Sean Carroll

Category: Science

  • How many dimensions are there?

    When the fall quarter started, there were six papers that I absolutely had to finish by the end of the term. Three have been completed, two are very close, and the last one — sadly, I think the deadline has irrevocably passed, and it’s not going to make it. So here’s the upshot.

    About a year ago I gave a talk at the Philosophy of Science Association annual meeting in Austin. The topic of the session was “The Dimensions of Space,” and my talk was on “Why Three Spatial Dimensions Just Aren’t Enough” (pdf slides). I gave an overview of the idea of extra dimensions, how they arose historically and the role they currently play in string theory.

    But in retrospect, I didn’t do a very good job with one of the most basic questions: how many dimensions does spacetime really have, according to string theory? The answer used to be easy: ten, with six of them curled up into a tiny manifold that we couldn’t see. But in the 1990’s we saw the “Second Superstring Revolution,” featuring ideas about D-branes, duality, and the unification of what used to be thought of as five distinct versions of string theory.

    One of the most important ideas in the second revolution came from Ed Witten. Ordinarily, we like to examine field theories and string theories at weak coupling, where perturbation theory works well (QED, for example, is well-described by perturbation theory because the fine-structure constant α = 1/137 is a small number). Witten figured out that when you take the strong-coupling limit of certain ten-dimensional string theories, new degrees of freedom begin to show up (or more accurately, begin to become light, in the sense of having a low mass). Some of these degrees of freedom form a series of states with increasing masses. This is precisely what happens when you have an extra dimension: modes of ordinary fields that wrap around the extra dimension will have a tower of increasing masses, known as Kaluza-Klein modes.

    In other words: the strong-coupling limit of certain ten-dimensional string theories is an eleven-dimensional theory! In fact, at low energies, it’s eleven-dimensional supergravity, which had been studied for years, but whose connection to string theory had been kind of murky. Now we know that 11-d supergravity and the five ten-dimensional string theories are just six different low-energy weakly-coupled limits of some single big theory, which we call M-theory even though we don’t know what it really is. (Even though the 11-d theory can arise as the strong-coupling limit of a 10-d string theory, it is itself weakly coupled in its own right; this is an example of strong-weak coupling duality.)

    So … how many dimensions are there really? If one limit of the theory is 11-dimensional, and others are 10-dimensional, which is right?

    I’ve heard respected string theorists come down on different sides of the question: it’s really ten-dimensional, it’s really eleven. (Some have plumped for twelve, but that’s obviously crazy.) But it’s more accurate just to say that there is no unique answer to this question. “The dimensionality of spacetime” is not something that has a well-defined value in string theory; it’s an approximate notion that is more or less useful in different circumstances. If you look at spacetime a certain way, it can look ten-dimensional, and another way it can look like eleven. In yet other configurations, thank goodness, it looks like four!

    And it only gets worse. According to Juan Maldacena’s famous gravity-gauge theory correspondence (AdS/CFT), we can have a theory that is equally well described as a ten-dimensional theory of gravity, or a four-dimensional gauge theory without any gravity at all. It might sound like the degrees of freedom don’t match up, but ultimately infinity=infinity, so a lot of surprising things can happen.

    This story is one of the reasons for both optimism and pessimism about the prospects for connecting string theory to the real world. On the one hand, string theory keeps leading us to discover amazing new things: it wasn’t as if anyone guessed ahead of time that there should be dualities between theories in different dimensions, it was forced on us by pushing the equations as far as they would go. On the other, it’s hard to tell how many more counterintuitive breakthroughs will be required before we can figure out how our four-dimensional observed universe fits into the picture (if ever). But it’s nice to know that the best answer to a seemingly-profound question is sometimes to unask it.

  • Another suburban legend shattered

    BeeThe laws of physics are safe for now.

    It occasionally comes to pass that someone, for reasons that frankly escape me, would like to make the point that science doesn’t know everything. It doesn’t, of course, which is so obvious that the point hardly needs making. Equally obviously, science does know some things; when it comes to mundane features of the natural world, one hopes that existing puzzles will eventually be figured out.

