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Ten Questions for the Philosophy of Cosmology

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Last week I spent an enjoyable few days in Tenerife, one of the Canary Islands, for a conference on the Philosophy of Cosmology. The slides for all the talks are now online; videos aren’t up yet, but I understand they are forthcoming.

Stephen Hawking did not actually attend our meeting -- he was at the hotel for a different event. But he stopped by for an informal session on the arrow of time. Photo by Vishnya Maudlin.
Stephen Hawking did not actually attend our meeting — he was at the hotel for a different event. But he stopped by for an informal session on the arrow of time. Photo by Vishnya Maudlin.

It was a thought-provoking meeting, but one of my thoughts was: “We don’t really have a well-defined field called Philosophy of Cosmology.” At least, not yet. Talks were given by philosophers and by cosmologists; the philosophers generally gave good talks on the philosophy of physics, while some of the cosmologists gave solid-but-standard talks on cosmology. Some of the other cosmologists tried their hand at philosophy, and I thought those were generally less successful. Which is to be expected — it’s a sign that we need to do more work to set the foundations for this new subdiscipline.

A big part of defining an area of study is deciding on a set of questions that we all agree are worth thinking about. As a tiny step in that direction, here is my attempt to highlight ten questions — and various sub-questions — that naturally fall under the rubric of Philosophy of Cosmology. They fall under other rubrics as well, of course, as well as featuring significant overlap with each other. So there’s a certain amount of arbitrariness here — suggestions for improvements are welcome.

Here we go:

  1. In what sense, if any, is the universe fine-tuned? When can we say that physical parameters (cosmological constant, scale of electroweak symmetry breaking) or initial conditions are “unnatural”? What sets the appropriate measure with respect to which we judge naturalness of physical and cosmological parameters? Is there an explanation for cosmological coincidences such as the approximate equality between the density of matter and vacuum energy? Does inflation solve these problems, or exacerbate them? What conclusions should we draw from the existence of fine-tuning?
  2. How is the arrow of time related to the special state of the early universe? What is the best way to formulate the past hypothesis (the early universe was in a low entropy state) and the statistical postulate (uniform distribution within macrostates)? Can the early state be explained as a generic feature of dynamical processes, or is it associated with a specific quantum state of the universe, or should it be understood as a separate law of nature? In what way, if any, does the special early state help explain the temporal asymmetries of memory, causality, and quantum measurement?
  3. What is the proper role of the anthropic principle? Can anthropic reasoning be used to make reliable predictions? How do we define the appropriate reference class of observers? Given such a class, is there any reason to think of ourselves as “typical” within it? Does the prediction of freak observers (Boltzmann Brains) count as evidence against a cosmological scenario?
  4. What part should unobservable realms play in cosmological models? Does cosmic evolution naturally generate pocket universes, baby universes, or many branches of the wave function? Are other “universes” part of science if they can never be observed? How do we evaluate such models, and does the traditional process of scientific theory choice need to be adapted to account for non-falsifiable predictions? How confident can we ever be in early-universe scenarios such as inflation?
  5. What is the quantum state of the universe, and how does it evolve? Is there a unique prescription for calculating the wave function of the universe? Under what conditions are different parts of the quantum state “real,” in the sense that observers within them should be counted? What aspects of cosmology depend on competing formulations of quantum mechanics (Everett, dynamical collapse, hidden variables, etc.)? Do quantum fluctuations happen in equilibrium? What role does decoherence play in cosmic evolution? How does do quantum and classical probabilities arise in cosmological predictions? What defines classical histories within the quantum state?
  6. Are space and time emergent or fundamental? Is quantum gravity a theory of quantized spacetime, or is spacetime only an approximation valid in a certain regime? What are the fundamental degrees of freedom? Is there a well-defined Hilbert space for the universe, and what is its dimensionality? Is time evolution fundamental, or does time emerge from correlations within a static state?
  7. What is the role of infinity in cosmology? Can the universe be infinitely big? Are the fundamental laws ultimate discrete? Can there be an essential difference between “infinite” and “really big”? Can the arrow of time be explained if the universe has an infinite amount of room in which to evolve? Are there preferred ways to compare infinitely big subsets of an infinite space of states?
  8. Can the universe have a beginning, or can it be eternal? Does a universe with a first moment require a cause or deeper explanation? Are there reasons why there is something rather than nothing? Can the universe be cyclic, with a consistent arrow of time? Could it be eternal and statistically symmetric around some moment of lowest entropy?
  9. How do physical laws and causality apply to the universe as a whole? Can laws be said to change or evolve? Does the universe as a whole maximize some interesting quantity such as simplicity, goodness, interestingness, or fecundity? Should laws be understood as governing/generative entities, or are they just a convenient way to compactly represent a large number of facts? Is the universe complete in itself, or does it require external factors to sustain it? Do the laws of physics require ultimate explanations, or can they simply be?
  10. How do complex structures and order come into existence and evolve? Is complexity a transient phenomenon that depends on entropy generation? Are there general principles governing physical, biological, and psychological complexity? Is the appearance of life likely or inevitable? Does consciousness play a central role in accounting for the universe?

