Work Habits of the Easily Frustrated
Back when I was a post-doc, I used to have the occasional arguments with my boss regarding the proper approach to intractable problems. He was firmly of the opinion that there was no problem that couldn't be solved by just staying in the lab continuously until it was solved, while I tended to disagree. After a few hours of futility, my brain just shuts down, and I stop being able to think of new approaches to the problem. Once that happens, unless the problem in question can be solved by rote, mechanical manipulations, I'm useless.
I've always found that when I'm stuck on some problem that just won't give, the best course of action is to set it aside for a few hours, and start fresh after a break. At least half of the major lab problems that got solved in my post-doc days were solved when the solution occurred to me on the walk home after shutting down for the night, or on the walk back in the next morning. Most of the time, I wanted to kick myself for having missed something that seemed so incredibly obvious after a few hours of sleep.
I was reminded of this this morning, when I thought of the solutions to two different problems that were plaguing me yesterday over my morning blogroll. One of them was experimental, having to do with the strange grounding habits of the data acquisition board one of my students is setting up. The other was theoretical, having to do with some number crunching I've been doing (at home, due to software licensing issues), and involved simulated Fabry-Perot transmission peaks ending up in strange places. Both were nagging me all last evening, and continued to bug me this morning. Then, somewhere between Crooked Timber and Making Light, the two solutions hit me almost simulataneously: The experimental problem could be easily resolved by grounding one of the other inputs, while the theoretical problem was the result of two factor-of-two errors that nearly offset one another.
(Vaguely Relevant Geek Joke: A colleague mentioned seeing an oral exam in which a student worked through a derivation on the chalkboard, and ended up with has answer having the wrong sign. "I seem to have made a sign error," he said. "No," corrected one of his professors, "you seem to have made an odd number of sign errors.")
A quick trip into the lab, and a strategically placed 50-ohm terminator fixed the one, and a half-hour of number crunching at home resolved the other. Which leaves me the afternoon free, to spend kicking myself for not seeing the answers sooner...
Making Quarks Out of Nothing at All
In a previous post, I gave a quick outline of the Standard Model of elementary particles, and how it relates to the recent discovery of a new particle. The best illustration of the process is probably the picture on the Ohio University reference page: A deuterium nucleus (one proton and one neutron) is sitting there, minding its own business, when a photon comes along and whacks into it. After being hit by the photon, a bunch of other stuff comes out, including the new "pentaquark" particle.
In terms of the basic quark model set out in the previous post, this seems a little weird. You start out with a collection of six quarks, bound into two nucleons: the neutron is two "down"s and an "up," while the proton is two "up"s and a "down." What you get out is, well strange: you've still got one proton, but now there's also a negative kaon, consisting of a "strange" and an "anti-up" stuck together, and this "pentaquark," containing two "up," two "down," and one "anti-strange." That's a total of four more quarks than you started with. Where did the rest of them come from?
The answer to that question drags in "The World's Most Famous Equation", Einstein's E = m c2 (E is the "Rest energy" of a particle, "m" is the mass, and "c" is the speed of light). This equation tells us that mass and energy are the same thing-- particles have energy just by virtue of having mass, while a sufficiently large quantity of energy can be treated as mass. It's what gives us atomic bombs, and nuclear power, and explains why the stars shine, and why weird things happen in particle physics experiments.
The equivalence of energy and mass is a surprising result, because it runs counter to our everyday experience. You don't think of moving objects as gaining some extra heft by virtue of moving-- if anything, you expect people who move around a lot to lose mass as a result...
The reason for this is that c is a tremendously large number-- 300,000,000 m/s-- so the mass gain due to everyday sorts of motions is negligible. An 80-kg man jogging along at 5 m/s has kinetic energy which would be equivalent to (roughly) 10-14 kg of mass, or 0.00000000001 grams. That's a few thousand times less than the mass of a single cell. It takes a phenomenal amount of energy to add up to a measurable amount of mass.
Of course, when you get down to the subatomic scale, the masses are very small-- A proton has a rest mass of 1.672 10-27 kg (roughly 10-7 joules of energy, or the amount of kinetic energy associated with an ant scurrying along the floor), and its component quarks have even lower masses. It's not exactly easy to generate enough energy to add up to a couple of quark masses, but it's nowhere near as difficult as trying to generate enough to add up to a macroscopic amount of stuff.
