From Eternity to Book Club: Chapter Fourteen

By Sean Carroll | April 13, 2010 8:43 am

Welcome to this week’s installment of the From Eternity to Here book club. We’re on to Chapter Fourteen, “Inflation and the Multiverse.” Only one more episode to go! It’s like the upcoming finale of Lost, with a slightly lower level of message-board frenzy.


There is a lot to say about eternal inflation, but let’s just focus on one consequence: While the universe we see looks very smooth on large scales, on even larger (unobservable) scales the universe would be very far from smooth. The large-scale uniformity of our observed universe sometimes tempts cosmologists into assuming that it must keep going like that infinitely far in every direction. But that was always an assumption that made our lives easier, not a conclusion from any rigorous chain of reasoning. The scenario of eternal inflation predicts that the universe does not continue on smoothly as far as it goes; far beyond our observable horizon, things eventually begin to look very different. Indeed, somewhere out there, inflation is still going on. This scenario is obviously very speculative at this point, but it’s important to keep in mind that the universe on ultra-large scales is, if anything, likely to be very different than the tiny patch of universe to which we have immediate access.

This is a fairly straightforward chapter, trying to explain how inflation works. Given that by this point the reader already is familiar with dark energy making the universe accelerate, and with the fine-tuning problem represented by the low entropy of the early universe, the basic case isn’t that hard to put together. Of course we have an additional non-traditional goal as well: to illuminate the tension between the usual story we tell about inflation and the “information-conserving evolution of our comoving patch” story we told in the last chapter. Here’s where I argue that inflation is not the panacea it’s sometimes presented as, primarily because it’s not that easy to take all the degrees of freedom within the universe we observe and pack them delicately into a tiny patch dominated by false vacuum energy. Put that way, it doesn’t seem all that surprising, but too many people don’t want to get the message.

This is also the chapter where we first introduce the idea of the multiverse. (The multiverse occupies less than 15 pages or so in the entire book, but to read some reactions you would think it was the dominant theme. The publicists and I must share some of the blame for that perspective, as it is an irresistible thing to mention when talking about the book.) Mostly I wanted to demystify the idea of the multiverse, presenting it as a perfectly natural outgrowth of the idea of inflation. What we’re supposed to make of it is of course a different story.

Looking back, I think the chapter is a mixed success. I like the gripping narrative of the opening pages. But the actual explanation of inflation is kind of workmanlike and uninspiring. I really put a lot of effort into coming up with novel explanations of entropy and quantum mechanics, which didn’t simply rehash the expositions found in other books; but for inflation I didn’t try as hard. Partly simply because of looming deadlines, partly because I was eager to get to the rest of the book. Hopefully the basic points are more or less clear.

  • Blake Stacey

    I think it worked out OK, partly because workmanlike (or worse) explanations of basic QM are all over the place, which in my personal experience is less so for inflation. It’s harder to sound like a rehash of other books when there are fewer of those other books to worry about. Of course, this could just be an artefact of my pop-sci reading habits, i.e., sampling bias, so count yourself lucky.

  • Clifford

    You did it! With this chapter, you finally lost me. Congratulations. A lot of good stuff here. Very informative.

    Question: Could you give a little more technical detail on what a magnetic monopole is because I think most people think of magnetism as simple a (epi-)phenomena caused by charges in relative motion, Maxwell’s equations and all that? Even the quantum intrinsic spin of charged particles have 2 poles, right; so, how can monpoles exist? If there’s one thing in the book that makes most people dubious, it’s monopoles.

  • Sean

    Of all the things in this chapter, it was the monopoles that lost you? Last thing I would have guessed.

    Not sure how to give the best explanation. Sure, we often think of magnetic fields as being caused by charges in motion, but that’s because there aren’t any monopoles in the real world. Think about how electric and magnetic fields behave in empty space, with no charges or currents around, for example by looking at Maxwell’s equations and setting ρ and J to zero. The answer: they behave exactly the same! The difference is that electric field lines can end on sources, which we call “electric charges.” But it’s easy to imagine changing Maxwell’s equations to include magnetic charges as well, restoring the perfect symmetry. Those would be magnetic monopoles — particles on which lines of magnetic field come to an end.

