Blogs / Cosmic Variance

Over the last couple of months I’ve been working on a new project with an undergraduate student and a postdoc. I’m not really ready to talk about the details yet, but one thing that became clear during our work was that we would understand the results of our numerical solutions much better if we had a movie of them. This is pretty standard these days and (particularly when you have a smart, motivated and fast student) one can obtain quite sophisticated animated solutions that allow one to develop a feeling for rather unintuitive results.

Having said this, I must confess that my own research isn’t one of the areas of science that typically lends itself to spectacular and artistic visualization. And I’m always therefore a little jealous of those people whose results allow dramatic representations.

A number of these are being featured in Wired’s Best Science Visualization Videos of 2009. These are drawn from across all of science and what they all have in common, aside from their usefulness in their respective fields, is their great beauty.

The closest one of these to my own area is the quite stunning movie of the simulation of a type Ia supernova explosion, credited to Brad Gallagher, George Jordan, Dean Townsley, Robert Fisher, Nathan Hearn, Jim Truan and Don Lamb.

A good theoretical description of these objects is certainly fascinating astrophysics in its own right. However, as we’ve discussed many times on this blog, it is also an important step in understanding how, and the extent to which, type Ia supernovae can serve as standardizable candles, with which we may track the expansion history of the universe. The current understanding of this has been enough to discover the fact that the universe is accelerating, but our future plans are to exploit it further, to help provide insight into the origin of cosmic acceleration. A detailed understanding of how supernova explosions occur would be a valuable contribution to this quest.

And they’re just lovely to watch.

We’re all waiting for the LHC to restart. Current plans call for collisions later this year, but at lower energies than originally hoped.

Why is it so hard to say for sure? Here’s a nice article in the CERN Bulletin that lays out some of the difficulties.

Due to the huge amount of inter-dependency between different areas of work in the LHC, even a small change can necessitate a complete overhaul of the schedule. For example, something as simple as cleaning a water cooling tower – required regularly by Swiss law to prevent Legionella – has a huge impact on the planning: “When you clean the water tanks it means we don’t have water-cooling for the compressors, that means we can’t run the cryogenics, so the temperature starts to go up,” explains Myers. “If a sector gets above 100 K, then the expansion effects of heating can cause problems, and we could have to replace parts.”

That may be cold comfort (get it? cold comfort!), but it’s the real world. I have no strong opinions about the job CERN is doing, except to recognize that this is the most complicated machine ever built, so patience is probably called for. The particles and interactions are going to be the same next year as they were last year. (Or if they’re not, that would be even more interesting.)

A paper just appeared in Physical Review Letters with a provocative title: “A Quantum Solution to the Arrow-of-Time Dilemma,” by Lorenzo Maccone. Actually just “Quantum…”, not “A Quantum…”, because among the various idiosyncrasies of PRL is that paper titles do not begin with articles. Don’t ask me why.

But a solution to the arrow-of-time dilemma would certainly be nice, quantum or otherwise, so the paper has received a bit of attention (Focus, Ars Technica). Unfortunately, I don’t think this paper qualifies.

The arrow-of-time dilemma, you will recall, arises from the tension between the apparent reversibility of the fundamental laws of physics (putting aside collapse of the wave function for the moment) and the obvious irreversibility of the macroscopic world. The latter is manifested by the growth of entropy with time, as codified in the Second Law of Thermodynamics. So a solution to this dilemma would be an explanation of how reversible laws on small scales can give rise to irreversible behavior on large scales.

The answer isn’t actually that mysterious, it’s just unsatisfying. Namely, the early universe was in a state of extremely low entropy. If you accept that, everything else follows from the nineteenth-century work of Boltzmann and others. The problem then is, why should the universe be like that? Why should the state of the universe be so different at one end of time than at the other? Why isn’t the universe just in a high-entropy state almost all the time, as we would expect if its state were chosen randomly? Some of us have ideas, but the problem is certainly unsolved.

So you might like to do better, and that’s what Maccone tries to do in this paper. He forgets about cosmology, and tries to explain the arrow of time using nothing more than ordinary quantum mechanics, plus some ideas from information theory.

