Tegmark’s Level II Multiverse: bubble universes

bubble universes
bubble universes (Photo credit: Pedro Moura Pinheiro)

I recently finished reading Max Tegmark’s latest book, ‘Our Mathematical Universe‘, about his views on multiverses and the ultimate nature of reality.  This is the second in a series of posts on the concepts and views he covers in the book.  Tegmark postulates four levels of multiverse.  

In the first post of this series, I described Termark’s Level I multiverse, which arises from space being infinite and the patterns of atoms in our local observable universe eventually being duplicated, with and without variations, in far off regions of space.

This post is on his Level II multiverse, which is a description of the bubble universes from eternal inflation.

There is strong and abundant evidence that our known universe started in a hot dense state about 14 billion years ago, commonly called the big bang.  It has been expanding and cooling ever since.

However, there were unexplained aspects of the visible universe that complicated the picture.  The main one was that the furthest teaches of the visible universe had the same temperature in all directions, even though those remote regions had never had a chance to interact and come into thermal equilibrium.

In order to explain the universe as we see it, cosmologists realized that a rapid exponential expansion must have happened in the earliest instances of the observable universe.  During this period, called cosmic inflation, the universe would have expanded by a factor of at least 1026.  Once inflation was complete, the universe would have proceeded following the classic big bang timeline, going through the hot dense state and later expanding and cooling enough for normal matter and eventually galaxies to form.

What caused inflation?  No one is sure, but quantum fluctuations are usually thought to be involved.  Inflation expanded those quantum fluctuations into the universe wide variances that later led to the formation of galaxies.  Some models actually posit that inflation is space’s natural state, and that the real question is what caused it to end?

If inflation is the natural state, and an event of some type such as a random quantum fluctuation caused it to end, and if space is infinite, then this event may not have caused inflation to end throughout all of space.  There may be regions of space where inflation never ended, where it is eternal.  Indeed, it may not have ended in most regions of space.  Our universe may be a low probability bubble where inflation has ended, or perhaps slowed down to the more stately expansion we see today.

But a low probability event is not a zero probability event.  So there may be other regions where inflation stopped, where other bubble universes formed.  If so, we would be separated from these other bubble universes by a perpetually hyper inflating space.

If we could somehow leave our bubble (we can’t, more on that later), it would be fruitless to try to reach another bubble, because inflationary space would be expanding at an unimaginable rate.  We’d never be able to catch up.  For that matter, we’d never be able to return to our own bubble since the space we traveled would also have continued to expand, isolating us beyond all hope.

Although the fundamental laws of physics would be the same in each bubble universe, it’s thought that different random factors in formation of each bubble may cause the effective laws of physics to vary, notably in many of the physical constants that, in this universe, appear to be random.

The idea is that this would provide an explanation for what appears to be fine tuning in our universe.  In most universes, the physical laws and constants would not allow for life.  The fact that we are here contemplating this shows that we’re in one of the few universes that do have conditions for life to form.  Of course, this assumes that those constants aren’t what they are in our universe due to some unknown physical necessity.

Is the Level II multiverse compatible with the Level I multiverse?  After all, the Level I multiverse assumed infinite space.  The Level II does as well, but doesn’t being in a bubble inherently mean that our universe is not infinite, at least at the Level I level?  Furthermore, wouldn’t it be possible, in principle, for us to travel to the boundary of our bubble and enter inflationary space?

The answer is that the Level I and Level II multiverses are compatible, because within our bubble, space is infinite.  How can this be?  How can we have an infinite universe within a finite bubble?  Warning: the answer is weird, and hard to explain.  I’m probably going to fail.  Tegmark attempts an explanation in the book.  He’s an excellent writer, but I found Brian Greene’s explanation of this in ‘The Hidden Reality’ to be a bit more understandable.

It has to do with the relativity of time.  We’ve known since Einstein that time flows differently depending on how fast you’re moving, or how intense gravity is.  In short, time flows slower when the density of energy is high, and faster when the density of energy is lower.  Not only is time relative, but so is simultaneity, that is, whether two events happened at the same time or not, is relative.

The bubble universe is constantly growing into inflationary space, bringing in new regions of space where inflation is coming to an end.  From outside the bubble, the new outer regions are just beginning their big bang, their expansion and cooling, while the inner regions are well along into forming galaxies.

The bubble will expand forever, bring in new regions, ending inflation in those regions, infinitely far into the future, meaning that infinitely into the future, the bubble will be infinitely large.  Of course, inflationary space is expanding much faster, so there’s no danger of the bubble eating everything.

But time flows differently within the bubble.  Remember the relativity of simultaneity?

Ok, here’s the punchline.  Within the bubble, all regions came out of inflation simultaneously.  So, infinite time and expansion in inflationary space translates into infinite space, right from the beginning, within the bubble.  Furthermore, we can’t travel to the boundary of the bubble, because the boundary is the big bang.

Yep, I warned you it was weird and hard to understand.  It’s easier to understand with visual aids, which both Tegmark and Greene use in their books.  I tried to find something on the web, but came up empty handed.  Sorry.

Ok, so this multiverse is much more complicated than the Level I concept, which it ostensibly contains.  It also makes a lot more assumptions.  The first is inflation, which is actually turning out to be a good one with the new BICEP2 data.  But is it the right inflationary model?  Is inflation eternal?  Is space infinite, or at least large enough for these bubbles to form?  If they form, do the physical laws and/or constants vary among them?

There’s also the question of where all this continually hyper inflating space and energy is coming from.  Tegmark, while affirming the evidence in our observable universe that it does happen at least on some scale, admits to being a bit apprehensive about this, as though maybe reality is the ultimate Ponzi scheme, where a helluva bill may come due someday.

