Blogs / Cosmic Variance

One of the big hopes of particle- and astro-physicists over the next few years is to experimentally pin down the nature of dark matter. In a perfect world, we’ll make the dark matter particle at the LHC, observe gamma rays produced when dark matter annihilates in the galaxy, and detect it directly in experiments here on Earth. The world isn’t always perfect, but sometimes it’s even better, so everyone is sitting on the edges of their seats waiting to hear what the experiments tell us.

For the direct-detection strategy here on Earth, we build giant detectors and wait for ambient dark-matter particles to interact with something in the detector. If the dark matter is a weakly interacting massive particle (WIMP), that’s not so hard; the difficult part is distinguishing a purported signal from various backgrounds. To know what the signal should be, of course, we need to know how many dark matter particles are zipping through the laboratory. It should be a good number: roughly speaking, there would be about one weak-scale-sized dark matter particle per coffee-cup-volume in the universe, and in our galaxy these particles will typically be trucking along at around 300 kilometers per second.

Still, you’d like an accurate estimate of how much dark matter there is supposed to be in your detector. That’s what Riccardo Catena and Piero Ullio claim to have provided:

A novel determination of the local dark matter density
Authors: Riccardo Catena, Piero Ullio

Abstract: We present a novel study on the problem of constructing mass models for the Milky Way, concentrating on features regarding the dark matter halo component. We have considered a variegated sample of dynamical observables for the Galaxy, including several results which have appeared recently, and studied a 7- or 8-dimensional parameter space - defining the Galaxy model - by implementing a Bayesian approach to the parameter estimation based on a Markov Chain Monte Carlo method. The main result of this analysis is a novel determination of the local dark matter halo density which, assuming spherical symmetry and either an Einasto or an NFW density profile is found to be around 0.39 GeV cm$^{-3}$ with a 1-$\sigma$ error bar of about 7%; more precisely we find a $\rho_{DM}(R_0) = 0.385 \pm 0.027 \rm GeV cm^{-3}$ for the Einasto profile and $\rho_{DM}(R_0) = 0.389 \pm 0.025 \rm GeV cm^{-3}$ for the NFW. This is in contrast to the standard assumption that $\rho_{DM}(R_0)$ is about 0.3 GeV cm$^{-3}$ with an uncertainty of a factor of 2 to 3. A very precise determination of the local halo density is very important for interpreting direct dark matter detection experiments. Indeed the results we produced, together with the recent accurate determination of the local circular velocity, should be very useful to considerably narrow astrophysical uncertainties on direct dark matter detection.

So they’re claiming the density is about .39 GeV per cubic centimeter (where one GeV is about the mass of the proton), whereas the standard figure is something closer to .30 GeV per cubic centimeter. More importantly, they claim to trust their estimate to a precision of about 7%, while the usual number is supposed to be uncertain by a factor of 2 or 3.

I’m not expert enough to judge whether they are right, but it would certainly be very impressive to pin down the density to such high precision. They do assume spherical symmetry, however, which I suspect is not a very good assumption. There are ongoing arguments about how lumpy the distribution of galactic dark matter really is, and I can easily imagine that lumpiness can distort the local density by much more than 7%. But work like this is going to be very important in interpreting the results, if (when?) we do directly detect the dark matter.

One of the more fun physics stories that I’ve seen recently is from an area of research quite removed from my own, but that I have found fascinating for a while now. I have been fortunate to have excellent condensed matter colleagues at both my recent institutions, and quite a number of them are interested in soft condensed matter - classical physics that describes the behavior of large numbers of particles, far from equilibrium, often when entropic considerations dominate the dynamics.

The field covers such diverse systems as the behavior of biological membranes and the dynamics of grain in silos, and contains many examples in which nontrivial geometry and topology lead to the possibility of discovering new phenomena that, unlike in my own field, can increasingly often be checked in a laboratory experiment designed and built in a relatively short time.

The story that caught my eye (via Wired Science) recently concerns the behavior of a system that is so simple that you would think we know all that there is to be known about it - falling sand.