Chances are very small that anyone else interested in the field, forced at gunpoint to pick the ten biggest questions, would choose exactly these ten. Such are the wild and wooly early days of any field, when the frontier is unexplored and the conventional wisdom has yet to be settled. Feel free to make suggestions.

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Cosmological Attractors

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I want to tell you about a paper I recently wrote with grad student Grant Remmen, about how much inflation we should expect to have occurred in the early universe. But that paper leans heavily on an earlier one that Grant and I wrote, about phase space and cosmological attractor solutions — one that I never got around to blogging about. So you’re going to hear about that one first! It’s pretty awesome in its own right. (Sadly “cosmological attractors” has nothing at all to do with the hypothetical notion of attractive cosmologists.)

Attractor Solutions in Scalar-Field Cosmology
Grant N. Remmen, Sean M. Carroll

Models of cosmological scalar fields often feature “attractor solutions” to which the system evolves for a wide range of initial conditions. There is some tension between this well-known fact and another well-known fact: Liouville’s theorem forbids true attractor behavior in a Hamiltonian system. In universes with vanishing spatial curvature, the field variables (\phi, \dot\phi) specify the system completely, defining an effective phase space. We investigate whether one can define a unique conserved measure on this effective phase space, showing that it exists for m2φ2 potentials and deriving conditions for its existence in more general theories. We show that apparent attractors are places where this conserved measure diverges in the (\phi, \dot\phi) variables and suggest a physical understanding of attractor behavior that is compatible with Liouville’s theorem.

This paper investigates a well-known phenomenon in inflationary cosmology: the existence of purported “attractor” solutions. There is a bit of lore that says that an inflationary scalar field might start off doing all sorts of things, but will quickly settle down to a preferred kind of evolution, known as the attractor. But that lore is nominally at odds with a mathematical theorem: in classical mechanics, closed systems never have attractor solutions! That’s because “attractor” means “many initial conditions are driven to the same condition,” while Liouville’s theorem says “a set of initial conditions maintains its volume as it evolves.” So what’s going on?

Let’s consider the simplest kind of model: you just have a single scalar field φ, and a potential energy function V(φ), in the context of an expanding universe with no other forms of matter or energy. That fully specifies the model, but then you have to specify the actual trajectory that the field takes as it evolves. Any trajectory is fixed by giving certain initial data in the form of the value of the field φ and its “velocity” \dot\phi. For a very simple potential like V(φ) ~ φ2, the trajectories look like this:

attractors

This is the “effective phase space” of the model — in a spatially flat universe (and only there), specifying φ and its velocity uniquely determines a trajectory, shown as the lines on the plot. See the dark lines that start horizontally, then spiral toward the origin? Those are the attractor solutions. Other trajectories (dashed lines) basically zoom right to the attractor, then stick nearby for the rest of their evolution. Physically, the expansion of the universe acts as a kind of friction; away from the attractor the friction is too small to matter, but once you get there friction begins to dominate and the the field rolls very slowly. So the idea is that there aren’t really that many different kinds of possible evolution; a “generic” initial condition will just snap onto the attractor and go from there.

This story seems to be in blatant contradiction with Liouville’s Theorem, which roughly says that there cannot be true attractors, because volumes in phase space (the space of initial conditions, i.e. coordinates and momenta) remain constant under time-evolution. Whereas in the picture above, volumes get squeezed to zero because every trajectory flows to the 1-dimensional attractor, and then of course eventually converges to the origin. But we know that the above plot really does show what the trajectories do, and we also know that Liouville’s theorem is correct and does apply to this situation. Our goal for the paper was to show how everything actually fits together.

Obviously (when you think about it, and know a little bit about phase space), the problem is with the coordinates on the above graph. In particular, \dot\phi might be the “velocity” of the field, but it definitely isn’t its “momentum,” in the strict mathematical sense. The canonical momentum is actually a^3\dot\phi, where a is the scale factor that measures the size of the universe. And the scale factor changes with time, so there is no simple translation between the nice plot we saw above and the “true” phase space — which should, after all, also include the scale factor itself as well as its canonical momentum.

So there are good reasons of convenience to draw the plot above, but it doesn’t really correspond to phase space. As a result, it looks like there are attractors, although there really aren’t — at least not by the strict mathematical definition. It’s just a convenient, though possibly misleading, nomenclature used by cosmologists.

Still, there is something physically relevant about these cosmological attractors (which we will still call “attractors” even if they don’t match the technical definition). If it’s not “trajectories in phase space focus onto them,” what is it? To investigate this, Grant and I turned to a formalism for defining the measure on the space of trajectories (rather than just points in phase space), originally studied by Gibbons, Hawking, and Stewart and further investigated by Heywood Tam and me a couple of years ago.