Only time will tell, maybe.

The next post in this series will be on Tegmark’s Level III multiverse, where we’ll learn that we’re really just getting started pulling space and energy out of our hat.

26 thoughts on “Tegmark’s Level II Multiverse: bubble universes

  1. Very nice article, SAP. You did a good job of explaining how the bubbles work and can contain infinite space. It might have been good to get more of a sense about how plausible you find the whole thing, although I assume you are agnostic and regard that as a question for the experts.

    “”What caused inflation? No one is sure, but quantum fluctuations are usually thought to be involved. ”

    Hmm, I don’t think that’s right. Quantum fluctuations are responsible for breaking the homogeneity of the early universe and for our evidence for inflation, but not for the inflation itself I don’t think

    My own thoughts:

    The level II multiverse is the one of which I am least sure.

    (Granted, it must exist somewhere in the level IV multiverse if it is mathematically consistent, but I am not sure that we will find that our universe exists in such an inflationary multiverse).

    One problem I have with the idea as I understand it is that it seems to mark one particular region of space as the true centre of the universe, i.e. that region that was first created as the bubble began to form. There’s no reason this couldn’t be true but it just feels a little suspect. I wonder if perhaps time is a bit more omnidirectional or of higher dimensionality in the hyperinflating space so that we can take an expanding bubble to begin forming not from any specific point. I think I would need a diagram to explain my thoughts here.

    Also, I am not at all persuaded by the anthropic argument for the level II multiverse as the level IV multiverse (which I think is logically necessary) takes care of that.

    That said, I’m not at all saying that I believe the level II multiverse is false, I just don’t yet see any reason to believe it is true, (neither does Tegmark as I understand it).


    1. Thanks DM!

      On quantum fluctuations, maybe a better way to phrase it was a random quantum event of some kind. If not random, then why would it happen in some regions but not others? Of course, no one really knows why inflation stopped. Maybe the reason was a universe wide change, ruling out bubbles.

      On a center of the universe, it might be apparent for someone outside of the bubble, but no one inside the bubble could ever figure out where it was. Well, at least assuming that it does expand infinitely far in the future. If the expansion does ever end, then suddenly there is a center, and a boundary, and that would be very weird. That said, you may be right about extra dimensions. Maybe Tegmark and Greene simplified those out for communication.

      My attitude overall toward bubble universes is skeptical agnosticism due to the multiple assumptions that would have to be borne out. To me, each assumption lowers the likelihood of it being true. For example, it might be true but with every bubble having the same laws and constants.


      1. I wouldn’t necessarily be so quick to identify random with quantum. There could be indeterministic laws of nature other than quantum mechanics.

        In any case, “in some regions but not others” does not require randomness. The digits of Pi have repeated digits in some regions but not others, yet each digit is entirely determined.


  2. Disagreeable Me…
    i read your article “the universe is made of mathematics”. And i must say that i’m really impressed! As proving the universe is mathematically you were able to fully prove that it is physical. You really have done that in a perfect way. There is still a small problem. Physical Universe is not quite what is the Real Universe. but this is not important at the moment. of course, i have don’t added to this the divine forces that humans invented themselves according to their needs. Thank you also for the beautiful text.
    i’m sorry (SAP) that i littering your blog. i hope you can forgive me?


      1. i hope SAP doesn’t kill me!!! i also hope (i think we all) that your entries appear on wordpress (not only on blogspot). Thank you for your reply! about my comments… actually, i can’t keep up with what you write (You, SAP, Steve) and what to think about commenting… maybe in a few years as i be a little wiser…


          1. I don’t really find much of a difference in commenting on the two, although I think WordPress allowing Twitter and Facebook authentication gives it a slight advantage. Since they’re already logged into WP, it’s marginally more convenient for a WP user to comment on another WP site, but that probably applies in reverse for Blogspot users.

            What I find that WordPress.com has is better community building. They make it a little easier for bloggers to discover each other through the follow mechanism and the wordpress reader. Using social networks can bring in a lot of readers, but most of the commenting seems to come from fellow bloggers.

            What I do find irritating about wordpress.com is our inability to put javascript in the widgets. That constrains what you can put in your sidebar, headers, footers, etc. But that’s something that few bloggers probably care about.


          2. I just tried to make a comment on your blog. I selected to log in as WordPress, but it is insisting that I am Anonymous and giving me a Captcha question that I find impossible to answer. No doubt I could persist and get there eventually, but it’s a hurdle. Last time I left a comment on your site I did it as Anonymous and explained who I was in the comment.


      1. Thank you that i was not condemned. (about wordpress-blogspot) additional difficulty for me is that i often use the mobile device. and here (note 2 … 5.5′) wordpress looks better!


  3. Have you seen this ‘SAP’? It sounds as though it’s causing something of a stir:

    ‘The fourth state of matter: Consciousness’ by Max Tegmark

    … I don’t subscribe, but:

    ‘Why Physicists Are Saying Consciousness Is A State Of Matter, Like a Solid, A Liquid Or A Gas’
    View at Medium.com

    Consciousness as a State of Matter’, Tegmark 2014

    Click to access 1401.1219v2.pdf


    1. I wouldn’t read too much into it, amanimal. As far as I can see he’s just proposing a new perspective on the problem, not really a new physical principle. He is also suggesting that there must be physical properties correlated to consciousness so that consciousness could be detected empirically by the observation of such properties.


    2. He talks about this in the book too. I often wince when physicists talk about consciousness. They have a tendency to treat it as a physics problem. Now I firmly believe it is ultimately physics, but trying to address it at that level is like treating a software algorithm as a physics problem. The vast majority of neuroscientists see consciousness as an information processing phenomenon, not something that requires new physics to explain.


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