In the video above, a stream of sand is allowed to fall over several feet, and is filmed using a high speed video camera that falls at the same speed as the sand. The result, as you can see, is that the sand forms “droplets” just as water would, even though most people would not think of granular materials as anything like a liquid. The work was performed by Heinrich Jaeger’s group at the University of Chicago, and published in the current issue of Nature, which also deemed it worthy of a News and Views article and an Editor’s Summary (subscription required for all these things, unfortunately).

Interestingly, this system is still not fully understood - although it is clearly displaying liquid-like characteristics, the scales of the droplets and the forces involved are very different from the traditional regimes in which liquids are described - so there’s still work to be done. You can see many other examples of behavior like this on Jaeger’s granular materials page, with even more videos. The one I liked best is this granular jet one

Remember - that ball isn’t falling into a thick liquid - that’s sand!

There are apparently all kinds of applications of this kind of work. but I just think it’s beautiful all on its own.

As Sean mentioned yesterday, earlier this week the two of us recorded an episode of bloggingheads.tv, which appeared this morning and can be viewed below.

Although Sean is a veteran, it was my first time, and I wasn’t really sure what to expect, and as a result I was a little apprehensive about recording it. However, once we got going it was very enjoyable, and rather quickly it no longer felt so odd to be chatting over the phone while staring at myself on the monitor.

An hour sped by as we discussed the constituents of the universe, the mysteries surrounding baryonic matter, dark matter and cosmic acceleration, and just touched on the anthropic approach to the cosmological constant problem. We’re planning to do another one of these before too long, in which I think we’ll discuss inflation and more esoteric topics such as the early universe, the multiverse and (I strongly expect) the arrow of time.

Hope you enjoy it.

Update: Here’s a link to the bloggingheads.tv page, where a variety of download formats are available.

In the Fall I’ll be starting teaching again, after a semester away on sabbatical and then enjoying teaching relief during my first semester at Penn. I’ll be teaching a course that I truly love, and that I’ve taught a number of times before - Mathematical Methods of Physics I, to a class of beginning graduate students, and some interested seniors.

The backbone of this course, as I teach it, is rather traditional, since the topics involved are things that form the basis of the toolbox that professional physicists need. From year to year I have added various extra topics (some differential geometry, some topology, some group theory, …), but I always cover

• Analysis of Complex Functions
• Exact and Approximate Evaluation of Sums and Integrals
• Exact and Approximate Solution of Ordinary Differential Equations
• Transform Calculus
• Sturm-Liouville Theory
• The Calculus of Variations

One challenge in a course like this is to maintain the connection with actual applications of the techniques one is covering. Since I was originally taught this material in a set of courses as a mathematics undergraduate, my own take on the material can be rather formal, and I have worked over the years to balance this out. However, as you might guess, my own examples are predominantly drawn from those areas of physics with which I am most familiar - for example, supersymmetry, and the restrictions that holomorphy places on superpotentials, is a nice illustration of the power of complex analysis.

But this course is supposed to provide a basis for all graduate students, including those with interests in other branches of theoretical physics or, indeed, experimental physics or observational astrophysics and cosmology. There are, of course, rather general things that one can do that should be of use to everyone, such as the use of Fourier and Laplace transforms in solving heat, diffusion, and other equations. And the calculus of variations appears everywhere already. There are also, incidentally, lots of cute things one can do in the opposite direction, like cooking up examples of oscillating systems in which the sum over all modes gives the total energy, which is easy to calculate another way, and using this to provide a way to compute infinite sums. Nevertheless, what I really yearn for are even more examples illustrating the use of some of the above topics from other branches of physics.

I could, of course, annoy my colleagues with this question, but I thought that opening it up to Cosmic Variance readers might provide some novel suggestions. So, if you have some unusual example, brief enough to be useful in a class, of the use of any of the above in any branch of physics (even particle physics and cosmology - there’s plenty I don’t know there also), I’d appreciate you filling me in in the comments.

