In the Fall semester, which is approaching at a far too rapid rate, I am teaching a new advanced graduate course PHY795: Modern Cosmology. Although this will certainly be a huge amount of work, I’m very much looking forward to exposing our graduate students to the topics I spend most of my life thinking about.

As part of my preparation, I have recently turned to explaining the question of baryogenesis - how did the measured excess of matter over antimatter in the universe arise dynamically as the universe evolved? I have discussed this question once before, and also described one of the possible and testable ways in which this may have occurred, through nonperturbative finite temperature dynamics in small extensions of the standard model of particle physics.

In explaining these ideas, I chose to avoid anything more than a passing reference to how baryon number violating transitions take place in such theories, writing

In the standard electroweak theory baryon number is an exact global symmetry. However, baryon number is violated at the quantum level through nonperturbative processes - it is an anomalous symmetry. This feature is closely related to the nontrivial vacuum structure of the electroweak theory.

At zero temperature, baryon number violating events are exponentially suppressed (this is most certainly a good thing, since we would like the protons making up our bodies to remain stable). However, at temperatures above or comparable to the critical temperature of the electroweak phase transition, B-violating vacuum transitions may occur frequently due to thermal activation.

I chose this route because the physics involved - that of nonperturbative physics in chiral quantum field theories - is a difficult one, the technicalities of which I thought would be beyond the level of the post.

However, in preparing for my class, I found myself going over a favorite analogy for some of this physics and thought I’d give it a shot here. I don’t quite recall where I first came across this analogy, although it may have been in a review article by either Emil Mottola or Peter Arnold, which I read when I was a graduate student. What follows will be a little more technical than usual, but I’m hoping that most people with some physics training will get something out of it.

The vacuum of the electroweak theory is degenerate - there are infinitely many vacua, related by large gauge transformations. The field theories constructed around these vacua are entirely equivalent, but transitions between these vacua result in the anomalous production of fermions, which is the method by which the baryon number may change.

Fortunately for us (who wants our protons to spontaneously decay away?), these baryon number violating transitions are forbidden classically and, in fact, even at the perturbative quantum level - baryon number is an exact global symmetry of the theory. Therefore, at zero temperature, the only way baryon number violating processes can occur is through quantum tunneling between the classical vacua of the theory. This in itself is nonperturbative physics, and the relevant calculation yields that if the universe were always close to zero temperature, not one event would have occurred within the present Hubble volume ever in the history of the universe. However, when we include the effects of nonzero temperature, classical transitions between vacua become possible due to thermal activation.

For an analogy to this heady mix of perturbative-nonperturbative physics and finite temperature field theory, it turns out we can lean on a physical system about which most physicists learn in high school or college - the simple pendulum!

This system is a mass m suspended at the end of an arm of length l, and confined to rotate ideally in the plane. The system possesses a periodic vacuum structure labeled by integer n since, measuring angles in radians as scientists do, the system is identical in a minimum energy state whenever the angle θ in the figure is given by 2nπ. It is in this sense analogous to the electroweak theory, and you are to imagine that fermions would be produced should the system make a transition between vacua labeled by different values of n.

If we say that the vacua have zero gravitational potential energy, then the potential energy for any value of the angle θ is simply given by mg[1-cos(θ)], where g is the acceleration due to gravity. Notice that, because there is a cosine in this expression, all the information about the multiple vacua I mentioned is right there in the energy.

If a physicist wanted to understand the classical or low energy quantum mechanics of this system, they might take this potential energy and make it simpler with the approximation that the angle is always small (really what one means by low energy). In that case, if we keep only up to second order in the angle (i.e. do perturbation theory), the potential energy becomes the simplest one we know of - the harmonic oscillator - and is easily solvable. (Actually, the truth is that the full problem is solvable, but anything more complicated probably won’t be, and the approximation is what I’m trying to explain here).

But we do play a price for this approximation - all information about the periodic vacua is lost.

If we think about raising the temperature of the system, we soon run into trouble. Suppose the pendulum is coupled to a thermal bath. Then it will be thermally excited to states of higher and higher energy as the temperature is raised. Obviously, before we start calculating, we can see that as the temperature becomes comparable with the height of the barrier preventing transitions between vacua, it becomes possible for the pendulum to make transitions between vacua, crossing the point θ = π randomly, at an unsuppressed rate. But note that these have to be nonperturbative transitions, since they probe the periodic structure of the vacuum, which is not captured at all by perturbation theory.