The interesting thing about the “GHS measure” on the space of trajectories is that it diverges — becomes infinitely big — for cosmologies that are spatially flat. That is, almost all universes are spatially flat — if you were to pick a homogeneous and isotropic cosmology out of a hat, it would have zero spatial curvature with probability unity. (Which means that the flatness problem you were taught as a young cosmologist is just a sad misunderstanding — more about that later in another post.) That’s fine, but it makes it mathematically tricky to study those flat universes, since the measure is infinity there. Heywood and I proposed a way to regulate this infinity to get a finite answer, but that was a mistake on our part — upon further review, our regularization was not invariant under time-evolution, as it should have been.

That left an open problem — what is the correct measure on the space of flat universes? This is what Grant and I tackled, and basically solved. Long story short, we studied the necessary and sufficient conditions for there to be the right kind of measure on the effective phase space shown in the plot above, and argued that such a measure (1) exists, and (2) is apparently unique, at least in the simple case of a quadratic potential (and probably more generally). That is, we basically reverse-engineered the measure from the requirement that Liouville’s theorem be obeyed!

So there is such a measure, but it’s very different from the naïve “graph-paper measure” that one is tempted to use for the effective phase space plotted above. (A temptation to which almost everyone in the field gives in.) Unsurprisingly, the measure blows up on the attractor, and near the origin. That is, what looks like an attractor when you plot it in these coordinates is really a sign that the density of trajectories grows very large there — which is the least surprising thing in the world, really.

At the end of the day, despite the fact that we mildly scold fellow cosmologists for their sloppy use of the word “attractor,” the physical insights connected to this idea go through essentially unaltered. The field and its velocity are the variables that are most readily observable (or describable) by us, and in terms of these variables the apparent attractor behavior is definitely there. The real usefulness of our paper would come when we wanted to actually use the measure we constructed, for example to calculate the expected amount of inflation in a given model — which is what we did in our more recent paper, to be described later.

This paper, by the way, was one from which I took equations for the blackboards in an episode of Bones. It was fun to hear Richard Schiff, famous as Toby from The West Wing, play a physicist who explains his alibi by saying “I was constructing an invariant measure on the phase space of cosmological spacetimes.” 

richard-schiff-on-bones

The episode itself is great, you should watch it if you can. But I warn you — you will cry.

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Physicists Should Stop Saying Silly Things about Philosophy

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The last few years have seen a number of prominent scientists step up to microphones and belittle the value of philosophy. Stephen Hawking, Lawrence Krauss, and Neil deGrasse Tyson are well-known examples. To redress the balance a bit, philosopher of physics Wayne Myrvold has asked some physicists to explain why talking to philosophers has actually been useful to them. I was one of the respondents, and you can read my entry at the Rotman Institute blog. I was going to cross-post my response here, but instead let me try to say the same thing in different words.

Roughly speaking, physicists tend to have three different kinds of lazy critiques of philosophy: one that is totally dopey, one that is frustratingly annoying, and one that is deeply depressing.

  • “Philosophy tries to understand the universe by pure thought, without collecting experimental data.”

This is the totally dopey criticism. Yes, most philosophers do not actually go out and collect data (although there are exceptions). But it makes no sense to jump right from there to the accusation that philosophy completely ignores the empirical information we have collected about the world. When science (or common-sense observation) reveals something interesting and important about the world, philosophers obviously take it into account. (Aside: of course there are bad philosophers, who do all sorts of stupid things, just as there are bad practitioners of every field. Let’s concentrate on the good ones, of whom there are plenty.)

Philosophers do, indeed, tend to think a lot. This is not a bad thing. All of scientific practice involves some degree of “pure thought.” Philosophers are, by their nature, more interested in foundational questions where the latest wrinkle in the data is of less importance than it would be to a model-building phenomenologist. But at its best, the practice of philosophy of physics is continuous with the practice of physics itself. Many of the best philosophers of physics were trained as physicists, and eventually realized that the problems they cared most about weren’t valued in physics departments, so they switched to philosophy. But those problems — the basic nature of the ultimate architecture of reality at its deepest levels — are just physics problems, really. And some amount of rigorous thought is necessary to make any progress on them. Shutting up and calculating isn’t good enough.

  • “Philosophy is completely useless to the everyday job of a working physicist.”

Now we have the frustratingly annoying critique. Because: duh. If your criterion for “being interesting or important” comes down to “is useful to me in my work,” you’re going to be leading a fairly intellectually impoverished existence. Nobody denies that the vast majority of physics gets by perfectly well without any input from philosophy at all. (“We need to calculate this loop integral! Quick, get me a philosopher!”) But it also gets by without input from biology, and history, and literature. Philosophy is interesting because of its intrinsic interest, not because it’s a handmaiden to physics. I think that philosophers themselves sometimes get too defensive about this, trying to come up with reasons why philosophy is useful to physics. Who cares?