The equivalence of mass and energy means that, under the right circumstances, you can switch back and forth from one to the other. Anybody who's read any science fiction is probably aware of one direction of switch: If you bring together a normal particle and it's antimatter complement (a proton and an anti-proton, for example), they'll annihilate one another, and convert their mass entirely into energy (usually in the form of photons). If you could do this on a macroscopic scale, it would be a very efficient way of generating a lot of energy very quickly, which is why SF novels and TV shows tend to power their black-box stardrives with antimatter reactors of some kind.
What's less well known is that the opposite reaction can also occur. If you have a photon with a high enough energy, it can spontaneously create mass, in the form of a matter-antimatter pair. The photon energy required is equal to the mass of two particles of whatever variety you're after, which typically puts these photons well into the gamma ray range. In terms of the quantities people usually think about when dealing with light, these are photons with very short wavelengths-- the photon needed to produce an electron-positron pair has a wavelength that's roughly 1/500,000th of visible light.
(Once you get into this kind of range, the wavelengths are much smaller than the size of a single atom, so it doesn't really make sense to talk about them in wave terms. For that reason, in the gamma-ray region of the electromagnetic spectrum, people stop talking about wave properties, and just refer to the energy content of the photons-- "1 MeV" photons, for example (1 MeV = 1,000,000 eV, where an eV ("electron volt") is the energy a single electron gets from accelerating through a potential of one volt). Due to the equivalence of mass and energy, it's also conventional to give particle masses in terms of the energy content, so an electron is said to have a mass of "0.511 MeV/c2," meaning that the mass is such that multiplying by c2 would give you 511,000 eV of energy.)
The bigger the mass of the particle, the bigger the energy needed to produce a particle-antiparticle pair. Electrons are the easiest particles to generate, and the energies go up from there. Quarks require more energy to create than electrons do, and different types of quarks require different amounts of energy, as they have different masses. As noted in the comments to the previous post, particle mass is what distinguishes the different "generations" of particles. "Generation I" particles like "up" and "down" quarks have lighter masses than "strange" and "charm" quarks ("generation II"), which are lighter than "top" and "bottom" quarks ("generation III"). This is also what gives you the prohibition against moving up in generations-- you can split a heavy particle into lighter ones, but you can't go from a light particle to a heavy one without dumping in a lot of energy.
But once you get enough energy together, you can convert that energy into particle-antiparticle pairs, essentially creating new stuff out of thin air. This is the whole idea behind particle accelerators-- if you crank a beam of protons up to very close to the speed of light, you give those particles a fantastic amount of energy. When they slam into something, that kinetic energy is released, and can be converted into new kinds of particles. This is how all the particles other than protons, neutrons, and electrons were detected.
The pair creation effect is also why single quarks are never seen-- if you start with two quarks that are stuck together, you need to put energy into the system in order to try to pull them apart. The farther apart they get, the more energy they acquire (think of it as sort of like stretching a spring-- the more you stretch it, the harder you need to pull), until there's enough energy in the system to create a new quark-anti-quark pair. When that happens, two new particles pop into existence, and you end up with two new pairs of quarks. The harder you try to pull them apart, the heavier the new particles that pop into existence, but you can never pull a single quark out of a pair.
So, bringing this all the way back around to answer the question that started this post off, the "pentaquark" is formed by creating particles out of thin air (improbable as that may seem). A deuterium nucleus is sitting there, mining its own business, when a hugely energetic photon slams into it. The photon energy (and some of the energy that was holding the deuterium nucleus and its components together) goes into creating four new quarks out of nothing: an "up" and an "anti-up", and a "strange" and an "anti-strange." The "strange" and the "anti-up" pair off, and leave as a kaon, while the "anti-strange" and the "up" join up with the three quarks that used to be the neutron, and form the "pentaquark" (which later decays into a neutron and another kaon).
Put that way, it almost sounds easy... Of course, the tricky part is figuring out just what happened in the incredibly short period of time it takes those particles to pop into existence, fly apart, and decay into other things. But that will wait for another post.
While I'm noting posts at other blogs (I'll get back to the physics stuff-- dehydration after a fierce round of lunchtime basketball in a gym without air conditioning wiped me out yesterday, so part 2 will be delayed), Derek Lowe has a post about absurd chemical labelling requirements that strikes a chord.
We've been subjected to a chemical safety kick at work, recently, owing to an EPA decision to start cracking down on colleges and universities. While I'm not a chemist, we do keep bottles of solvents (acetone and methanol, mostly) in the optics labs, for the purpose of cleaning optics, so I've been peripherally involved in this mess.