This situation is analogous to most familiar calculations in the electroweak theory, in which perturbation theory is usually a safe tool to use. Such an approximation scheme is only valid when the energy of the system is much less than the height of the barrier separating vacua (in the electroweak theory this is known as the sphaleron). In that limit, quantum tunneling between vacua is exponentially suppressed as expected. But in the early universe, when temperatures are much higher than the barrier height, perturbation theory must be abandoned, and these effects, and the associated violation of baryon number, are rampant.

Back in March we had a guest post by Anthony Aguirre about the Foundational Questions Institute, a new effort to support “research at the foundations of physics and cosmology, particularly new frontiers and innovative ideas integral to a deep understanding of reality, but unlikely to be supported by conventional funding sources.” Today the FQXi (that’s the official acronym, sorry) announced their first round of grant awardees.

It’s a very good list, and Anthony and Max Tegmark are to be congratulated for funding some very interesting science. If anything, I could see almost all of these proposals receiving money from the NSF or DOE or NASA, although perhaps it might have been more difficult. We see well-known string theorists (for example Steve Giddings, Brian Greene, Eva Silverstein), early-universe cosmologists (Richard Easther, Alex Vilenkin), late-universe astrophysicists (Fred Adams, Avi Loeb), general relativists (Justin Khoury, Ken Olum), loop-quantizers (Olaf Dreyer, Fotini Markopoulou), respectable physicists taking the opportunity to be a little more speculative than usual (Louis Crane, Janna Levin), and even some experimentalists working on the foundations of quantum mechanics (Markus Aspelmeyer, former guest-poster Paul Kwiat), as well as a bunch of others.

Nothing in there about finding God by doing theoretical physics. Which might have been a non-trivial worry, since currently the sole source of funding for FQXi is the John Templeton Foundation. The Templeton Foundation was set up “to encourage a fresh appreciation of the critical importance — for all peoples and cultures — of the moral and spiritual dimensions of life,” and in particular has worked to promote a reconciliation between science and religion. I am not a big fan of such reconciliation, in the sense that I think it is completely and woefully misguided. This has led me in the past to decline to participate in Templeton-sponsored activities, and the close connection between Templeton and FQXi was enough to dissuade me from applying for money from them myself.

Gareth Cook has written a nice article in the Boston Globe about FQXi and the grant program, in which I am quoted as saying that bringing science and religion together is a bad thing. Absolutely accurate, but the space constraints of a newspaper article make it hard to convey much subtlety. The FQXi folks have stated definitively that their own mission is certainly not to reconcile science and religion; in case of doubt, they’ve put it succinctly in their FAQ:

I’ve read that a goal of JTF [John Templeton Foundation] is to “reconcile science and religion.” Is this part of the FQXi mission?

No.

Indeed, they’ve been quite clear that the Templeton Foundation has just given them a pot of money and been otherwise hands-off, which is good news. And that they would like to get additional sources of funding. My own current worry — which is extremely mild, to be clear — is that the publicity generated by FQXi’s activities will be good for Templeton’s larger purpose, to which I am opposed.

But at the moment the focus should be on recognizing Max and Anthony and their friends for steering a substantial amount of money to some very interesting research. If they succeed at getting additional sources of funding, I may even apply myself one day!

Update: More quotes in this piece from Inside Higher Ed.

Warren Moon always wanted to be a quarterback. He had all the physical tools, as well as tremendous leadership abilities and a fierce determination to win. Only one problem: he was black. As stupid as it may sound, not too long ago conventional wisdom held that black people couldn’t be quarterbacks — they were athletes, not thinkers.

Moon was a successful high school football player in LA, despite playing in the kind of atmosphere where you received death threats from gang members playing for the opposing team. But he couldn’t get a scholarship offer from a major college. Well, that’s not exactly right — he did get offers, but only under the condition that he switch positions to running back or defensive back. One school, Arizona State, recruited him as a quarterback, but rescinded their scholarship offer after they signed two other (white) quarterbacks.