And if any of my students-to-be are reading this - beware; it’s possible that good suggestions you see here, that don’t make it into class, may turn up on exams - who knows?

After the FQXi Essay Contest, I was asked to comment on some of the essays besides my own, but I never did. Mostly because I didn’t take the time to read them all (there were an awful lot), but also because I just don’t know what to say about many of them. In her essay (which I liked), Fotini Markopoulou divides the world in two:

There are two kinds of people in quantum gravity. Those who think that timelessness is the most beautiful and deepest insight in general relativity, if not modern science, and those who simply cannot comprehend what timelessness can mean and see evidence for time in everything in nature. What sets this split of opinions apart form any other disagreement in science is that almost no one ever changes their mind…

That’s just about right (although perhaps there are also other splits with the same quality). Julian Barbour, whose essay finished first in the judging, has famously championed the view that time does not exist, even writing quite a successful book about it. In a recent Bloggingheads discussion with Craig Callender, Barbour talks a bit more about his view.

To which all I can muster is: I don’t get it. There are a set of technical arguments, which for the most part I do get, that can be used to make it seem as if time does not exist. In ordinary classical mechanics, we can perform some formal tricks to remove the time variable from the conventional equations of physics. More dramatically, in general relativity or quantum gravity we can express Einstein’s equation (at least in certain circumstances) in a form where time does not appear. On the other hand, we can usually re-write any of these equations in a form where time does appear (at least, again, in certain circumstances).

But none of these technical arguments are really the point. What I don’t understand — and this is a sincere lack of understanding on my part, not an indirect claim that this perspective is wrong — is what’s supposed to be so great about timelessness. What are we supposed to gain from thinking in this way? What problems is it supposed to solve?

Put it this way: clearly time appears to exist, at first glance. Even the timelessness crowd somehow manages to submit their essay competition entries by the deadline, and finish their Bloggingheads dialogues within an hour. So the claim “time does not exist” certainly doesn’t mean the same kind of thing as “unicorns do not exist.” It must mean (I suppose) that, while we all find time very useful in our everyday lives, there is a deeper level of description in which time doesn’t appear at all; it only emerges in some sort of approximate description of reality. But that approximate description seems extremely valid and useful, including all of the phenomena in the observable universe. Surely it behooves us to take this purportedly-non-fundamental notion seriously, and attempt to understand some of its puzzling features? Moreover, even if “time” doesn’t turn out to be fundamental, why would that tempt you into saying that it doesn’t exist? Protons are made of quarks, but you don’t hear particle physicists going around claiming that protons don’t exist.

The problem is not that I disagree with the timelessness crowd, it’s that I don’t see the point. I am not motivated to make the effort to carefully read what they are writing, because I am very unclear about what is to be gained by doing so. If anyone could spell out straightforwardly what I might be able to understand by thinking of the world in the language of timelessness, I’d be very happy to re-orient my attitude and take these works seriously.

Black holes are black because you can’t go faster than the speed of light. So what about the speed of sound?

Of course there is no problem in having something go faster than sound, but sound waves themselves are stuck with that speed limit. That fairly elementary fact inspired Bill Unruh years back to propose a clever idea: a black hole that you could make in the laboratory, but using sound rather than light. He called them dumb holes, although I’m not sure people get the right idea when they hear that name.

I used to think that this was an amusing thought experiment, but was believed to be unrealistic to actually attempt. But now Lahav et al. have apparently done it! (Via Swans on Tea and arXiv blog.)

A sonic black hole in a density-inverted Bose-Einstein condensate
Authors: O. Lahav, A. Itah, A. Blumkin, C. Gordon, J. Steinhauer

Abstract: We have created the analogue of a black hole in a Bose-Einstein condensate. In this sonic black hole, sound waves, rather than light waves, cannot escape the event horizon. The black hole is realized via a counterintuitive density inversion, in which an attractive potential repels the atoms. This allows for measured flow speeds which cross and exceed the speed of sound by an order of magnitude. The Landau critical velocity is therefore surpassed. The point where the flow speed equals the speed of sound is the event horizon. The effective gravity is determined from the profiles of the velocity and speed of sound.