    One of the favorite anecdotes for the don’t-know-everything crowd involves the flight of the honeybee. As you may have heard, “bees shouldn’t be able to fly,” according to science as we know it. In fact, this idea goes back to French entomologists August Magnan and André Sainte-Lague, who in 1934 calculated that bee flight was aerodynamically impossible. Since bees have been observed to fly, the smart money has always been that Magnan and Sainte-Lague were, in scientific parlance, “wrong.” But that’s not the same as understanding how the darn insects actually do flit around.

    Now we know. Bioengineers Michael Dickinson, Douglas Altshuler and colleages have analyzed the flight of the bumblebee (if you will), using a combination of high-speed photography and robotic models. The trick is that bees have flight muscles that have evolved differently from those of other insects — unintelligent design, I suppose. Consequently, they flap much faster than any other animal their size, and emply a unique rotation of their wings.

    Chalk up another success for science. I understand that Dickinson and Altshuler will now start working on how to get experimental predictions out of string theory.

  • Flacks

    Steven Verhey, a biologist at Central Washington University, had an idea: try to teach his Basic Biology class a little bit about how scientists actually think, by presenting arguments both in favor of evolution (as embodied in Richard Dawkins’ book The Blind Watchmaker) and creationism/intelligent design (as embodied in Jonathan Wells’ Icons of Evolution). Verhey is no creationist himself, but thought it would be a good way to teach the students some critical-thinking skills along with some biology. Interesting discussions at The Panda’s Thumb and Pharyngula.

    As far as whether or not a discussion of creationism/ID is a smart thing to have in an introductory biology course, there are good arguments on both sides; it is a nice example of the difference between real science and ideology, but on the other hand it takes a lot of time that could be spent teaching the actual core material. I have no strong feelings either way.

    But I couldn’t help but highlight two sentences from Verhey’s description of one event in his class. The Discovery Institute, main propaganda machine for ID, is located in Seattle, not far from CWU. So Verhey actually invited Jonathan Wells to come talk to his class, and Wells agreed.

    Since Ellensburg is just 1.5 hours east of Seattle, home of the Discovery Institute, that first time I also invited Jonathan Wells to speak to my class and to give a special university-wide seminar. He was accompanied by a handler from the PR department at DI, who passed out DVDs.

    You know, I give lots of talks about various scientific topics, and in all honesty, it has never even occured to me to be accompanied by a handler from the PR department at my university. Do you still wonder why we keep insisting that there is no science going on here, just public relations?

    On the other hand, I’m open-minded and willing to learn. Maybe I’ll start showing up at talks accompanied by my own PR person. Those DVD’s aren’t going to hand out themselves.

  • Spacetime and black holes

    As I type, the students in my Spacetime and Black Holes class are putting the finishing touches on their final exams. Unlike Clifford, I prefer to give take-home finals rather than in-class ones. Not a strong conviction, really; it’s just easier to think of interesting problems that can be worked out over a couple of hours than ones that can be done in half an hour or so. Here’s the final (pdf), if you’d like to take a whack at it. The colorful problem 4 was suggested by Ishai Ben-Dov, the TA; the terse calculational ones were mine.

    This is one of my favorite classes to teach, and this quarter the group was especially lively and fun. It’s an undergraduate introduction to general relativity, using Jim Hartle’s book. (It’s okay, Jim uses my book when he teaches the graduate course.) GR is not a part of the undergrad curriculum at most places in the U.S., believe it or not. (There are plenty of grad schools that don’t offer it, and almost none where it is a requirement.) Here in the World Year of Physics, it’s astonishing that the huge majority of physics majors will get their bachelor’s degrees without knowing what a black hole is.