This has led to the discovery of insane rules like the prohibition on keeping methanol in a squirt bottle. That tiny little nozzle through which the liquid will emerge when you squeeze the bottle? That makes it an "open container," through which the solvent can escape, a few molecules at a time. That's a safety hazard, apparently, so I had to buy a bunch of screw-top bottles for my solvents.
(On the positive side, though, it did motivate me to get rid of the large bottle of cyanide that the previous owner of the lab had left in a cabinet in the back of the room, thus dramatically reducing my chances of ending up as a Nero Wolfe villain...)
My favorite chemical safety ritual was the annual inspection at NIST, back when I worked there. Again, we didn't keep all that many chemicals around (acetone, methanol, ethanol, some alkali metals, and some laser dyes), but what was there was subject to very strict labelling rules. Highly toxic things had red labels ("Danger!"), sort-of-toxic things had yellow labels ("Caution!") and exceptionally flammable materials got orange labels ("Explosion Hazard!").
Best of all, though, were the green labels for bottles of not-particularly-toxic chemicals. These labels were mandatory, and we got lectured every year about the need to apply them. The text on the mandatory green labels? "Protective Labelling Not Required."
Chris "Junius" Bertram, Henry and Maria "Gallowglass" Farrell, Kieran "Kieran Healy" Healy, and Brian "Not Previously On My Blogroll" Weatherson have teamed up to start a new group weblog, Crooked Timber. I'm not sure what advantages the group format offers, but it ought to be an interesting place.
If you can't get enough Harry Potter, make sure to read this post about an A. S. Byatt article about the books. Especially make sure to scroll down and read Ruth Feingold's comment-- there's more heat than light in most of the comments, and a whole lot of people missing the actual point of the article, but she makes some excellent points.
A few days ago, I linked to a news story about this paper in Physical Review Letters describing the discovery of a new type of subatomic particle. The abstract of the paper is, of course, almost perfectly opaque, but you can get a better idea of what this is all about from news stories-- see, for example, the Jefferson Lab news release, or this story from Nature, which provides a fairly succinct summary of the whole thing:
A class of subatomic particle, consisting of five quarks rather than the normal two or three, has been discovered by physicists in Japan. Theorists had expected combinations of four or more to exist, but experiments over the past 30 years had failed to detect them.
This is a big story, but a tough one to explain in general terms. I'm going to attempt it anyway, as much for my own benefit as anything else-- my understanding of particle physics barely passes the undergraduate level, and attempting to write a coherent explanation of this experiment will force me to get a slightly better grip on the material. The best way to learn a subject is to try to teach it to others, and all that.
The biggest problem faced in trying to explain the importance of a new type of subatomic particle is the fact that we've already got so many of the damned things. Enrico Fermi famously remarked "If I could remember the names of all these particles, I'd be a botanist," and approached from the top down, there's an unmistakable similarity. You've got the familiar protons, neutrons, and electrons, plus a dizzying array of other particles-- muons, pions, kaons, etas, lambdas, sigmas, W's, Z's, and a bunch of others. The textbook I used for modern physics last fall lists 37 distinct particle types, and that doesn't count anti-particles. These dozens of particles are then divided into various groups (mesons, hadrons, bosons, leptons) using a rather mysterious set of rules.
On top of that, all these things decay into other forms with frightening rapidity, so that a neutron can decay into a proton, an electron, and a neutrino, while a pion turns into a muon and a neutrino, and a muon into an electron and a couple of neutrinos. There are rules about what reactions are allowed (kaons can decay into pions, but pions can't become protons), which things interact with what other things, and the whole structure seems frighteningly arbitrary. It's a huge mess.
What ties this all together for physicists is a picture called the "Standard Model," which is appealing because it allows everything to be tied together into a single spiffy chart. (This particular version is a little out of date, but it has the virtue of being more compact than the big poster version...) Clears everything up, doesn't it?
The Standard Model says that the entire universe is made up of three classes of particles: quarks, leptons, and bosons (which serve as force carriers). Everything else is some combination of these things. For the moment, the force bosons (the rightmost column of the simple chart) don't really matter-- we'll come back to those later on.
Leptons are probably the easiest group of particles to explain, as they're the only kind of fundamental particles we see directly. Electrons are leptons, and so are neutrinos. There are two other electron-like leptons: muons and tau particles. They behave sort of like heavy electrons, only they're unstable, and quickly decay into other particles (muons into electrons and neutrinos, taus into muons and neutrinos).