The idea is simply that you get a fluid flowing faster than its speed of sound in some region, so that the sound waves cannot escape the “horizon” bounding that region. (The flow speed has to change within the material; taking a balloon full of air and putting it on a supersonic jet doesn’t count.)

But the reason this could some day be very exciting is when quantum mechanics gets into the game. Just like black holes, dumb holes should have “Hawking radiation” — but instead of particles, the holes should emit quantized sound waves (conventionally known as “phonons”). That would be very interesting to observe, although the experimental state of the art isn’t there yet.

To be clear, we wouldn’t be learning much about quantum gravity if we observed Hawking phonons from dumb holes. The underlying physics is still that of atoms (and, in this case, a Bose-Einstein condensate), not that of general relativity. Indeed, one of Unruh’s original motivations was to show that the physics on small scales didn’t affect the prediction of Hawking radiation. So the prediction of Hawking phonons should be rock-solid, no matter how little we know about quantum gravity. Still, it would be very cool.

Suppose you (and perhaps a competing team) had an incredibly exciting discovery that you wrote up and submitted to Nature.

Now suppose that you (and the competing team) simultaneously posted your (competing) papers to the ArXiv preprint server (which essentially all astronomers and physicists visit daily). But, suppose you then wrote in the comments “Submitted to Nature. Under press embargo”.

In other words, you wrote the equivalent of “Well, we’ve submitted this to Nature, but they won’t might not accept it or publish it if the news gets into the press, so can all of you reading this just not actually, you know, tell anyone? Oh, but can you make sure that you give us credit for the discovery, instead of the competing team? Thx!”

So, instead of blogging about the Incredibly Exciting Discovery (which I’d loooove to talk about), I’m writing about what a ridiculous fiction the authors are asking us all to participate in, for the sake of the authors’ potentially getting a publication accepted to Nature. The authors advertised a paper to thousands of interesting, engaged scientists, who are then supposed to keep their mouths shut so that the authors can get a paper into a particular journal — one that is not noticeably more influential in astrophysics (i.e. the difference between Nature and non-Nature is not nearly as big a deal as it is in biology).

Look folks, either come up with an agreement with the competing team to both shut your yaps until both your papers are simultaneously released from embargo, or suck it up and just submit the paper to the Astrophysical Journal or some other high prestige journal that doesn’t require Nature’s crazy embargo rules. Your result is terrific, you should be rightly proud, and Nature should be honored to publish your work. But, if a publication in Nature is really the goal you’re after, asking all the rest of us to be complicit is a bit silly.

Plus, I’m wiling to bet that Dennis Overbye skims astro-ph…

Update: Lots of good discussion and insight in the comments, so worth clicking through.

Via Dmitry Podolsky, a series of YouTube videos from Stanford encompassing an entire course by Lenny Susskind on general relativity. I didn’t look closely enough to figure out exactly what level the lectures are pitched at, but it looks like a fairly standard advanced-undergrad or beginning-grad introduction to the subject. (For which I could recommend an excellent textbook, if you’re interested.) This is the first lecture; there are more.

It’s fantastic that Stanford is giving this away. I don’t worry that it will replace the conventional university. The right distinction is not “people who would physically go to the lectures” vs. “people who will just watch the videos”; it’s between “people who can watch the videos” and “people who have no access to lectures like this.” And Susskind is a great lecturer.