Nevertheless, there are some physics questions where philosophical input actually is useful. Foundational questions, such as the quantum measurement problem, the arrow of time, the nature of probability, and so on. Again, a huge majority of working physicists don’t ever worry about these problems. But some of us do! And frankly, if more physicists who wrote in these areas would make the effort to talk to philosophers, they would save themselves from making a lot of simple mistakes.

  • “Philosophers care too much about deep-sounding meta-questions, instead of sticking to what can be observed and calculated.”

Finally, the deeply depressing critique. Here we see the unfortunate consequence of a lifetime spent in an academic/educational system that is focused on taking ambitious dreams and crushing them into easily-quantified units of productive work. The idea is apparently that developing a new technique for calculating a certain wave function is an honorable enterprise worthy of support, while trying to understand what wave functions actually are and how they capture reality is a boring waste of time. I suspect that a substantial majority of physicists who use quantum mechanics in their everyday work are uninterested in or downright hostile to attempts to understand the quantum measurement problem.

This makes me sad. I don’t know about all those other folks, but personally I did not fall in love with science as a kid because I was swept up in the romance of finding slightly more efficient calculational techniques. Don’t get me wrong — finding more efficient calculational techniques is crucially important, and I cheerfully do it myself when I think I might have something to contribute. But it’s not the point — it’s a step along the way to the point.

The point, I take it, is to understand how nature works. Part of that is knowing how to do calculations, but another part is asking deep questions about what it all means. That’s what got me interested in science, anyway. And part of that task is understanding the foundational aspects of our physical picture of the world, digging deeply into issues that go well beyond merely being able to calculate things. It’s a shame that so many physicists don’t see how good philosophy of science can contribute to this quest. The universe is much bigger than we are and stranger than we tend to imagine, and I for one welcome all the help we can get in trying to figure it out.

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Squelching Boltzmann Brains (And Maybe Eternal Inflation)

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There’s no question that quantum fluctuations play a crucial role in modern cosmology, as the recent BICEP2 observations have reminded us. According to inflation, all of the structures we see in the universe, from galaxies up to superclusters and beyond, originated as tiny quantum fluctuations in the very early universe, as did the gravitational waves seen by BICEP2. But quantum fluctuations are a bit of a mixed blessing: in addition to providing an origin for density perturbations and gravitational waves (good!), they are also supposed to give rise to Boltzmann brains (bad) and eternal inflation (good or bad, depending on taste). Nobody would deny that it behooves cosmologists to understand quantum fluctuations as well as they can, especially since our theories involve mysterious aspects of physics operating at absurdly high energies.

Kim Boddy, Jason Pollack and I have been re-examining how quantum fluctuations work in cosmology, and in a new paper we’ve come to a surprising conclusion: cosmologists have been getting it wrong for decades now. In an expanding universe that has nothing in it but vacuum energy, there simply aren’t any quantum fluctuations at all. Our approach shows that the conventional understanding of inflationary perturbations gets the right answer, although the perturbations aren’t due to “fluctuations”; they’re due to an effective measurement of the quantum state of the inflaton field when the universe reheats at the end of inflation. In contrast, less empirically-grounded ideas such as Boltzmann brains and eternal inflation both rely crucially on treating fluctuations as true dynamical events, occurring in real time — and we say that’s just wrong.

All very dramatically at odds with the conventional wisdom, if we’re right. Which means, of course, that there’s always a chance we’re wrong (although we don’t think it’s a big chance). This paper is pretty conceptual, which a skeptic might take as a euphemism for “hand-waving”; we’re planning on digging into some of the mathematical details in future work, but for the time being our paper should be mostly understandable to anyone who knows undergraduate quantum mechanics. Here’s the abstract:

De Sitter Space Without Quantum Fluctuations
Kimberly K. Boddy, Sean M. Carroll, and Jason Pollack

We argue that, under certain plausible assumptions, de Sitter space settles into a quiescent vacuum in which there are no quantum fluctuations. Quantum fluctuations require time-dependent histories of out-of-equilibrium recording devices, which are absent in stationary states. For a massive scalar field in a fixed de Sitter background, the cosmic no-hair theorem implies that the state of the patch approaches the vacuum, where there are no fluctuations. We argue that an analogous conclusion holds whenever a patch of de Sitter is embedded in a larger theory with an infinite-dimensional Hilbert space, including semiclassical quantum gravity with false vacua or complementarity in theories with at least one Minkowski vacuum. This reasoning provides an escape from the Boltzmann brain problem in such theories. It also implies that vacuum states do not uptunnel to higher-energy vacua and that perturbations do not decohere while slow-roll inflation occurs, suggesting that eternal inflation is much less common than often supposed. On the other hand, if a de Sitter patch is a closed system with a finite-dimensional Hilbert space, there will be Poincaré recurrences and Boltzmann fluctuations into lower-entropy states. Our analysis does not alter the conventional understanding of the origin of density fluctuations from primordial inflation, since reheating naturally generates a high-entropy environment and leads to decoherence.