  • KiwiDamien

    I think Sean left out an important part of the story (haven’t got the book with me, so I cannot check if it is in there, but I assume it is).

    In the standard model, electromagnetism is a little bit odd as it is described by a U(1) gauge theory. All the other forces are described by non-abelian groups, and as such there charges have a certain structure to them. For U(1) you can make the charges anything you like, but there remains this curious fact that in nature the charges do seem do be quantized. Any attempt to unify the three forces (strong, weak, E&M) will “embed” the U(1) into a higher group and as such there will be constraints placed on the available charges. This is a good thing, as a grand unified theory would be able to explain why only certain values of electric charge exist (1/3, 2/3 and 1 in “conventional units”). However grand unified theories typically make two nasty predictions as well:
    1) Proton decay (quarks are now able to change into leptons)
    This is what makes them disfavored.
    2) The additional structure to the electromagnetism not only quantises charge, but also predicts monopoles.

    Initially the monopoles were not a big problem — even though we had not seen any at accelerators we could just claim they were at ultra-high energies. If the energy was very high then of course we would not have enough energy to produce them and it was no surprise we had not seen them. The problem returned when particle physicists finally considered cosmology: the universe ws a very hot place according to the big bang, and so in the early universe there would have been enough energy to produce monopoles.

    Even worse, these monopoles would very quickly be non-relativistic. As the “radius” of the universe doubled, the number of monopoles would go down by a factor of 8 (the same as the volume). However everything we have around us would still be relativistic and would dilute by a factor of 16. To fit the monopoles in, they would have this “dilution advantage” for a long time, and the prediction would be that we would be completely littered with monopoles.

    Note that the fact that they are magnetic (or monopoles) has nothing to do with the cosmology argument. That argument is based solely on kinematics — or how heavy the particles are. So now theorists were confined on both ends: any new particles could not be too light because then we would have seen them already in accelerators (or they have very small couplings etc). New particles also could not be ultra-heavy, because then we would have them dominate us today (or cause the universe to collapse already). The only “out” with not being able to produce ultra-heavy particles was if, somehow, our story of the big bang was incomplete…..

    That is one of the things inflation claimed to step in and fix.

  • Peter Lynds

    Hi Sean,

    Congratulations on the book.

    Given that you seem to believe that the past is infinite (a point also illustrated by your book’s title), how do you reconcile this with the conclusion that, if this were so, it would be impossible for the multiverse to evolve, not only to where we find ourselves today, but forward (in a manner of speaking) at all? After all, time is infinite in the other direction. One might deny that the quantum vacuum is temporal, but if so, a fluctuation could not be be said to precede and be causal to the big bang.

    Best wishes


  • Lab Lemming

    What is the attraction of the standard model if all of its high profile predictions don’t work? For example, science has spent huge sums of money and time looking for hydrogen decay (to no avail), and the lack of monopoles requires this whole inflation deal to explain. Given that the utility of a scientific theory is its ability to predict observations, I am wondering why this standard model is useful to anyone, if every time they try to predict something with it, the predicted object is not found?

    Or are there oodles and oodles of vanilla not-so-spectacular low-budget predictions that it works fine for, which fly under the radar of non-physicists?

  • Sean

    KiwiDamien– Indeed, the monopole problem is discussed in the book as a motivation for inflation.

    Peter– I don’t understand the objection. Why is there a contradiction between time stretching forever and the multiverse evolving?

    Lab Lemming– I presume you mean the Standard Model of particle physics, not the cosmology standard model. Both have many successful predictions; the SM of particle physics has been predicting things that have been verified in experiments for thirty years now. For example, the existence of the W and Z bosons, the top quark, precision electroweak tests, and so on. Proton decay and monopoles are not predictions of the Standard Model; they’re predictions of grand unified theories, which are much more speculative.

  • Peter Lynds

    Hi Sean,

    Thanks. The same problem applies whether one thinks of our universe having an infinite past or a multiverse having one. In both cases, it would be impossible for the universe/multiverse to evolve because the past or other direction of evolution would go forever; there would be no point from which such an evolution could begin. I guess it could help to think of a ruler with one direction of it going forever, and then asking how one could get to the opposite/finite end coming from the infinite direction.