While surfing through the Guardian’s collection of the 20 best Hubble images, among many that I’ve seen and used before I came across this remarkable one that was completely new to me

Besides being quite stunning (and reminding me of one of the Star-Trek movies), I was struck by the caption, which reminded me that

A delicate ribbon of gas, the remnant of a supernova explosion more than 1,000 years ago. On or around 1 May AD 1006, observers from Africa to Europe and the Far East witnessed the arrival of light from what is now called SN 1006, the final death throes of a white dwarf star nearly 7,000 light-years away. The supernova was probably the brightest star ever seen by humans, surpassing Venus as the brightest object in the night time sky after the Moon. It was visible even during the day for weeks, and remained visible to the naked eye for at least two and a half years

It is wonderful that we have the partial accounts of astrophysical events from so long ago, but at best they constitute mostly qualitative descriptions that allow us to place some bounds on certain processes and hypothesize about what the event must have looked like back then. However, it did make me wonder what astronomy and astrophysics might be like a comparable or greater time in the future. Future astronomers will have at their disposal huge and detailed datasets, containing images and precision astrometry stretching over thousands of years. If we had had such technology when SN 1006 was first seen, we would have a complete record of its explosion, expansion, and cooling. In fact we’d have such records for a huge number of astrophysical events.

In the far future we might even hope for the same in cosmology - for example a completely new microwave sky to help us beat down cosmic variance. Of course that’s assuming we survive the death of the sun, asteroids, global warming and, of course, zombies. And if we’re that lucky, we’d better make the most of it. Because if cosmic acceleration is here to stay, distant objects will gradually move outside of our horizon, and our detailed astrophysics and cosmology observations, and images like the one above, will be all we’ll have to remind us of the rich and beautiful universe that used to surround us.

I spent most of last week back in Cleveland, at Case Western Reserve University, where I spent three delightful years working with Tanmay Vachaspati, Glenn Starkmann, and Lawrence Krauss (who recently left). The occasion was a workshop on Tests of Gravity and Gravitational Physics, organized by the Center for Education and Research in Cosmology and Astrophysics (CERCA).

An interesting mix of theoretical cosmologists, relativists, particle physicists, observers and experimentalists participated, and the aim was to pull and tug at the loose threads in various ideas of modifying gravity, while talking about how we might perform sensible tests of the theory in new regimes in the near future. Most of the program consisted of talks, both theoretical and experimental, which you can download from the main site. The theory talks ranged from Nima Arkani-Hamed’s talk on why general relativity (GR) is so remarkably robust, with the take-home message “Don’t modify gravity - understand it”, to Bill Unruh’s description of his “dumb Hole” analog models for black holes, and the discussion of the associated analogous phenomenon to Hawking radiation. On the experimental side, there were great talks covering tabletop tests of sub-millimeter gravity - like the one by Blayne Heckel - all the way up to tests of gravity on the scale of galaxies and above - like Stacy McGaugh’s talk on tests of MOND.

As well as taking part in the general discussions and chairing a session, my role in all this was to sit on a panel for a discussion of “Modified Gravity: What does it buy? and at What Price?”

Nima moderated the discussion, and the other panel members were Eanna Flanagan, Nemanja Kaloper, Glenn Starkman and Bob Wald. While everyone had their own particular take on this, a common theme was that the theoretical and observational constraints are such that we currently do not have any modifications to GR that are compelling, despite our attempts to find a way to address the cosmological constant problem, explain cosmic acceleration, and search for alternatives to the dark matter paradigm. This doesn’t mean it isn’t worth trying, of course, although Nima made a spirited argument that it is hard to maintain the important holographic (and hence nonlocal) features of general relativity in any modified theory that isn’t of the simple scalar-tensor type, and that this is an argument that we shouldn’t expect nontrivial modifications. Rather, he argued, we should search for a dual S-matrix description that applies in flat space (unlike AdS/CFT) and that may allow us a better understanding of, for example, the cosmological constant problem.

This was all heavy stuff, but it didn’t consume our entire time in Cleveland. Tuesday evening saw the workshop dinner and it turned out that our hosts had arranged some after dinner entertainment, in the form of an improvisational comedy team. These guys were big on audience participation, and I was one of the first people chosen to mildly (I hope) embarrass themselves. At first this seemed like a heavy price to pay for dinner. However, trust me, subsequently seeing Tanmay Vachaspati, Bill Unruh and George Pickett up there made me realize it was well worth every blush and squirm.

Update: Dmitry Podolsky has a couple of very nice posts over at NEQNET with quite a few details about the talks, including Nima’s.