Determined to play the position he wanted to play, Moon went to junior college for a year, where he personally sent game films to major programs throughout the country. He was finally offered a scholarship by the University of Washington, where the team had been plagued by racial tensions. At UW he was the target of relentless taunting from fans, and his own teammates expressed skepticism of his ability. Nevertheless, in his senior year Moon led the Huskies to their first Rose Bowl in fifteen years, where they beat Michigan in a stunning upset.

Moon was named MVP of the Rose Bowl, but when the NFL draft came around, nobody was interested. He wasn’t invited to any combines or private workouts for teams. Word was out that he refused to convert to defensive back or tight end, which were the only positions at which NFL teams would consider him. As Moon put it, “The quarterback is the face of the organization, and white owners still weren’t ready for that face to be a black man. The owners wanted somebody to take to the country club, and they weren’t ready for that to be a black man.”

Undaunted, he signed with the Edmonton Eskimos of the Canadian Football League. In six years in the CFL, he led the Eskimos to five Grey Cup championships, winning two championship-game MVP awards, and set a league record for passing yards in 1983. He was inducted into the CFL Hall of Fame in 2001.

The NFL finally caught on, and Moon was signed by the Houston Oilers in 1984. He and his family were again the subject of death threats, and his wife and children were eventually forced to watch the games from a private stadium box. After one game in 1991, on the verge of signing a new contract, he had to explain to his nine-year-old son what it meant when a fan in the stands had yelled “I can’t believe they gave that f—— n—– $14.3 million.”

Moon persevered, setting the Oilers club record for passing yards in his first year, but didn’t really come into his own until his third year in the NFL. He led the league in passing in 1990 and 1991, joining Dan Fouts and Dan Marino as the only quarterbacks to ever post consecutive 4,000-yard seasons. He went to the Pro Bowl nine times. By the time he retired in 2001, he was third all-time in NFL passing yardage behind Marino and John Elway, despite having played his first six years in the CFL. If he had played in the NFL for those six years, throwing for 2,500 yard per year (an extremely conservative estimate), he would have finished his career as the league’s all-time leading passer by a substantial margin.

Warren Moon wasn’t the first black quarterback in the NFL, but he set an example that made it enormously easier for others to follow in his footsteps. There are now several African-Americans starring at quarterback in the NFL; sufficient evidence, in the eyes of some, to say “See? Racism doesn’t exist!” Ignoring decades of history, they will tell you with a straight face that the competitive pressures of running a professional sports franchise make it impossible to be racist, since any non-racist organization will be able to scoop up all the undervalued players. (Somehow that sounds familiar.) This from the same folks who, not too long ago, argued that “the White community” was entitled to disenfranchise blacks because Whites were “the advanced race.”

Today, Warren Moon is being inducted into the Pro Football Hall of Fame, becoming the first player ever to be in both the CFL and NFL Halls — oh yes, and the first black quarterback to be inducted. Congratulations, Warren; thanks to the example you set, you won’t be alone for long.

The 2006 SLAC Summer Institute has shut its doors and the participants are wending their way back home. I’ve taken off early, am sprawled on the couch, and thought I’d report on the contest before I start my nap.

It’s a Summer Institute tradition to sponsor a contest; we pose a thought-provoking question on the first day, the students have the next two-weeks to ponder the question with deep thoughts and ultimately submit their best answer by the end of the school. We have a lot of fun with the event and it grows more popular each year. Here’s a CV report on last year’s contest. It’s a fun way to get the students to think out of the box.

This year’s question was simply:

What will be the most surprising discovery at the LHC?

in sync with this year’s Institute theme. The contestents were warned that a simple and obvious answer such as “Supersymmetry” would most likely not garner the prize. We had 35 rather diverse entries in the end, which were judged by a panel of distinguished experts.

Unfortunately the most distinguished member, clearly the camel (whose name is Michael Jackson, incidentally), was stuck in Rajasthan and not able to attend the panel meeting.