    That ‘s not to say the opposite idea–that of the universe having a beginning a finite time in the past—isn’t equally contradictory, due to the need for a cause for that beginning, and a cause for that, and so on, ad finitum. The idea that the universe was created by a random quantum fluctuation wouldn’t appear to get around the problem because it assumes the existence of an infinite past of quantum vacuum, and then the earlier problem applies.

    Best wishes


  • Ray

    @peter lynds
    who says the evolution of the universe has to begin?

    I think your problem can be resolved by labeling all times with real numbers. Since minus infinity is NOT a real number we can’t think of the evolution from that point onwards anyway. While there is no largest nor smallest real number, the difference between any two real numbers is finite. Hence if we pick the state of the universe at any actual time in the past, it will evolve to the present state in a finite amount of time. I don’t think even this is a requirement for the history of the universe to make sense though.

  • Sean

    There’s nothing wrong with the universe lasting forever in both directions of time. That’s what would be true in Newtonian mechanics, for example. Or in quantum mechanics, if the time-dependent Schrodinger equation is correct.

  • Peter Lynds

    Hi Sean,

    Thanks. Saying that the universe has both an infinite past and infinite future doesn’t resolve the problem. One is still faced with trying to explain how evolution is possible from an infinite past.

    Hi Ray,

    Thanks. Yes, but by doing this, one is both trying to imply that the past is infinite (by implication of there always being a smaller or larger real number), but then also deny it. Either the past really is infinite or it isn’t.

    Best wishes


  • Lab Lemming

    Sorry, I meant Grand Unified Theory, not standard model. Although I suspect that the neutrino science enabled by the failed search for H decay was probably more useful than H decay would have been had it been found.

  • Will

    Can I ask what the EM Lagrangian looks like with the addition of magnetic monopoles? The normal div.B and curl B equations are geometric in nature, so presumably you have to define something other than the normal maxwell tensor?


  • Juan

    It should be pointed out that the time reversal symmetry of the Schrodinger equation is only possible because we are dealing with complex numbers and an imaginary diffusion coefficient. If we dealt only with real numbers, then we are dealing with the tried and true heat equation, which is not symmetric under time reversal. It should also be pointed out that the Schrodinger equation is only computing the wave function, which controls probabilities and not classical trajectories.

    In the quantum world, we can understand unfolding events as a Markov process where time is treated as an absolute parameter. This means that the process is ignorant of the signed value of time. As an example, in a coin flipping scenario, reversing time is not going to produce the past history of coin tosses. IOW, tossing the coin at time -1 will have the same 50-50 probability as tossing the coin at time 1.

    What is surprising then is that the Schrodinger equation tells us that it is just as unlikely to reach a particular state in the past as it is to reach a particular state in the future, e.g. the past is just as unpredictable as the future. It is only when we transition into the classical realm, the one mappable to real numbers, that we see time reversal asymmetry and the notion of past and present. There past events have more concrete values, and we have a more solid concept of history.

  • Juan R. González-Álvarez

    To Sean, Peter Lynds and Ray,

    Past cannot be infinite, because this would imply that time cannot flow. This is explained to broad audiences in the section “How does time evolves?” in the bottom part of the next link

    If anyone needs the technical details, can ask me.

  • Juan R. González-Álvarez

    To Juan,

    The time symmetry of the Schrödinger equation is associated to the use of real numbers (or more rigorously to hermiticity) for the evolution of quantum states. It is just when we relax this and consider complex eigenvalues for the Hamiltonian that an irreversible component arises in the evolution. In standard literature, the dissipativity condition is then defined as Im{H} =< 0. Semi-phenomenological models of this class are useful to study the (exponential) decay of instable particles.

    What you call the "true heat equation" is only an approximation to more general heat equations that also work for strong gradients of temperature and for systems with memory (non-Markovian).

    I want to emphasize that the Schrödinger equation is deterministic. If you know the state of the system at instant t you can know any other instant both in the future or the past. And the classical limit of quantum mechanics is also deterministic and time-reversible.

  • Ray


    The discussion at

    assumes the 2nd law of thermodynamics, which is not fundamental. Sean is postulating a scenario where the second law isn’t true before a certain time. Read the last chapter.