The basic idea is simple: what we call “quantum fluctuations” aren’t true, dynamical events that occur in isolated quantum systems. Rather, they are a poetic way of describing the fact that when we observe such systems, the outcomes are randomly distributed rather than deterministically predictable. …

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Guest Post: Max Tegmark on Cosmic Inflation

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Max TegmarkMost readers will doubtless be familiar with Max Tegmark, the MIT cosmologist who successfully balances down-and-dirty data analysis of large-scale structure and the microwave background with more speculative big-picture ideas about quantum mechanics and the nature of reality. Max has a new book out — Our Mathematical Universe: My Quest for the Ultimate Nature of Reality — in which he takes the reader on a journey from atoms and the solar system to a many-layered multiverse.

In the wake of the recent results indicating gravitational waves in the cosmic microwave background, here Max delves into the idea of inflation — what it really does, and what some of the implications are.

Thanks to the relentless efforts of the BICEP2 team during balmy -100F half-year-long nights at the South Pole, inflation has for the first time become not only something economists worry about, but also a theory for our cosmic origins that’s really hard to dismiss. As Sean has reported here on this blog, the implications are huge. Of course we need independent confirmation of the BICEP2 results before uncorking the champagne, but in the mean time, we’re forced to take quite seriously that everything in our observable universe was once smaller than a billionth the size of a proton, containing less mass than an apple, and doubled its size at least 80 times, once every hundredth of a trillionth of a trillionth of a trillionth of a second, until it was more massive than our entire observable universe.

We still don’t know what, if anything, came before inflation, but this is nonetheless a huge step forward in understanding our cosmic origins. Without inflation, we had to explain why there were over a million trillion trillion trillion trillion kilograms of stuff in existence, carefully arranged to be almost perfectly uniform while flying apart at huge speeds that were fine-tuned to 24 decimal places. The traditional answer in the textbooks was that we had no clue why things started out this way, and should simply assume it. Inflation puts the “bang” into our Big Bang by providing a physical mechanism for creating all those kilograms and even explains why they were expanding in such a special way. The amount of mass needed to get inflation started is less than that in an apple, so even though inflation doesn’t explain the origin of everything, there’s a lot less stuff left to explain the origin of.

If we take inflation seriously, then we need to stop saying that inflation happened shortly after our Big Bang, because it happened before it, creating it. It is inappropriate to define our Hot Big Bang as the beginning of time, because we don’t know whether time actually had a beginning, and because the early stages of inflation were neither strikingly hot nor big nor much of a bang. As that tiny speck of inflating substance doubled its diameter 80 times, the velocities with which its parts were flying away from one another increased by the same factor 2^80. Its volume increased by that factor cubed, i.e., 2^240, and so did its mass, since its density remained approximately constant. The temperature of any particles left over from before inflation soon dropped to near zero, with the only remaining heat coming from same Hawking/Unruh quantum fluctuations that generated the gravitational waves.

Taken together, this in my opinion means that the early stages of inflation are better thought of not as a Hot Big Bang but as a Cold Little Swoosh, because at that time our universe was not that hot (getting a thousand times hotter once inflation ended), not that big (less massive than an apple and less than a billionth of the size of a proton) and not much of a bang (with expansion velocities a trillion trillion times slower than after inflation). In other words, a Hot Big Bang did not precede and cause inflation. Instead, a Cold Little Swoosh preceded and caused our Hot Big Bang.

Since the BICEP2 breakthrough is generating such huge interest in inflation, I’ve decided to post my entire book chapter on inflation here so that you can get an up-to-date and self-contained account of what it’s all about. Here are some of the questions answered:

  • What does the theory of inflation really predict?
  • What physics does it assume?
  • Doesn’t creation of the matter around us from almost nothing violate energy conservation?
  • How could an infinite space get created in a finite time?
  • How is this linked to the BICEP2 signal?
  • What remarkable prize did Alan Guth win in 2005?

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Post-Debate Reflections

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We’ve returned from the lovely city of New Orleans, where within a short period of time I was able to sample shrimp and grits, bread pudding soufflé, turtle soup, chicken gumbo, soft-shelled crab with crawfish étouffée, and of course beignets. Oh yes, also participated in the Greer-Heard Forum, where I debated William Lane Craig, and then continued the discussion the next day along with Alex Rosenberg, Tim Maudlin, James Sinclair, and Robin Collins. The whole event was recorded, and will be released on the internet soon — hopefully within a couple of days.

[Update: Here is the video:]

"God & Cosmology" - 2014 Greer-Heard Forum

In the meantime I thought I’d provide some quick post-debate reflections. Overall I think it went pretty well, although I certainly could have done better. Then again I’m biased, both by being hard on myself in terms of the debate performance, but understandably of the opinion that my actual ideas are correct. I think I mostly reached my primary goal of explaining why many of us think theism is undermined by modern science, and in particular why there is no support to be found for it in modern cosmology. For other perspectives see Rational Skepticism or the Reasonable Faith forums.