Some of the entries were quite imaginative! In one, a member of the SLAC theory group conjectured that the most surprising discovery would be the production of Little Green Men. Since this has already been the subject of a light, yet entertaining, novel called Einstein’s Bridge about the cancellation of the Superconducting SuperCollider, the panel thought this entry somewhat lacked in originality. But agreed it would be surprising, particularly if they came to eat us. Condoleezza Rice submitted an entry on her way to the Middle East. Recall that Condi has a long association with Stanford after being on the faculty and serving as Provost and no doubts keeps a keen eye on the SLAC Summer Institute. She proposed the discovery of stable black hole remnants with associated physics indicative of noncommutative spacetime. Now, that would indeed be surprising, but alas did not garner the enthusiasm of the panel. One can only hope she has more luck in the Middle East.

After much debate over a considerable quantity of South African Cabernet, the panel settled on two Honorable Mentions and a Winner. The first Honorable Mention:

An experimentalist will develop a way to test string theory.

Actually the panel was inclined to award this entry first place, but then discovered it was submitted by one of the lecturers. The second Honorable Mention described the production of quasi-stable black holes as a spectacular signature of quantum gravity. And the winning entry is (drum roll, please….)

From the WW scattering cross section, we know that the unitarity of the optical theory breaks down at 1.7 TeV. To prevent this breakdown of unitarity, either the Higgs boson or the Kaluza-Klein gauge bosons (that come from other theories) need to be discovered. The biggest surprise at the LHC (or one of the biggest surprises) would be if neither the Higgs boson nor the KK bosons (nor any of the other particles coming from the other theories) were discovered. The unitarity theorem would break down, thus signaling Quantum Mechanics needs to be overhauled! A more complete theory would need to evolve of which QM would just be an approximation! Maybe something like SuperQM?

The panel thoroughly enjoyed the idea of discovering a Super-Quantum Mechanics at the LHC. Kudos to Jo Ostra from the University of Notre Dame who recieved a bottle of California’s finest sparkling wine and the Institute’s autographed copy of QCD and Collider Physics, donated by James Stirling. I hope she enjoys the wine and the book, but perhaps not necessarily at the same time!

Well, I was going to wait until Monday, since today is one of the worst days to launch a new blog, but one cannot hide from pingbacks.

In addition to my writing here on Cosmic Variance, I’ll be blogging over at a new blog called Asymptotia. It is still in an early stage of construction (I only completed the basic structures last night), but it should be able to handle some visitors if you’d like to go over and try the new furniture, kick off your shoes and visit for a while. You don’t need a hard hat any more, but some of the edges might still be a little rough.

What can you find there? Right now there are some pictures from the California State Science Fair, updates about the garden, and an architectural stop in Marseille to see one of Le Corbusier’s famous buildings.

Upcoming posts you’ll find there, which I’ll do over the weekend, I hope:

A report on an excellent talk here at Aspen’s Institute for Environmental Studies by Kevin Knobloch, the president of the Union of Concerned Scientists. The subject was Global Warming.

A report on a fascinating colloquium by Charles Stevens of the Salk Institute, given here at the Aspen Center for Physics yesterday. The subect was something like “How Theory in Biology is Similar to and Different from Theory in Physics”. He gives some lovely examples, including scaling laws in the architechture of the brain.

-cvj

In the course of a long life, you’re going to get asked to recommend a good book to read. What should you say? Of course a sensible answer depends on who is asking, but we don’t know that, so let’s limit ourselves to books that tickle our own fancies. And we can assume, given the high-powered sophistication of this here blog you’re reading, that The Da Vinci Code won’t be first on your list. In fact, let’s also assume that you wouldn’t suggest Pride and Prejudice or Ulysses, as the idea is to make suggestions that your interlocutor may not actually have heard of.

So here’s my list — five novels that haven’t ascended into the literary canon (and are unlikely to do so), yet had me gasping with delight or shuddering with (a pleasant kind of) horror. My own personal cutoff for being obscure enough to count as an interesting recommendation was “less well known than Flaubert’s Parrot,” which otherwise might have made the list.