    We didn’t have an undergrad GR course at Chicago until a few years ago, when I started it. To nobody’s surprise, it’s become quite popular. Each of the three times I’ve taught it, we’ve had over 40 students; this in a department with maybe 20-30 physics majors graduating each year. At one point I proposed an undergraduate course in classical field theory, which would have been a nice complement to the GR course. It would have covered Lagrangian field theory, symmetries and Noether’s theorem, four-vector fields, gauge invariance, elementary Lie groups, nonabelian symmetries, spontaneous symmetry breaking and the Higgs mechanism, topological defects. If we were ambitious, perhaps fermions and the Dirac equation. But this was judged to be excessively vulgar (you shouldn’t teach classical field theory without teaching quantum field theory), so it was never offered.

    The real trick with GR, of course, is covering the necessary mathematical background without completely losing the physical applications. Jim’s book does this by covering the geodesic equation (motion of free particles) and the Schwarzschild solution (the gravitational field around a spherical body) without worrying about tensors, covariant derivatives, the curvature tensor, or Einstein’s equation. It’s like doing Coulomb’s law for electrostatics before doing Maxwell’s equations — in other words, completely respectable. Personally, after studing Schwarzschild orbits and black holes, I zoom through the Riemann tensor and Einstein’s equation, just so they don’t think they’re missing anything.

    And when the students pick up the final to spend the next 24 hours thinking about general relativity, I try to remind them: “Three months ago, you didn’t even know what any of these words meant.”

    Update: replaced a nearly-unreadable pdf file for the exam with a much cleaner one.

  • The Kansas School Board is right

    I find myself nodding in agreement with the wisdom of the Kansas Board of Education. Not very much agreement, to be sure; the recent move to introduce official skepticism about evolution into its new public school science standards is just bad. Bad, bad Kansas.

    But, amidst the bemoaning of this setback for Enlightenment values, we all had a little fun with the school board’s attempt to change the definition of science, as Risa has already pointed out. (See also John Rennie at the new Scientific American blog.) Seems that they have decided to open the door to explanations other than the purely natural — obviously, so that they can include religious (“supernatural”) explanations within a science curriculum.

    But only after reading Dennis Overbye’s story in yesterday’s New York Times did I really understand what they had done. Here’s the new definition of “science”:

    The changes in the official state definition are subtle and lawyerly, and involve mainly the removal of two words: “natural explanations.” But they are a red flag to scientists, who say the changes obliterate the distinction between the natural and the supernatural that goes back to Galileo and the foundations of science.

    The old definition reads in part, “Science is the human activity of seeking natural explanations for what we observe in the world around us.” The new one calls science “a systematic method of continuing investigation that uses observation, hypothesis testing, measurement, experimentation, logical argument and theory building to lead to more adequate explanations of natural phenomena.”

    At the risk of alienating all my friends — the school board is right. Science isn’t about finding “natural” explanations vs. “supernatural” ones; it’s about finding correct explanations, without any presupposition about what form they may take. The distinguishing feature of science isn’t in the explanations themselves, it’s in the process by which we find them. Namely, we toss out hypotheses, compare them to data, and look for the hypotheses which account for the largest number of phenomena in the simplest possible way. Simplicity here is in the sense of “algorithmic compressibility” — the number of bits, if you like, required to specify the mechanism that purports to do all this explaining.

    What the Kansas school board has tried to do is to open the door for unbiased consideration of natural and supernatural explanations by a common standard — that of scientific investigation. This is just what I’ve been arguing for all along. Scientists have to get off this kick that science and religion are completely distinct magisteria that have nothing to do with each other. Quite the contrary; religion (at least in its common Western forms) goes around making claims about how the world works, and it’s perfectly appropriate to judge such claims by the same standards that we judge any other suggested hypotheses about nature.