Clockwise from top left: William Lane Craig, Alex Rosenberg, Sean Carroll, James Sinclair, Robert Stewart (Greer-Heard organizer), Tim Maudlin, and Robin Collins.
Clockwise from top left: William Lane Craig, Alex Rosenberg, Sean Carroll, James Sinclair, Robert Stewart (Greer-Heard organizer), Tim Maudlin, and Robin Collins. Screenshot by Maryanne Spikes.

Short version: I think it went well, although I can easily think of several ways I could have done better. On the substance, my major points were that the demand for “causes” and “explanations” is completely inappropriate for modern fundamental physics/cosmology, and that theism is not taken seriously in professional cosmological circles because it is hopelessly ill-defined (no matter what happens in the universe, you can argue that God would have wanted it that way). He defended two of his favorite arguments, the “cosmological argument” and the fine-tuning argument; no real surprises there. In terms of style, from my perspective things got a bit frustrating, because the following pattern repeated multiple times: Craig would make an argument, I would reply, and Craig would just repeat the original argument. For example, he said that Boltzmann Brains were a problem for the multiverse; I said that they were a problem for certain multiverse models but not others, which is actually good because they help us to distinguish viable from non-viable models; and his response was the multiverse was not a viable theory because of the Boltzmann Brain problem. Or, he said that if the universe began to exist there must be a transcendent cause; I said that everyday notions of causation don’t apply to the beginning of the universe and explained why they might apply approximately inside the universe but not to it; and his response was that if the universe could just pop into existence, why not bicycles? I was honestly a bit surprised at the lack of real-time interaction, since one of Craig’s supporters’ biggest complaints is that his opponents don’t ever directly respond to his points, and I tried hard to do exactly that. To be fair, I bypassed some of his arguments (see below) because I thought they were irrelevant, and wanted to focus on the important issues; he might feel differently. I’m sure that others will have their own opinions, but soon enough the videos will allow all to judge for themselves. Overall I was moderately satisfied that I made the responses I had hoped to make, clarified some points, and gave folks something to think about.

Longer version (much longer, sorry): the format was 20-minute opening talks by each speaker (Craig going first), followed by 12-minute rebuttals, and then 8-minute closing statements. Among the pre-debate advice I was given was “make it a discussion, not a debate” and “don’t let WLC speak first,” both of which I intentionally ignored. I wanted all along to play by his rules, in front of his crowd, and do the best job I could do without any excuses. …

Post-Debate ReflectionsRead More »

Post-Debate Reflections Read More »

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Greatest Hits

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Blogging is a real-time, often informal affair, and most posts aren’t meant to be interesting forever. But some might be. Here I’m collecting some of my most useful or interesting blogging over the years, originally at Blogspot and later at Discover magazine). In 2012 I went solo again, moving back here. For other kinds of writing see my CV, or writings.

Late-Universe Cosmology

Early-Universe Cosmology

Relativity

Quantum Mechanics

Particles/Fields/Strings

Other Science

Meta-Science

Philosophy

Religion

Academia

Politics

Other

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The Higgs Boson vs. Boltzmann Brains

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Kim Boddy and I have just written a new paper, with maybe my favorite title ever.

Can the Higgs Boson Save Us From the Menace of the Boltzmann Brains?
Kimberly K. Boddy, Sean M. Carroll
(Submitted on 21 Aug 2013)

The standard ΛCDM model provides an excellent fit to current cosmological observations but suffers from a potentially serious Boltzmann Brain problem. If the universe enters a de Sitter vacuum phase that is truly eternal, there will be a finite temperature in empty space and corresponding thermal fluctuations. Among these fluctuations will be intelligent observers, as well as configurations that reproduce any local region of the current universe to arbitrary precision. We discuss the possibility that the escape from this unacceptable situation may be found in known physics: vacuum instability induced by the Higgs field. Avoiding Boltzmann Brains in a measure-independent way requires a decay timescale of order the current age of the universe, which can be achieved if the top quark pole mass is approximately 178 GeV. Otherwise we must invoke new physics or a particular cosmological measure before we can consider ΛCDM to be an empirical success.

We apply some far-out-sounding ideas to very down-to-Earth physics. Among other things, we’re suggesting that the mass of the top quark might be heavier than most people think, and that our universe will decay in another ten billion years or so. Here’s a somewhat long-winded explanation.

A room full of monkeys, hitting keys randomly on a typewriter, will eventually bang out a perfect copy of Hamlet. Assuming, of course, that their typing is perfectly random, and that it keeps up for a long time. An extremely long time indeed, much longer than the current age of the universe. So this is an amusing thought experiment, not a viable proposal for creating new works of literature (or old ones).