1. The Debt to Pleasure, John Lanchester. This one is a favorite of various CV bloggers, as I recall. A wonderfully dark novel, structured loosely around a series of recipes. You won’t learn any new culinary tricks, but you’ll be drawn into the wicked plotting of Tarquin Winot as he spins his schemes with considerable savoir faire. The first book I recommend to people I think highly of.
2. Thus Was Adonis Murdered, Sarah Caudwell. The opposite of dark, although there is a murder, and a good deal of British tax law. Caudwell has written a mystery novel populated by barristers of supernatural wit and cleverness, resulting in one of the most consistently amusing books I’ve ever read.
3. The Wasp Factory, Iain Banks. Back to darkness. Banks is a prolific author, alternating between “straight” fiction and science fiction novels. This was his first, and it’s a masterpiece of twisted imagination. There’s a surprise ending, but the convoluted path by which you get there has a terrifying internal logic.
4. Love in a Dead Language, Lee Siegel. No, not that Lee Siegel. This one is a professor of religion at the University of Hawaii, who has written the best postmodern-pastiche novel I’ve come across. Structured loosely as a translation of the Kama Sutra, complete with puzzles and self-reference and fourth-wall breaking. Likely to be most appreciated by academics.
5. The Book of Revelation, Rupert Thomson. Picked up on a whim in an airport bookstore, this is a disturbing short novel about a ballet dancer who is kidnapped by a group of women and used for their sexual pleasure. The quick response is “that doesn’t sound so bad,” but the truth is that is very much is. This book is a thoughtful examination of deep issues of identity, freedom, and obsession.

I could confidently recommend any of them, with the understanding that my tastes are not exactly universal. Your mileage may vary.

Cornelia Dean, in today’s New York Times, has a collective review of a number of new books about the relationship between science and belief in Santa Claus. Here’s the key graf:

Of course, just as the professors of Christmas spirit cannot prove (except to themselves) that Santa Claus exists, the advocates for secular holidayism acknowledge that they cannot prove (not yet, anyway ) that Santa does not exist.

This is the crucial point that can’t be emphasized enough in discussions of the Christmas problem. These scientists, always talking about how they can “prove” this or that about the universe. But, if they’re honest, they admit that they can’t prove Santa doesn’t exist. Sure, we’ve had people up at the North Pole looking around, and they didn’t see any evidence of his workshop. But the belief in an actual physical workshop, right there on the ice and with elves and whatnot, is just a colorful remnant of an earlier, less sophisticated Christmasology. Today we understand that Santa is an ineffable spirit, who doesn’t directly intervene in the physical realm (except for Christmas eve, of course). Science and Christmas should be understood as distinct and non-overlapping realms of inquiry; they may work together, but can never come directly into opposition. And yes, there’s good evidence that many presents are actually brought out by parents rather than by Kris Kringle himself, but it seems implausible that all of them are. Santa is just a more elegant hypothesis.

Most of all: without the transcendent moral guidance that Santa provides, how will we know which children are naughty, and which are nice? Are we supposed to leave that up to individuals and communities to decide? Without Santa’s equitable system of rewards and punishments (coal), there would be no reason whatsoever for kids to behave themselves. They would just run around, tearing wings of of flies, setting schools on fire, murdering their enemies. No matter what you might think about the empirical case for and against the existence of Santa, we can all agree that the world is a better place if we believe in him.

PZ has more.

Drinking tea at high altitude again. Still a bad idea…. must remember to bring a pressure cooker next time. See this link if you don’t know what I’m talking about. Yes, on my short tour of research hideaways this Summer, I’m at another monastery, the Aspen Center for Physics, where I’ll be continuing my quest to get some coherent research thoughts fully explored before the end of the Summer and my other academic duties begin in earnest. For some of the time I’m here, I’ll overlap with a couple of workshops in my area (and other interesting ones besides), and hence several old friends and colleagues, which is always very nice to do. I’m coming in near the middle of the workshop entitled “String Theory, Gauge Theory & Particle Physics”, and have already today heard two excellent outdoor talks, one by Savdeep Sethi entitled “Can Time End?” and the other by Frederik Denef entitled “Factorization of BPS Degeneracies and the OSV Conjecture”.