I don’t think that there’s anything wrong with the actual technical results in the paper — at a cursory glance, it looks fine to me. What I don’t agree with is the claim that it explains the arrow of time. Let’s just quote the abstract in full:

The arrow of time dilemma: the laws of physics are invariant for time inversion, whereas the familiar phenomena we see everyday are not (i.e. entropy increases). I show that, within a quantum mechanical framework, all phenomena which leave a trail of information behind (and hence can be studied by physics) are those where entropy necessarily increases or remains constant. All phenomena where the entropy decreases must not leave any information of their having happened. This situation is completely indistinguishable from their not having happened at all. In the light of this observation, the second law of thermodynamics is reduced to a mere tautology: physics cannot study those processes where entropy has decreased, even if they were commonplace.

So the claim is that entropy necessarily increases in “all phenomena which leave a trail of information behind” — i.e., any time something happens for which we can possibly have a memory of it happening. So if entropy decreases, we can have no recollection that it happened; therefore we always find that entropy seems to be increasing. Q.E.D.

But that doesn’t really address the problem. The fact that we “remember” the direction of time in which entropy is lower, if any such direction exists, is pretty well-established among people who think about these things, going all the way back to Boltzmann. (Chapter Nine.) But in the real world, we don’t simply see entropy increasing; we see it increase by a lot. The early universe has an entropy of 10⁸⁸ or less; the current universe has an entropy of 10¹⁰¹ or more, for an increase of more than a factor of 10¹³ — a giant number. And it increases in a consistent way throughout our observable universe. It’s not just that we have an arrow of time — it’s that we have an arrow of time that stretches coherently over an enormous region of space and time.

This paper has nothing to say about that. If you don’t have some explanation for why the early universe had a low entropy, you would expect it to have a high entropy. Then you would expect to see small fluctuations around that high-entropy state. And, indeed, if any complex observers were to arise in the course of one of those fluctuations, they would “remember” the direction of time with lower entropy. The problem is that small fluctuations are much more likely than large ones, so you predict with overwhelming confidence that those observers should find themselves in the smallest fluctuations possible, freak observers surrounded by an otherwise high-entropy state. They would be, to coin a pithy phrase, Boltzmann brains. Back to square one.

Again, everything about Maccone’s paper seems right to me, except for the grand claims about the arrow of time. It looks like a perfectly reasonable and interesting result in quantum information theory. But if you assume a low-entropy initial condition for the universe, you don’t really need any such fancy results — everything follows the path set out by Boltzmann years ago. And if you don’t assume that, you don’t really explain our universe. So the dilemma lives on.

I’ve posted before about Galaxy Zoo, and see also Phil Plait’s posts introducting the zoo, oncounterintuitive results and what do to if you find something weird.

They had a pretty cool collective result recently, discovering tiny galaxies that are rapidly forming stars, that they call “green pea galaxies” (which is apparently a different sort of beast from the non-galaxy I called a green crayon in my initial post) — see here for more or here for the paper itself.

Anyways, Galaxy Zoo has just announced a new project, the supernova zoo.

This time, not only are we classifying galaxies, but we’re hunting supernovae : exploding stars. Images of likely supernova candidates captured by a telescope in California are being fed to our website at http://supernovae.galaxyzoo.org”. Astronomers are standing by in the Canary Islands to follow up on the most exciting possibilities, but
first we need your help to decide where to point the telescope. Please take the time to go to the site, read the tutorial – and then start hunting.

I have to say I love the image of “astronomers standing by”. I tried it (classifying supernovae, not standing by) — it’s pretty cool, and actually a bit challenging. What you actually do is answer a series of questions about a supernova candidate, to determine whether it’s a good candidate or just a messed up image.

Here’s an obvious good one:

And one where the candidate (right image) is distorted so it doesn’t look like a star.

To my mind it’s not nearly as interesting as the galaxy zoo, because images of galaxies are just way cooler than low-resolution images of supernovae (supernovae remants are another story of course). But it’s a great use of human eyes, and a pretty good way to waste a few lazy August afternoons. It will definitely be interesting to see if the data is useful enough to help the supernovae followup substantially.

