow even bigger.

There are two standard ways to get past such an energy barrier. In the first way, we use thermal fluctuations. In the second one (the more fun one, since it can happen even at zero temperature), we use quantum tunneling to get from no bubble, to bubble. Once we have the bubble it expands.

Now, you might ask, what does this have to do with the Universe dying?

Well, imagine the whole Universe is filled with phase A, but there is a phase B lurking around with less energy density. If a bubble of phase B happens to nucleate, then such a bubble will expand (usually it will accelerate very quickly to reach the maximum speed in the universe: the speed if light) and get bigger as time goes by eating everything in its way (including us). The Universe filled with phase A gets eaten up by a universe with phase B. We call that the end of the Universe A.

You need to add a little bit more information to make this story somewhat consistent with (classical) gravity, but not too much. This was done by Coleman and De Luccia, way back in 1987. You can find some information about this history here. Incidentally, this has been used to describe how inflating universes might be nucleated from nothing, and people who study the Landscape of string vacua have been trying to understand how this tunneling between vacua might seed the Universe we see in some form or another from a process where these tunneling events explore all possibilities.

Guth's "old inflation" involved tunneling.

You can reincarnate that into Today’s version of “The end is near, but not too near”. We know the end is not too near, because if it was, it would have already happened. I’m going to skip this statistical estimate: all  you have to understand is that the expected time that it would take to statistically nucleate that bubble somewhere has to be at least the age of the currently known universe (give or take). I think the only reason this got any traction was because the Higgs potential in just the Standard model, with no dark matter,  with no nothing more in all its possible incarnations is involved in it somehow.

Next week: see baby Universe being born! Isn’t it cute? That’s the last thing you’ll ever see: Now you die!

Fine print: Ab initio calculations of the “vacuum energies” and “tunneling rates” between various phases are not model-independent. It could be that the age of the current Universe is in the trillions or quadrillions of years if a few details are changed. And all of these details depend on the physics at energy scales much larger than the standard model, the precise details of which we don’t know much at all. The main reason these numbers can change so much is because a tunneling rate is calculated by taking the exponential of a negative number. Order one changes in the quantity we exponentiate lead to huge changes in estimates for lifetimes.

If you like TRF guest blogs, don't overlook the guest category.


  1. Very nice article! I hope this is a regular feature!

  2. So, where landscape and its 10^500 vacua has gone ?

  3. Dear NumCracker, do you realize that your comment is completely off-topic i.e. has almost nothing to do with the topic discussed above?

  4. Physically,
    the effect can be interpreted as an object moving from the "false
    vacuum" (where = 0) to the more stable "true vacuum" (where = v).
    Gravitationally, it is similar to the more familiar case of moving from
    the hilltop to the valley. In the case of Higgs field, the
    transformation is accompanied with a "phase change", which endows mass
    to some of the particles.

  5. Hmmmm.....

    The Topography of Energy is an important one and preceding Genus development a correlation needs to take place with real world results?

    The geometrical propensity for development follows a historical development process in that geometry, so, one would have to see it emerging as if from as a "geometrical principle?" Then such correlation would see it self as a baby universe?


  6. Lubos, do you know why so many string theorists concentrate on the early universe? does string theory have a complete theory about the first fractions of a second of the big bang? is it possible that astronomical observations could help string theory? there could be future observations that have to do with inflation and primary CMB anisotropies could probably help the theory?

  7. Thanks for this nice reading :-)

  8. Well, in case our universe is supposed to be born from tunneling among many false vacua embedded in the landscape such a construction had to exist and allow degeneracies, right? In the aforementioned paper it is shown that The minima (our Universe) is unique, so I would like to understand how the tunneling in the picture presented in this blog-entry would be possibly conciliated to that unique groundstate. Thks

  9. A tangential (or not completely off-topic) question:

    Is not the very short abstract linked-to-below containing a stunning typo, or is only I who am so perfectly stupid and/or ignorant?!OpenDocument

  10. For our Universe A to be eaten up by a Universe B, Universe B would have to hold the exact same physical laws as ours, right ?

  11. Hi, I am not sure whether I agree with your claim about many string theorists doing early cosmology. The number seems small to me. The convincing results in this subdiscipline are very limited if any - but at the end, string theory more than anything else should be equipped to answer similar questions.

    Future observations are likely to shift the evidence from some effective theories to others, I am not sure whether the deepest stringy-like questions would get a boost. There are all the non-Gaussianities, B-waves etc. etc. that would say a lot if observed. I don't expect this to happen this year so it's perhaps a premature question.

  12. So one has to reconcile finite properties of the "boxed universe" for what can be transposed as the outward cumulative virtue as expansion alone?

    So using material world processes to be emulated by contrasting experimental procedures is to acknowledge, the parameters of such finite thinking.:)

    So, in the microscopic processes of particulate reconstruction values determined as energy decay products, what value such a lineage if it does not find "such a location" that while microscopic in design has cosmological implications? There is such a place?

    The "Jet" draws ones eyes toward cosmological motivations as distinctive of possible QGP processes?


  13. Thank you very much David! But true phase transitions are defined just at the the thermodynamic limit, right? So in the case you've explained, could one also take that limit rigorously (i.e. letting spatial volume go to infinite during inflation) without spoiling that whole physical scenario? Best

  14. I don’t know Berenstein but the combination of his writing style and the photo give me a general idea of what sort of guy he is. I think I would like him.

  15. I understand ... :-(

    It is too bad, that these ***holes now have entered Physics SE too and are tolerated there :-(
    I dont like the question either, so the only thing you could probably do is state a closevote and I can flag it as not constructive, what I will do now ...

    It is really troublesome how much the trolls have taken over.

  16. Yep, that is what I thnk too :-)
    He looks and writes like a very nice person.

    My first very popular book about fundamental physics I have read some years ago " Out of this world" contained many many pictures Lumo has taken, and my immediate reaction when looking at them was:

    Wow these are all nice people doing awsome and cool stuff :-D


  17. You surrender? They won? Not so long as interesting statements about "Nature (continue) to encode partial and probabilistic knowledge about Nature" so you can relate interesting statements to others using your talent to do so.
    The internet is both a blessing and a curse. There is uncertainty in communication in this e-day so I may be wrong but sound like you must have been having an off moment to have felt this way.
    Certainly the internet gives billions and billions a chance to sell or believe any perpetual bifurcating Everett super entropic gravity showing with tennis racket graphs that the multi-verse is technicolor. Anyone can disagree with whatever regardless what they actually think. Proving that "not even wrong" is a catchy phrase does not support that Pauli actually convinced God he was not composed of a string or that we lacked a brane.
    Many things of little lasting value often are bought by the ignorant and sell for far more than their value . Anyone who has capacity to understand and is interested to understand will not be long fooled. The rest are the losers if such a word applies.
    Your 2011 answer on "what-experiment-would-disprove-string-theory" answered the string theory deniers fully. As to SUSY, Dilaton seems by his SE answers and comments to your posts knows that anyone who knows anything about history and physics knows that the headlines quoted are silly and incorrect hype.

  18. Of course all theoretical physicists share a lot of intellectual and emotional DNA with Sheldon Cooper. I really feel like I know David Berenstein even though I don’t. He’s gotta be a fun guy.

  19. Well Gene, Berenstein is the B in the famous BMN paper for the pp
    wave limit correspondence which was a milestone of AdS/CFT.
    I wish only he could blog more often about Stringy issues; I’m this close from removing his blog from my Google reader… Sorry David:-)