  • Sean

    Will– You can’t write down a simple Lagrangian with magnetic monopoles based only on the usual E&M vector potential. In grand unified theories, you start with a larger symmetry group (like SU(5)), then break it using some scalar fields; the monopoles are then topological configurations of the scalar fields.

  • layman

    To Sean,

    Congrats on your book. If I may ask a question: can you (dis)prove “to any observer the size of the observable universe is the size of a black hole”?

    I have been told this is trivially true for a flat universe. Should inflation changes this? What would be the consequences to take this as a law?


  • Sean

    layman– If you look at the Friedmann equation for a flat matter-dominated universe, you can integrate the total mass within one Hubble radius. Then you can calculate the Schwarzschild radius for that much mass; it’s the same (to within some numerical factor) as the Hubble parameter. That has nothing to do with inflation, it’s a statement about a flat matter-dominated universe at the present time.

    But the universe isn’t a black hole; if anything, it’s a white hole. Black holes have singularities in the future, white holes have them in the past.

  • CarlN

    Sean has no problems with time stretching to infinity in both directions. However, the laws of physics tell us that time “progress” at a finite rate. Time could never cover the interval “from eternity to here” at any finite rate.

    Same for the future. There will never be a future time that is infinite into the future from present time. The proof is very simple.

  • Juan

    Apparently you didn’t actually read my comment, and it seems to me that you don’t understand that what the schrodinger equation is manipulating is the wave function, which is represented using a complex number field. This allows us to use complex conjugation to maintain time symmetry (or, as it has been crudely pointed out in the past, we can think of a backward moving universe as being made of anti-particles, and would behave exactly like our own to local observers). Sure, the schrodinger function is deterministic, but what it is determining is probabilities, and the time component tracks time between observations. Those observations are real valued observations. The Markovian processes with memory do represent our real universe, but the schrodinger equation is what governs the probability evolution between each coin flip.

  • Juan R. González-Álvarez

    To Ray,

    Sorry but the scenario described in the section cited above is not assuming the second law of thermodynamics.

  • Juan R. González-Álvarez

    To Juan,

    I did some remarks about how complex extensions of the Schrödinger equation can explain some of the phenomenology of irreversible systems, such as the decay of instable particles radioactive nuclei…

    Let me do some other minor comments to your last message. First the Schrödinger equation does not need to be manipulating a wave function as you affirm; it can be manipulating a Ket or a Bra in Dirac’s abstract notation. A Ket |Psi> in the general N-particle case, cannot be represented using a complex number field. I think that you confound the general quantum state with the special case described by wavefunctions as Y(x,t).

    I do not know what you mean by “a backward moving universe as being made of anti-particles”. It seems that you mean Stuckelberg-Feynman interpretation of antiparticles. Their model is not valid and in modern QFT, there is nothing like particles moving backward in time. There was a rather large discussion about this in newsgroup sci.physics.research the last two weeks.

    I have no idea about what you mean by your “The Markovian processes with memory do represent our real universe”. Moreover, it is not true that “the schrodinger equation is what governs the probability evolution between each coin flip”. The equation is only valid in the Markovian limit, pure state, no random terms f… In more general cases we use more general cases: from simple Ito-Schrödinger equations to more developed expression as Lindblad equation, Eu equation, the Brushels-Austin equation, etc.

  • Juan

    A Ket |Psi> in the general N-particle case, cannot be represented using a complex number field.
    I am not sure you understand these things well, I found a good article that describe bra-ket notation
    I think you should review these things.
    In any general sense, since real numbers are a subset of complex numbers, I can most certainly tell you that any number you produce has a complex number representation. What is really different between a real number and a complex number is that a complex number is intrinsically a vector (even though we do sometimes call them scalars, but that is a minor issue in semantics). In any case, because complex numbers and real numbers share the same cardinality I can do whatever the f… I want. It is their behavior under group operations that is important, and I you simple can’t get real numbers to do some of the things that you can do with complex numbers simply because the latter is intrinsically a vector. As far as your comments on being stuck on the “Stuckelberg-Feynman” interpretation of antiparticles, although that comment is intended to make you sound intelligent, it doesn’t. I only said that one could crudely understand these things as such, which to an intelligent person should be interpreted as meaning approximate and not a rigorous statement. I am not stuck on any interpretation, but apparently you are since you don’t understand the general use of the word Markovian.