Have at it! Maybe they’ll name the next supernovae “SN2009cosmicvariancereaders”.

As I advertised, the bloggingheads.tv discussion that Sean and I recorded on Wednesday is now posted

following on from on our first effort, and covering different, and somewhat more controversial topics.

Hope you enjoy it.

On Wednesday Sean and I recorded another episode of bloggingheads.tv. In our last outing we discussed the standard cosmology, dark matter, cosmic acceleration, and a number of other issues concerning the observed matter-energy content of today’s universe. This time, we thought we’d go all early universe on you and discuss the problems of the standard cosmology, inflation, its shortcomings, and ultimately the initial conditions of the universe. Some of these topics, such as inflation, have a rather tight connection to current observations, while others are more speculative and some are touching on the philosophical, at least at this stage in our understanding.

We’ll post a link to the new episode when it comes out tomorrow. At one stage Sean and I discuss the initial conditions for inflation, and in doing so we were led into the issues of eternal inflation, entropy and the arrow of time (I guess he’s written some sort of extended blog post about it). Leading up to this, however, I brought up the question of what it means to require a sufficiently large, smooth, potential energy dominated patch of the universe in order for inflation to begin. I referred to a paper I wrote many years ago with Tanmay Vachaspati and I thought that it might be useful to describe that work here. I’ve done this before, over at Orange Quark, but it can’t hurt to have a version here also. This will be a little more technical than usual, but far less technical than the actual paper (hopefully).

As I first learned about inflation, the idea can be summarized as the following: the universe is born and one can say very little about it since quantum gravity (whatever that is) is undoubtedly important at extremely early times. However, after some time (approximately the Planck time), the semi-classical universe emerges, and we can begin to analyze meaningfully such things as the dynamics of field theories, and the response of gravity to them. There is no a priori reason for the universe to be homogeneous at this epoch. However, local, causal particle dynamics can act to homogenize patches of the universe. After some time, a small patch becomes homogeneous and dominated by the vacuum energy of a scalar field. This patch then undergoes inflation – a quasi-exponential period of expansion in which the original small patch expands to a size many orders of magnitude larger than the observable universe today. This expansion explains the flatness of the universe, and its homogeneity on large scales today.

Now, there are a number of models of inflation in which the above story is modified (in particular, chaotic inflation), and I’ll get back to them later. For now let me focus on this claim of homogeneity in the theories I described above.

Why does inflation, as described, “solve” the homogeneity (or horizon) problem? Clearly, the idea is that the homogeneity of the initial pre-inflationary patch, explained by causal physics, is translated into the homogeneity of the larger space after the exponential expansion. At the risk of being pedantic, this can only be true if the original patch is made homogeneous by causal processes, otherwise homogeneity would once again be an assumption, albeit a less severe one.

What did we do in our paper? We first imagined that the early universe, emerging from the Planck epoch, was not inflating. To make progress we’ll need a few definitions, which I’ll define below in a more blog-friendly way than in the paper.

Let’s focus on spherically symmetric space-times and pick an origin. Then examine spherical surfaces centered on this origin. Such surfaces can be divided into three categories in the following way. Imagine sitting on such a surface with two flashlights, both pointing radially and close together. The flashlights can both be pointing outwards (away from the origin), or both pointing inwards (towards the origin). The categories are then:

1. NORMAL: When the flashlights point inwards, the rays converge to the origin. When they point outwards, the rays diverge away from the origin. This is how regular parts of space-time behave; for example, points in our universe closer to us than the horizon.
2. TRAPPED: When the flashlights point inwards, the rays converge to the origin. When they point outwards, the rays still converge to the origin. Such surfaces can be found inside the horizon of a black hole.
3. ANTI-TRAPPED: When the flashlights point inwards, the rays nevertheless diverge away from the origin. When they point outwards, the rays diverge away from the origin. Such surfaces can be found, for example, beyond the horizon in our universe.

Now, back to what our paper showed. If the universe is not born inflating, then we want to imagine that, at some later time, local, causal particle dynamics yield a patch that is homogeneous and vacuum-dominated, and thus begins to inflate. The fundamental question for us was; how small can this patch be?