There’s an interesting feature of what these thought-experiment monkeys end up producing. Let’s say you find a monkey who has just typed Act I of Hamlet with perfect fidelity. You might think “aha, here’s when it happens,” and expect Act II to come next. But by the conditions of the experiment, the next thing the monkey types should be perfectly random (by which we mean, chosen from a uniform distribution among all allowed typographical characters), and therefore independent of what has come before. The chances that you will actually get Act II next, just because you got Act I, are extraordinarily tiny. For every one time that your monkeys type Hamlet correctly, they will type it incorrectly an enormous number of times — small errors, large errors, all of the words but in random order, the entire text backwards, some scenes but not others, all of the lines but with different characters assigned to them, and so forth. Given that any one passage matches the original text, it is still overwhelmingly likely that the passages before and after are random nonsense.

That’s the Boltzmann Brain problem in a nutshell. Replace your typing monkeys with a box of atoms at some temperature, and let the atoms randomly bump into each other for an indefinite period of time. Almost all the time they will be in a disordered, high-entropy, equilibrium state. Eventually, just by chance, they will take the form of a smiley face, or Michelangelo’s David, or absolutely any configuration that is compatible with what’s inside the box. If you wait long enough, and your box is sufficiently large, you will get a person, a planet, a galaxy, the whole universe as we now know it. But given that some of the atoms fall into a familiar-looking arrangement, we still expect the rest of the atoms to be completely random. Just because you find a copy of the Mona Lisa, in other words, doesn’t mean that it was actually painted by Leonardo or anyone else; with overwhelming probability it simply coalesced gradually out of random motions. Just because you see what looks like a photograph, there’s no reason to believe it was preceded by an actual event that the photo purports to represent. If the random motions of the atoms create a person with firm memories of the past, all of those memories are overwhelmingly likely to be false.

This thought experiment was originally relevant because Boltzmann himself (and before him Lucretius, Hume, etc.) suggested that our world might be exactly this: a big box of gas, evolving for all eternity, out of which our current low-entropy state emerged as a random fluctuation. As was pointed out by Eddington, Feynman, and others, this idea doesn’t work, for the reasons just stated; given any one bit of universe that you might want to make (a person, a solar system, a galaxy, and exact duplicate of your current self), the rest of the world should still be in a maximum-entropy state, and it clearly is not. This is called the “Boltzmann Brain problem,” because one way of thinking about it is that the vast majority of intelligent observers in the universe should be disembodied brains that have randomly fluctuated out of the surrounding chaos, rather than evolving conventionally from a low-entropy past. That’s not really the point, though; the real problem is that such a fluctuation scenario is cognitively unstable — you can’t simultaneously believe it’s true, and have good reason for believing its true, because it predicts that all the “reasons” you think are so good have just randomly fluctuated into your head!

All of which would seemingly be little more than fodder for scholars of intellectual history, now that we know the universe is not an eternal box of gas. The observable universe, anyway, started a mere 13.8 billion years ago, in a very low-entropy Big Bang. That sounds like a long time, but the time required for random fluctuations to make anything interesting is enormously larger than that. (To make something highly ordered out of something with entropy S, you have to wait for a time of order eS. Since macroscopic objects have more than 1023 particles, S is at least that large. So we’re talking very long times indeed, so long that it doesn’t matter whether you’re measuring in microseconds or billions of years.) Besides, the universe is not a box of gas; it’s expanding and emptying out, right?

Ah, but things are a bit more complicated than that. We now know that the universe is not only expanding, but also accelerating. The simplest explanation for that — not the only one, of course — is that empty space is suffused with a fixed amount of vacuum energy, a.k.a. the cosmological constant. Vacuum energy doesn’t dilute away as the universe expands; there’s nothing in principle from stopping it from lasting forever. So even if the universe is finite in age now, there’s nothing to stop it from lasting indefinitely into the future.

But, you’re thinking, doesn’t the universe get emptier and emptier as it expands, leaving no particles to fluctuate? Only up to a point. A universe with vacuum energy accelerates forever, and as a result we are surrounded by a cosmological horizon — objects that are sufficiently far away can never get to us or even send signals, as the space in between expands too quickly. And, as Stephen Hawking and Gary Gibbons pointed out in the 1970’s, such a cosmology is similar to a black hole: there will be radiation associated with that horizon, with a constant temperature.

In other words, a universe with a cosmological constant is like a box of gas (the size of the horizon) which lasts forever with a fixed temperature. Which means there are random fluctuations. If we wait long enough, some region of the universe will fluctuate into absolutely any configuration of matter compatible with the local laws of physics. Atoms, viruses, people, dragons, what have you. The room you are in right now (or the atmosphere, if you’re outside) will be reconstructed, down to the slightest detail, an infinite number of times in the future. In the overwhelming majority of times that your local environment does get created, the rest of the universe will look like a high-entropy equilibrium state (in this case, empty space with a tiny temperature). All of those copies of you will think they have reliable memories of the past and an accurate picture of what the external world looks like — but they would be wrong. And you could be one of them.

