• The Hidden Reality – Part 1


    I’m currently reading Brian Greene‘s 2011 book, The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos.  As the extended title suggests, the book is about the Multiverse.  In fact, it is about the various cosmological theories that suggest or support some notion of an ensemble of universes.


    I have often intended to review books on my blog, only to find myself too eager to devour the book and unable to put it down long enough to put my thoughts to paper.  But I figure that this is a particularly important book, since theistic arguments such as the Kalām Cosmological Argument and the Fine Tuning Argument are, in my opinion, soundly defeated or rendered entirely irrelevant by even the logical possibility of a multiverse.  (Obviously, one must do more than just say the word “multiverse” to dispose of the arguments, but that is a matter for later posts.)  So I’ll do my best to review the book, chapter by chapter, as I work my way through it.  I won’t go into immense detail, but just give a quick indication of what each chapter is about.  It will, however, take a few posts…

    Before I begin, I should stress that I’m a mathematician, not a physicist.  So I won’t attempt to comment on the correctness of any cosmological theory.

    Chapter 1.  The bounds of reality – on parallel worlds

    In this chapter, Greene lays out the structure of the book, naming the various multiverse models he’ll explore in subsequent chapters.  But I thought one small passage was well worth quoting, as it indicates the kind of humble approach he takes:

    The subject of parallel universes is highly speculative.  No experiment or observation has established that any version of the idea is realized in nature.  So my point in writing this book is not to convince you that we’re part of a multiverse.  I’m not convinced – and, speaking generally, no one should be convinced – of anything not supported by hard data.  That said, I find it both curious and compelling that numerous developments in physics, if followed sufficiently far, bump into some variation on the parallel-universe theme.  It’s not that physicists are standing ready, multiverse nets in their hands, seeking to snare any passing theory that might be slotted, however awkwardly, into a parallel-universe paradigm.  Rather, all of the parallel-universe proposals that we will take seriously emerge unbidden from the mathematics of theories developed to explain conventional data and observations.  (pp 8-9)

    Theists often accuse physicists of “inventing” the multiverse, as a last resort, in order to avoid the conclusion of the above-mentioned theistic arguments.  I could comment further on this, and maybe I will in subsequent posts, but I think Greene’s words speak very well for themselves.

    Chapter 2.  Endless Doppelgängers – the quilted multiverse

    This chapter deals with the possibility that the universe is infinite in its spatial extent.  As Greene says on p10:

    Both possibilities – a cosmos that stretches infinitely far, and one that is huge but finite – are compatible with all our observations.

    As Greene explains, one corollary of the universe being infinite in its spatial extent is that there would be infinitely many exact copies of our universe somewhere out there, even though you might have to travel a vast distance until you got to one.  By “our universe”, we mean “our observable region of space”.  By “exact copy”, it is meant that, down to the tiniest of undetectable quantum difference, it would be impossible to tell the two apart.

    So, how far would you have to travel before you reached another exact copy of our universe?  Well, imagine you wrote down a one followed by 122 zeros:



    That’s a big number.  And now write down a one followed by that many zeros!  That’s an absolutely inconceivably big number – in fact, you couldn’t even do it if all the material in our observable universe was turned into pens and paper.  And you’d have to travel across a region of space the size of our observable universe that many times before you were likely to get to another exact copy of our observable universe.

    Of course, you might not care about all the distant stars of the Milky Way you’ve never even glanced at through a telescope, or even exactly what is happening on the surface of Jupiter.  If all you want is an exact copy of you, in an exact copy of your house, on an exact copy of the earth, orbiting an exact copy of the sun, then you wouldn’t have to go quite so far, though you’d still have to go a long way.

    Now, what kind of support could there be for our universe having infinite spatial extent?  Well, consider this.  Imagine you looked up from the north pole, using the most advanced telescope, and observed some of the first light (photons) that had left a star and was only just finally arriving at the earth after its long journey through space.  And imagine someone was doing the same thing from the south pole.  Since the light from those distant stars has only just reached the earth, hypothetical observers in one of those distant locations would certainly not have ever been able to see the other location (they’d only just be able to see us).  It stands to reason that from those distant places, hypothetical observers could see even more distant (from us) locations – locations that are beyond our ability to see, and are essentially invisible to us.  And hypothetical observers in those even more distant locations could see further still, and on it goes.  There seems to be no reason to suppose this could not, in principle, go on forever.  It might go on forever, or it might loop back on itself, but we don’t know.  Both possibilities are compatible with the data we possess.