    The thing is, if we judge popular religious vs. naturalist explanations for how the universe works by a common scientific standard, naturalism wins. Without breaking a sweat, frankly; by the beginning of the second half, we have to send in the scrubs from the bench, at the risk of being accused of running up the score. Intelligent Design, to take one obvious example, is laughably bad as a scientific hypothesis. It explains practically nothing (since it refuses to say anything about the nature of the designer, so we have no clue what such a designer would ever choose to design), while introducing a fantastic amount of new complexity in the form of an entirely distinct metaphysical category (the designer). I have no problem saying that ID is a “scientific hypothesis”; it’s just such a bad one that no sensible scientist would give it a moment’s thought if it weren’t for the massive public-relations campaign behind it.

    Science doesn’t home in on naturalistic explanations by assumption; it chooses them because those are the best ones. That doesn’t mean that we have to “teach the controversy” in high schools; the number of grossly inadequate scientific theories is far larger than we could ever address in such a context. But it’s about time that we admitted that science is perfectly capable of judging supernatural claims — and finding them sadly wanting.

  • Congratulations to Jennie!

    This is the time of year when a lot of undergraduate students are filling out applications to graduate school. So it’s nice to be reminded that all that effort occasionally pays off. Join me in congratulating brand-new Ph.D. Jennifer Chen, who successfully defended her thesis yesterday!

    Jennie’s previous work with me was on spontaneous inflation and the arrow of time, in which we tried (and even succeeded, I might claim) to answer a century-old question: why does the early universe have such low entropy? This work was briefly deemed press-worthy, and was the basis for our second-place winning essay in the Gravity Research Foundation essay competition.

    For her thesis work, Jennie looked at experimental constraints on light scalar fields in the universe. We’ve never detected a fundamental scalar field, for the sensible reason that they tend to be very massive. But one possible candidate for dark energy is an extremely light scalar field (a mass about 10-40 times the mass of the electron), known as “quintessence.” Some time back I explored how you might detect a quintessence field directly through its couplings to matter, rather than indirectly through the expansion of the universe, in my paper Quintessence and the Rest of the World. Basically there are two ways to do it: looking for very weak long-range forces via 5th-force experiments (light fields always give rise to long-range forces), and looking for gradual evolution of the “constants” of nature such as the fine-structure constant.

    Jennie took this idea and did a thorough job of exploring what the current data are telling us. For the 5th-force experiments, this meant exploring what the “charge” for different test masses would be, especially from the complicated effects of quarks and gluons. As particle physicists know but rarely admit, most of the mass in ordinary matter comes not from the fundamental masses of elementary particles themselves, but from the chromodynamic binding energy of quarks confined into protons and neutrons. Jennie showed that couplings to gluons and quarks would be the most significant contributor to the 5th-force effects from light scalars.

    The other idea, that coupling constants could evolve over the history of the universe due to the gradual evolution of a light scalar field, has received a lot of attention recently due to claims that the fine structure constant α (characterizing the strength of the electromagnetic interaction) actually does vary. This work looks at the spacing of spectral lines in systems at high redshift, and purportedly provides evidence that α has varied by about 10-5 between today and a redshift of a few. Other studies, it should be mentioned, claim that α actually does not vary at all, and place an upper limit.

    Here is Jennie’s plot of the data, with some theoretical curves (click for larger version).
    alpha vs. redshift
    This is the inferred value of α as a function of cosmological redshift. The points with the big error bars that lie below zero are from the group claiming to see a variation in α (the data have been binned for easier viewing). The points above those, consistent with zero, are from other groups looking at quasar spectra. The two points near the top left are interesting; the leftmost one is from the Oklo natural reactor, and the next one uses data from abundances of radioactive isotopes in meteors.

    The moral is simple enough: trying to fit the data with a simple quintessence model doesn’t readily accomodate the Oklo and meteor points, much less the new quasar data. Probably α is not changing, and if it is, it’s not doing so in a way we would expect in a simple model. That’s what complicated models are for, of course. But I wouldn’t bet a lot of money on this one.