That would be bad. …

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Erdős-Bacon

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This interview with Stephen Strogatz reminded me that I am frequently (well, maybe it happened once) asked what my Erdős-Bacon number is. The Erdős number, of course, is the number of degrees of separation between you and famous mathematician Paul Erdős, as judged by collaborations on research papers. Erdős has an Erdős number of zero; all of his collaborators (and there were many) have Erdős numbers of 1; their collaborators have Erdős numbers of 2, and so on. Bacon numbers work similarly, except that you’re looking at degrees of separation between you and Kevin Bacon, using appearances in movies or TV instead of papers.

Since you’re dying to know: my Erdős-Bacon number is six (at least using the relaxed standards typical in this game, according to which TV documentaries and appearances as “self” are counted). My Erdős number is four: I collaborated with Jim Bryan, who collaborated with Jason Fulman, who collaborated with Persi Diaconis, who collaborated with Paul Erdős. My Bacon number is two: I appeared in a NOVA special narrated by Jay Sanders, who appeared in Starting Over with Kevin Bacon. By the tricky mathematical operation known as “addition,” we end up with six.

That’s pretty typical for people who have finite EB numbers at all. Not as good as Strogatz himself, who has an EB number of four. And while I am tied with Stephen Hawking, I haven’t (as far as I know) appeared on any musical recordings, so I don’t have a finite Erdős-Bacon-Sabbath number. Always something left to shoot for.

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Firewalls, Burning Brightly

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The firewall puzzle is the claim that, if information is ultimately conserved as black holes evaporate via Hawking radiation, then an infalling observer sees a ferocious wall of high-energy radiation as they fall through the event horizon. This is contrary to everything we’ve ever believed about black holes based on classical and semi-classical reasoning, so if it’s true it’s kind of a big deal.

The argument in favor of firewalls is based on everyone’s favorite spooky physical phenomenon, quantum entanglement. Think of a Hawking photon near the event horizon of a very old (mostly-evaporated) black hole, about to sneak out to the outside world. If there is no firewall, the quantum state near the horizon is (pretty close to) the vacuum, which is unique. Therefore, the outgoing photon will be completely entangled with a partner ingoing photon — the negative-energy guy who is ultimately responsible for the black hole losing mass. However, if information is conserved, that outgoing photon must also be entangled with the radiation that left the hole much earlier. This is a problem because quantum entanglement is “monogamous” — one photon can’t be maximally entangled with two other photons at the same time. (Awww.) The simplest way out, so the story goes, is to break the entanglement between the ingoing and outgoing photons, which means the state is not close to the vacuum. Poof: firewall.

You folks read about this some time ago in a guest post by Joe Polchinski, one of the authors (with Ahmed Almheiri, Don Marolf, and James Sully, thus “AMPS”) of the original paper. I’m just updating now to let you know: almost a year later, the controversy has not gone away.

You can read about some of the current state of play in An Apologia for Firewalls, by the above authors plus Douglas Stanford. (Those of us with good Catholic educations understand that “apologia” means “defense,” not “apology.”) We also had a physics colloquium by Joe at Caltech last week, where he masterfully explained the basics of the black hole information paradox as well as the recent firewall brouhaha. Caltech is not very good at technology (don’t let the name fool you), so we don’t record our talks, but Joe did agree to put his slides up on the web, which you can now all enjoy. Aimed at physics students, so there might be an equation or two in there.

Just to point out a couple of intriguing ideas that have come along in response to the AMPS proposal, one paper that has deservedly received a lot of attention is An Infalling Observer in AdS/CFT by Kyriakos Papadodimas and Suvrat Raju. They consider the AdS/CFT correspondence, which relates a theory of gravity in anti-de Sitter space to a non-gravitational field theory on its boundary. One can model black holes in such a theory, and see what the boundary field theory has to say about them. Papadodimas and Raju argue that they don’t see any evidence of firewalls. It’s suggestive, but like many AdS/CFT constructions, comes across as a bit of a black box; even if there aren’t any firewalls, it’s hard to pinpoint exactly what part of the original AMPS argument is at fault.

More radically, there was just a new paper by Juan Maldacena and Lenny Susskind, Cool Horizons for Entangled Black Holes. These guys have tenure, so they aren’t afraid of putting forward some crazy-sounding ideas, which is what they’ve done here. (Note the enormous difference between “crazy-sounding” and “actually crazy.”) They are proposing that, when two particles are entangled, there is actually a tiny wormhole connecting them through spacetime. This seems bizarre from a classical general-relativity standpoint, since such wormholes would instantly collapse upon themselves; but they point out that their wormholes are “highly quantum objects.” They claim there is evidence that such a conjecture makes sense, although they can’t confidently argue that it gets rid of the firewalls.

I suspect further work is required. Good times.

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