The main tool we used is called the Raychaudhuri equation. It describes the rate of change of divergence of close by pairs of light rays, as I described above. The equation is a little complicated but, by considering the types of light rays I mentioned above (perpendicular to spherical surfaces), and by making two further assumptions: that the Einstein equations are satisfied, and that the weak energy condition holds (matter isn’t too weird), the most important consequence of the Raychaudhuri equation can be stated as: Light rays pointing inwards cannot emanate from a normal surface and cross an anti-trapped one.

What does this mean? Well, if the original inflating patch is smaller than the Hubble size of the background space-time, then, it can be shown that light rays violating the above statement must exist. Thus, we conclude that the size of the initial inflating patch is at least as large as the Hubble size of the background space-time. But this size is large compared to typical particle physics processes that can act to homogenize a region (actually, if the background space-time is radiation-dominated FRW, the Hubble size IS the causal horizon). Thus, in this simple context it is hard to see how such an initially homogeneous inflating patch might form. This was our main result.

However, one of the things Sean and I discussed on blogginheads.tv was eternal inflation – the idea, supported by careful calculations in some models, that it is possible that inflation, if it begins in one patch of the universe, gives rise to an infinite expanding space, which produces an infinite number of regions of the universe that look like ours. This provides a very different was to think about the probability for inflation beginning, and seems to provide a possible way around the problem we pointed out. Furthermore, it may provide a way to seek answers to some of the other big questions of the earliest times in the universe – many of which depend on a full understanding of the issue of initial conditions.

I’m sure you’ll be able to find a relevant book if you’re interested in learning more.

A question that we have all been asking has been answered today: What will be the LHC run energy?  A press release has just been issued from CERN Director General, Rolf Heuer, following the completion of tests on the LHC magnets and splices.  Here are the excepts which just beeped into my inbox:

The LHC will run for the first part of the 2009-2010 run at 3.5 TeV per beam, with the energy rising later in the run. That’s the conclusion that we’ve just arrived at in a meeting involving the experiments, the machine people and the CERN management. We’ve selected 3.5 TeV because it allows the LHC operators to gain experience of running the machine safely while opening up a new discovery region for the experiments.

The developments that have allowed us to get to this point are good progress in repairing the damage in sector 3-4 and the related consolidation work, and the conclusion of testing on the 10000 high-current electrical connections last week. With that milestone, every one of the connections has been tested and we now know exactly where we stand.

The procedure for the 2009 start-up will be to inject and capture beams in each direction, take collision data for a few shifts at the injection energy, and then commission the ramp to higher energy. The first high-energy data should be collected a few weeks after the first beam of 2009 is injected. The LHC will run at 3.5 TeV per beam until a significant data sample has been collected and the operations team has gained experience in running the machine. Thereafter, with the benefit of that experience, we’ll take the energy up towards 5 TeV per beam. At the end of 2010, we’ll run the LHC with lead-ions for the first time. After that, the LHC will shut down and we’ll get to work on moving the machine towards 7 TeV per beam.

This is welcome news.  Starting at injection energy (450 GeV/beam) for a few shifts is safe and smart.  Experimenters will be guaranteed to record some data which will be used to calibrate the detectors.  Detectors must be properly aligned and calibrated before we can have discoveries!  Then they will ramp up and run awhile at 3.5 TeV/beam, giving the LHC its long-awaited status of being the highest energy accelerator in the world.  A short run at this energy does not have much discovery room given the strong constraints on new physics from the Tevatron, but will mainly serve to further calibrate the detectors and build up experience running the machine.  Finally, a slow ramp up to 5 TeV/beam seems like a safe option for the machine, and allows for the possibility of discovery by the end of 2010!

The purpose of the LIGO experiment is to search for gravitational waves in the universe. They haven’t found any yet, but no good big-science experiment would be complete without a few cool spinoffs. They LIGO folks have an especially cool one: they’ve put a kilogram-sized pendulum and “cooled” it so effectively that it’s almost in its quantum-mechanical ground state. To be honest, I’m not exactly sure what this is good for, but it’s really cool. Ha ha, little physics humor there, get it? “Cool.”