  • Juan R. González-Álvarez

    To Juan,

    you confirmed my suspicion that you confound the ket |Psi> in the general N-particle case, with the special case described by wavefunctions as Y(x,t). Nowhere in the absoluteastronomy link that you gave above appears the word “field”, even once!

    As explained to you before, it is only the last special case of Y(x,t), which can be interpreted as a field and next quantized using the formalism of second quantization.

    You are right that “In any general sense, since real numbers are a subset of complex numbers, I can most certainly tell you that any number you produce has a complex number representation.” But this is a straw-man. Evidently the complex extensions of the Schrödinger equation used to explain some of the phenomenology of irreversible systems and of the arrow of time are those where purely real observables are extended by adding a non-zero imaginary part. If you read my messages with care, you would find the part where I gave the dissipation condition. I repeat it now: “In standard literature, the dissipativity condition is then defined as Im{H} =< 0”. When the imaginary part is zero, dissipation is zero and one recovers time symmetry.

    I fail again to follow parts of your message. You did not reply to my questions for clarifications and it seems that you are rejecting the well-known fact that the Schrödinger equation is Markovian with your “since you don’t understand the general use of the word Markovian”.

    The Schrödinger equation is valid only as approximation, when one ignores non-Markovian corrections, mixed states, random terms f… In the more general cases we use more general equations: from simple Ito-Schrödinger equations to more developed expression as Lindblad equation, Eu equation, the Brussels-Austin equation, etc.

    An introduction to the Lindblad equation is given in the above Wikipedia link linked in my previous message.

    I want just to add that the Brussels-Austin equation is based in a complex extension of the Liouville space and the condition for dissipativity is Im{Z} =< 0, where Z is an eigenvalue of the Liouvillian in a generalized space (beyond the Hilbert space of ordinary quantum mechanics). The applications to instable systems: particles, fields, etc. are found in standard literature in mainstream journals

  • layman

    Hi Sean,

    (I have a strange problem using chrome: each time I try to comment I’m redirected to Petrosky’s web page. It’s seems ok using explorer.)

    Thx for your answer, although I’m not sure to understand. You seem to say that what happens in a flat matter-dominated universe has nothing to do with inflation. Then I was unclear: my question is about whether the “to any observer the size of the observable universe is the size of a black hole”? assertion may also hold in a universe with a big vacuum energy, or cosmological constant.

    “the universe isn’t a black hole; if anything, it’s a white hole.”
    What if white holes were black holes seen from the inside?

  • Juan

    I don’t disagree with you Juan. I think that you are entirely right. I can insert an arbitrary variable into any equation and make it behave in a way that makes us happy. The question is whether the variable is used for an ad hoc approximation or whether it has real physical significance.
    In any case when it comes to states, we run into the same general questions of orthogonality, independence, exclusion, variance, collinearity, interaction, etc. These general issues are what we are trying to address when we build our models, and there is a growing proscriptive way of how to deal with these things when building a theory.
    In any case, putting aside the physical meaning of the word emergence, we see that how our equations behave emerges from our general use of the properties of numbers and how we construct more complex mathematical structures that incorporate those behaviors. The beauty and frustration of modern physics is that the real world almost behaves as objects we can define mathematical, but not quite. This is why I keep telling you that our disagreement is a semantical one and completely detached from the specifics of the application of math to particular problems.
    That we can model certain systems using a particular approach is useful, but whether it reveals a deeper physical understanding and linkage to fundamental behavior of mathematical objects is another issue.

    Also you need to be more careful with your use of onclick and urchinTracker

  • Juan

    You know what Juan. I want to apologize for my behavior.

  • Sleeth

    I’m very late coming to the book club (I was #7 on the library’s wait list). Ch.2’s comment option is long closed so I am posting here.

    Top of pg 39, If I read correctly, you are stating the apparent angular size of the Sun is about 1 degree across. If that were true, there would be more frequent lunar eclipses, but no total solar eclipses. I believe the value is about half that value, around 0.5 degrees or 32 arc minutes, approximately the same size as the disk of the moon.

  • Sean

    Yes; that was a typo.


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About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] .


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