    Now this doesn’t prove that the universe is infinite in its spatial extent.  Further, I doubt that anything could prove the universe was infinite (though I’m ignorant of physics, and there might be a way).  I mean, how long would you have count through an infinite collection of coins before you agreed that there were infinitely many?  A thousand coins?  A million?  A trillion raised to the trillionth power a trillion times?  But, equally, I don’t think there is any disproof of a spatially infinite universe.  As I’ve shown in a few posts (eg, Infinite dreams and Infinity minus infinity), the standard philosophical arguments against actual infinities don’t work.

    Greene calls this version of the multiverse the Quilted Multiverse, given that you could imagine the spatially infinite universe as consisting of a bunch of patches such that the borders of each patch are (in some complicated geometrical sense) the boundaries that hypothetical observers in the middle of the patches could not see past.  This is really not the usual kind of multiverse people speak of – in this scenario, there is (maybe) only one universe, but it contains infinitely many regions that are, for all intents and purposes, self contained universes, ours being just one of them.  I wonder if that’s the way it really is!

    Category: Book reviewMultiverseScience


    Article by: Reasonably Faithless

    Mathematician and former Christian
    • DRC

      The interplay between physics and philosophy has always fascinated me, so I’m looking forward to this book review series.

      I might disagree that a spatially infinite universe couldn’t be disproven. You could prove (in a scientific sense) the universe is finite if you found it had positive curvature so you could travel off in any direction and arrive on the other side. In the language of general relativity this would be a closed universe which is finite.

      • But by the same argument, you could prove that the universe was infinite if you found it had a non-positive curvature (which is in fact what we see). The problem, of course, is that we can’t be sure that the curvature is constant everywhere.

        We could prove that the universe is finite if we physically traveled all the way around it. I don’t think that’s in our budget though.

        • DRC

          I agree that not knowing the curvature everywhere prevents us from proving an infinite universe. Alternatively, the universe could be flat or negatively curved and have a hard edge so it’s finite, so knowing that it’s flat or negative doesn’t prove it’s infinite. For those reasons, I think the finite universe is *possibly* provable, but the infinite ones are unprovable.

          • Actually, I was careful to say “I don’t think there is any disproof of a spatially infinite universe” rather than “I don’t think there could be any disproof of a spatially infinite universe”. If someone proves that the universe has positive curvature, then I’ll be happy to accept that – we just have to go with what science shows (and I have no money placed on the universe being infinite). But, for now, I don’t think there’s anything pointing definitively to finite. But I definitely think it could be proven finite, at least in principle – eg, in a really tiny universe, you could see the back of your head!

            • DRC

              Ah, ok. I interpreted that sentence the other way.

          • But proving a finite universe from a positive curvature has the same problem. You could imagine that the universe is flat on large scales, but on a smaller scale, there some bumps. On any of those bumps, the curvature is positive, but the universe is still infinite.

            I tend to think changes in curvature are far more likely than hard edges. A hard edge requires new physics. A change in curvature just requires that mass is not uniformly distributed (contrary to observations so far). Given our current state of knowledge, I think an infinite universe is more likely than a finite one. I wouldn’t put money on it though because even if we could prove it, it would take a very long time, so the implied interest rate is too low.

            • DRC

              Yes it has the same problem if that’s all you know. I was saying you could prove a finite universe *if* it was positively curved which enabled you to travel around the universe (or see the back of your head with a telescope).

              I agree that smooth changes in curvature seem more likely than hard edges. Or at least if there are any hard edges, our current knowledge of physics can’t tell us much about it.

    • brad lencioni

      I own all of Brian Greene’s books, and I consider them to be among my favorites on my shelf. So I look very much forward to your discussions of The Hidden Reality 🙂

      As hard as an infinite universe is to conceive of, I think a finite one is at least as difficult to imagine.

      • I’ve probably said this elsewhere, maybe even in a conversation with you, Brad. But Dan Dennett put it well when he said that some questions have amazing answers, whichever one turns out to be true. If the universe is infinite, then WOW! If the universe is finite, then WOW! (WOW for different reasons in each case.)