  • Gravity to the rescue

    Apparently nuclear bombs and Bruce Willis are two things that are just too hard to control. So if a massive asteroid appears to be on a collision course with Earth, a couple of astronauts have invented a new way to save us from this cosmic menace: a gravity tractor.

    gravity tractor It’s a simple enough idea: instead of blowing up the asteroid, just use gravity to gently deflect it from its path. If you have plenty of warning, you can send up a spaceship that is as heavy as you can manage, and simply park it next to the asteroid. The gravitational pull of the ship will gradually tug the asteroid off course; a tiny force, indeed, but if you let it accumulate for a few years you might be able to do the job.

    I confess to a certain amount of skepticism. The gravitational field of such a ship will be incredibly tiny, and even if you plug in the numbers and it seems to work, I would worry that other trace effects (e.g. outgassing or radiation from the ship) won’t be equally important and work in the opposite direction. And when I heard a report about the idea on NPR, there was a curious statement from one of the idea’s supporters, that it would work well for asteroids of such-and-such a mass. Where I was taught about gravity, the acceleration is independent of the mass, so that was a little confusing. It may be that the size of the thing is important — if the asteroid center of mass is too far away from the tractor, you’re in trouble, since gravity falls of as 1/r2.

    But it’s certainly a more sensible idea than the one mentioned by John in an earlier comment, and again at the bottom of the gravity-tractor article: a space vehicle propelled by the pressure of the inflationary vacuum state, recently granted U.S. patent 6,960,975. That’s just completely crazy.

  • The soul of a space alien

    A couple of thousand years ago, we didn’t know much about how the universe works. It’s no surprise that our ancestors came up with a mishmash of beliefs about nature, humans, and our place in the cosmos.

    What is a consistent source of surprise is that so many people still cling to these dusty beliefs, no matter what variety of silliness it leads them to. One of the foundational beliefs of mainstream Western religions is that humans are somehow special in God’s eyes. Could anything shake us from such a conviction? Majikthise and Cynical-C point to one such thought experiment: a story from Catholic News Service about whether space aliens have souls. What would happen to our belief in our own singular status within creation if we found that there were other sentient beings out there, capable of thoughts and feelings and launching wars of choice?

    Jesuit Brother Guy Consolmagno has thought about it, and reached an interesting conclusion: it wouldn’t change anything.

    He said his aim with the booklet was to reassure Catholics “that you shouldn’t be afraid of these questions” and that “no matter what we learn, it doesn’t invalidate what we already know” and believe. In other words, scientific study and discovery and religion enrich one another, not cancel out each other.

    If new forms of life were to be discovered or highly advanced beings from outer space were to touch down on planet Earth, it would not mean “everything we believe in is wrong,” rather, “we’re going to find out that everything is truer in ways we couldn’t even yet have imagined,” he said.

    Not to be nit-picky, but the motto “no matter what we learn, it doesn’t invalidate what we already know” is not evidence that science and religion enrich each other, it is evidence of precisely the opposite. The distinguishing feature of science is precisely that it stands ready to invalidate its previous theories on the basis of new evidence. We approach the universe with an open mind, struggling to understand what it has to tell us; we don’t figure things out ahead of time and use the universe to fabricate a flattering story about ourselves.

    But the next sentence was my favorite:

    The Book of Genesis describes two stories of creation, and science, too, has more than one version of how the cosmos may have come into being.

    That’s a tad misleading right there. Genesis does indeed have two stories of creation, one right after the other (the first starts at Genesis 1:1, the second at Genesis 2:4). The two versions are completely contradictory — in the first, God creates plants, and then animals, and then man and woman simultaneously; in the second, God creates man out of dust, then plants a garden, and woman is only an afterthought. And everyone knows why there are two mutually exclusive stories right after each other: they came from two different texts, written by different people at different times, edited together later into a single document. Fascinating as history, but not a stable foundation on which to build a view of the universe.

    Scientists, it’s true, have lots of versions of how the cosmos may have come into being; heck, I have one myself. That’s how we work; we throw ideas out there, compare them to other pieces of information, and toss out the ones that don’t work. If new information comes along, we’re hoping that it conforms to our personally favorite ideas, but if not, that’s exciting and we look forward to learning something.