LIGO works by bouncing lasers down a pair of evacuated tubes four kilometers in length. The laser beams bounce off a mirror suspended from a pendulum, and then recombine back at the source, where you look for tiny changes in the phase of the light wave. If a gravitational wave passes by, it will gently disturb the pendulums, and the length the laser has to travel down one or the other tube will be slightly changed, leading to a detectable shift in the phase. But obviously they’re looking for an extremely tiny shift, so it’s important that those mirrors not be jiggling around just due to random noise. Thus, they need to be kept cool; a warm mirror will be jiggling just from its thermal motion, even before we start worrying about noisy trucks passing by the observatory.

Physicists are pretty good at getting things to be cold; they can cool down collections of atoms to under a billionth of a Kelvin (room temperature is about 300 Kelvin). But there we’re talking about relatively small collections of atoms, maybe a million at a time. Here we’re talking about a kilogram, which is a honking big number of atoms, something like 10²⁵. And the LIGO folks have cooled the oscillator down to about a millionth of a Kelvin, which is pretty cold.

The secret is that they don’t cool the entire mirror down to that low temperature. That would mean taking all of those 10²⁵ atoms and putting them close to their quantum-mechanical ground state. But instead of thinking of the mirror as a collection of individual atoms, you can think of it as a single “center of mass,” plus a bunch of individual displacements from that center for each of the atoms. Then forget about the individual atoms, and just worry about that center of mass. That’s what we do all the time in the real world; when you tell someone where you are, you give them a single position — you don’t individually specify the location of every atom in your body.

We can think of the center of mass as an isolated “degree of freedom,” and talk about its quantum state apart from that of all the other atoms. Ordinarily, if a big collection of atoms is in thermal equilibrium, each of its degrees of freedom is “excited” above its ground state by a similar amount. Every physicist learns about the simple harmonic oscillator, which is one of the most basic physical systems we can study — it’s just a pendulum. In quantum mechanics, the nice thing about such an oscillator is that it has discrete energy levels, equally spaced, that depend only on the frequency of the pendulum. There is a ground state with just a tiny bit of energy (the “zero-point energy”), then a bunch of higher energy levels, from the first excited state all the way up to infinity. The energy of the Nth excited state is just (N+1/2) times Planck’s constant, times the frequency of the oscillator.

What the LIGO folks have done is to isolate that single degree of freedom, the center of mass of the oscillator, and gently coax it into a very low quantum state: N is about 200, whereas at room temperature N would be about 40 billion. An amazing feat, for a collection of that many atoms.

So what can you do with it? Don’t ask me. But the LIGO scientists know they have something interesting on their hands, and are thinking of ways they can take advantage of this approach to the quantum realm. It’s different, but complementary, to the strategy of putting entire macroscopic objects in a coherent quantum state. (Notice that the linked article is still talking about 10¹⁰ atoms, not 10²⁵ atoms.) The LIGO mirror as a whole is still resolutely classical, even if the center-of-mass degree of freedom is near its quantum ground state. But taking big things and pushing them toward the quantum realm is a growth industry these days, and I’m sure we’ll be hearing more about clever applications of the process.

We’ve gotten a little bent out of shape over gravitational lensing recently (see here and here). But the fun doesn’t stop: gravitational lensing has now officially come into the 21st Century with the release of Eli Rykoff’s GravLens. (Not to be confused with GRAVLENS, Chuck Keeton’s immensely useful and powerful gravitational lensing modeling software). You can now lens a star, a galaxy, or an image of whatever or whomever you want (e.g., your favorite blogger), right in the comfort and safety of your own palm. GravLens is freely available at the iPhone application store. Go download it, and make yourself a beautiful Einstein Ring. This is your chance to support the fledgling “Physics applications for the iPhone” industry!

Children of light and children of darkness is the vision of physics that emerges from this chapter, as from other branches of physics. The children of light are the differential equations that predict the future from the present. The children of darkness are the factors that fix these initial conditions.

– Misner, Thorne, and Wheeler, Gravitation (1973), p. 555.