We found out the answer to the first question when Sav firmly ran out of time before he got to say all he wished to. Seriously, his talk (see papers hep-th/0603104, hep-th/0601062, and hep-th/0509204 on the arXiv) is all about the physics of certain types of spacetime singularities -such as the one that lives in our universe’s past- and whether we can make sense of the idea of space and time coming into being after such a singularity, while not existing prior to that. He describes certain recently constructed models using string and matrix theory which do give you some rather good control over such issues, it seems. The “funny region” -where time and space have no meaning- is handled (via a “dual” or “indirect” description) by a particular type of non-abelian gauge theory (for the non-expert: roughly the same sort of theory that, for example, describes how nuclei hold themselves together) which does not seem particularly exotic, despite the novel spacetime physics it allows them to get a handle on. This is typical of the kinds of things we’re understanding a lot better about spacetime in recent years (and long before the AdS/CFT example, I should mention), which is that many puzzling questions about spacetime -such as how to describe a complete breakdown of its existence as a nice, smooth arena in which we live to for example the (expected) more primitive state of earlier eras in the universe’s history- seem to be better phrased in terms of gauge theory questions.

Frederik (in action in the photo above) spoke about the subtleties in understanding the OSV conjecture, which is -if you’ve never heard of it- a nice conjecture relating properties of certain types of black holes to a seemingly irrelevant computation involving what are called topological string theories. I won’t go into it here, but refer you instead to discussions of it on Jacques’ blog. It is a technical discussion. Part of the issues of subtleties arising have to do with understanding the BPS spectrum -the spectrum of a very special set of objects in the theory which generically are extremely stable (and therefore useful to keep track of when you’re trying to understand the physics)- when the theory takes you to places where the spectrum changes. “Moving across curves of marginal stability” would be the technical term to use, if you wanted to be in the in crowd. Typically, what happens is that some of these BPS states (generically, extended objects or “branes” of various types… see several earlier posts of mine for what branes are) are in fact bound states of smaller objects (other types of brane), which fall apart in certain regimes, thus changing the spectrum of what BPS states you thought you had available to you. Getting the count right is really crucial in understanding the big picture of what is going on with the conjecture.

Continue reading ‘At The Other Monastery’

This will be familiar to anyone who reads John Baez’s This Week’s Finds in Mathematical Physics, but I can’t help but show these lovely exact solutions to the gravitational N-body problem. This one is beautiful in its simplicity: twenty-one point masses moving around in a figure-8.

The N-body problem is one of the most famous, and easily stated, problems in mathematical physics: find exact solutions to point masses moving under their mutual Newtonian gravitational forces (i.e. the inverse-square law). For N=2 the complete set of solutions is straightforward and has been known for a long time — each body moves in a conic section (circle, ellipse, parabola or hyperbola) around the center of mass. In fact, Kepler found the solution even before Newton came up with the problem!

But let N=3 and chaos breaks loose, quite literally. For a long time people recognized that the motion of three gravitating bodies would be a difficult problem, but there were hopes to at least characterize the kinds of solutions that might exist (even if we couldn’t write down the solutions explicitly). It became a celebrated goal for mathematical physicists, and the very amusing story behind how it was resolved is related in Peter Galison’s book Einstein’s Clocks and Poincare’s Maps. In 1885, a mathematical competition was announced in honor of the 60th birthday of King Oscar II of Sweden, and the three-body problem was one of the questions. (Feel free to muse about the likelihood of the birthday of any contemporary world leader being celebrated by mathematical competitions.) Henri Poincare was a favorite to win the prize, and he submitted an essay that demonstrated the stability of planetary motions in the three-body problem (actually the “restricted” problem, in which one test body moves in the gravitational field generated by two others). In other words, without knowing the exact solutions, we could at least be confident that the orbits wouldn’t go crazy; more technically, solutions starting with very similar initial conditions would give very similar orbits. Poincare’s work was hailed as brilliant, and he was awarded the prize.

But as his essay was being prepared for publication in Acta Mathematica, a couple of tiny problems were pointed out by Edvard Phragmen, a Swedish mathematician who was an assistant editor at the journal. Continue reading ‘N Bodies’

This painting by Dawn Meson depicts Kaluza Klein states from extra dimensions. Dawn Meson lives in the Bay Area and given her name is clearly destined to paint particle physics themes! Several of her paintings adorn the hallways here at SLAC (alas, none on the theory group floor); this one is my favorite.