    And when those space aliens get here, I’m definitely going to ask them what they think about the anthropic principle.

  • Sex in space!

    No, this isn’t one of those bait-and-switch titles. It really is about sex in space. Via Deepen the Mystery, a Guardian story on the hazards of sexual encounters on long-duration space missions.

    They should be out-of-this-world experiences. But US experts have warned that sex in space will bring problems not pleasure for men and women heading to the moon and Mars.

    A panel of scientists has told Nasa interplanetary passion could cause chaos to its latest plans to send humans on long missions.

    Cramped in spaceships for years, surrounded by the starry void, astronauts thoughts are bound to turn to romance, states the report, ‘Bioastronautics Roadmap: a risk reduction strategy for human exploration of space’.

    The resulting close encounters could have profound consequences, it adds. Without supplies of the necessary precautions, zero-gravity romps could lead to zero-gravity pregnancies.

    Snickering aside, I’m sure it’s a real problem — send a bunch of people into isolation in close quarters for a period of years, and something will happen.

    Now, I know that certain of my co-bloggers are reliable readers of the Guardian science section, but apparently they were going to keep this story to themselves. The extra value-added you get from Cosmic Variance, of course, is that we will actually link directly to the NASA Bioastronautics Roadmap from which the story derives. Although, as it turns out, a cursory inspection didn’t turn up anything nearly as off-color as you’d find in a novel by a recently indicted former high-ranking White House staffer. But this bit was interesting:

    Serious interpersonal conflicts have occurred in space flight. The failure of flight crews to cooperate and work effectively with each other or with flight controllers has been a periodic problem in both US and Russian space flight programs. Interpersonal distrust, dislike, misunderstanding and poor communication have led to potentially dangerous situations, such as crewmembers refusing to speak to one another during critical operations, or withdrawing from voice communications with ground controllers. Such problems of group cohesiveness have a high likelihood of occurrence in prolonged space flight and if not mitigated through prevention or intervention, they will pose grave risks to the mission. Lack of adequate personnel selection, team assembly, or training has been found to have deleterious effects on work performance in organizational research studies. The duration and distance of a Mars mission significantly increases this risk. The distance also reduces countermeasure options and increases the need for autonomous behavioral health support systems.

    Oh, great. I see a Stranger in a Strange Land scenario on our horizon.

  • Mainstream breakthrough

    Let’s get this right out of the way: yes, Cosmic Variance did make its first appearance in the New York Times. We get a passing mention in Dennis Overbye’s article about Lisa Randall, for Clifford’s justified annoyance at Ira Flatow’s remarks on Science Friday about Lisa’s appearance rather than her science.

    The NYT profile is a good one, managing to mix the personal with the scientific in a more interesting (and less objectionable) way. And they always do a nice job with the graphics; here is their version of the Randall-Sundrum brane-world construction. (Click to enlarge.)
    Randall-Sundrum universe
    Randall-Sundrum (versions one and two) is a great idea, one that I hope to discuss at length at some point. The basic notion is to have two three-branes (a three-brane has three dimensions of space and one of time) separated by a five-dimensional bulk that is highly curved. The nice feature is that the curvature acts not only on stuff passing through the bulk itself, but also works to rescale energies on one brane in relation to the other. So, what appears naturally to be very high-energy on one brane can be naturally low-energy on the other. This idea may help to explain the huge discrepancy (fifteen or so orders of magnitude) between the typical energy scales of particle physics (about one trillion electron volts, or one TeV) and that of gravity (the Planck scale, 1015 TeV).

    But all the publicity, of course, is currently associated with Lisa’s new book more than with any recent breakthroughs. As predicted, I’ve written a review of Warped Passages, along with Michio Kaku’s book Parallel Worlds, which has now appeared in American Scientist. You’ll see that these are very different books, and it shouldn’t be too hard to figure out which I liked better. The holidays are coming — if there’s nobody in your family you like enough to get them my book or Clifford’s, you wouldn’t go wrong buying them Lisa’s.