For arcane reasons, there are also three types of neutrinos ("electron," "muon," and "tau" neutrinos), all of which have extremely small masses, and hardly interact with anything. They've been the subject of much theoretical and experimental interest, and have even inspired the odd bit of doggerel. The six leptons appear in the bottom two rows of the chart linked above.
The third group of fundamental particles are the quarks (the top two rows of the chart linked above). In some sense, these are probably the most important particles in the Standard Model, as they're the ingredients making up protons and neutrons. Quarks are never seen alone, but always come clumped together in the form of other particles-- the ridiculous array of subatomic particles alluded to above are mostly different combinations of quarks.
There are six types of quarks, which matches the six types of leptons, and they're usually grouped into three pairs with related names. The most common are "up" and "down"-- an "up" quark has two thirds of a (positive) electron charge, while a "down" quark has one-third of a (negative) electron charge. Two "up"s and a "down" get you a proton (+1 charge), while two "down"s and an "up" make a neutron (no electric charge).
The other two pairs of quarks-- "strange" and "charm", and "top" and "bottom"-- are unstable, decaying into combinations of "up" and "down" quarks and anti-quarks (all the particles come in both matter and anti-matter varieties, so a proton is two "up"s and a "down," while an anti-proton is two "anti-up"s and an "anti-down") in very short order. A "strange" quark, for example, will decay into an "up", an "anti-up", and a "down."
Once you've got the quark model, all the baffling classifications of particle physics start to make sense. The particle classifications are based on how many quarks a particle contains-- "leptons" are particles which aren't quarks at all, while "hadrons" (the source of many a giggle-inducing typo) are particles made up of some combination of quarks. "Hadrons" are further divided into "baryons" and "mesons"-- loosely speaking, "baryons" are particles made up of three quarks (protons and neutrons are baryons), while "mesons" contain only two quarks (one quark, and one anti-quark, actually).
Putting together the six quarks and six leptons, a hierarchy of "generations" is quickly established. Ordinary matter is made up of "generation I" particles: "up" and "down" quarks, and electrons. The other two "generations" are unstable, and decay into "first generation" particles. Tau particles (generation III) can decay into muons (generation II) and thence into electrons (generation I), which are stable. "Top" quarks (generation III) can decay into "strange" and "charm" quarks (generation II), which decay into "up" and "down" quarks (generation I), which are stable. Under ordinary circumstances, there's no way to move up a generation.
All of this together explains the various decays-- what you end up with depends on what you start with. A pion, which starts out with two quarks ("up" and "anti-down", or "down" and "anti-up") can't turn into a proton, which has three quarks. If you start with something containing a "strange" quark (a kaon, say), it will decay into something involving "up" and "down" quarks, but something that starts out with only "up" and "down" quarks can never turn into a kaon.
You can also change a quark from one type to its complement (within the same generation) by emitting some leptons (for example, a neutron decays into a proton when one of the "down" quarks turns into an "up," plus an electron and a neutrino), which accounts for the rest of the rules regarding particle decays. In general, particles will keep decaying until there's nothing left but electrons, neutrinos, and up and down quarks.
Got that? It sounds horrifically complicated, but believe me, it's better than what went before. I've glossed over some of the rules governing decay possibilities, but that's as clear an outline of the Standard Model as I can manage. If you want another take on the whole thing, I recommend checking out The Particle Adventure, which goes over the all this stuff in slightly more detail, with fancy graphics.
So how does the new experiment fit into all this?
To this point, all the hadrons that have been observed have contained either two or three quarks. There are theories to explain why single quarks are never seen, but there's never been any obvious reason why particles containing four or five quarks can't exist. People have been looking for four- and five-quark particles for a long time now (thirty-odd years), but they turn out to be hard to find. The new "pentaquark" is the first such object observed, and consists of two "up"s, two "down"s and an "anti-strange" (there's still some debate, though, about whether it's really a single particle, or just a baryon and a meson orbiting one another at a very small separation).
Of course, a reasonable question to ask would be "How did they make this widget in the first place, starting with ordinary matter, containing only 'up' and 'down' quarks and electrons?" The answer to that question takes us into really strange territory, but will have to wait for another post.
What's Opera, Doc?
Mike Kozlowski speculates about the problems of classical music, and decides that the lack of descriptive titles is responsible for classical music being "less popular than it ought to be." I agree that it's hard to keep classical pieces straight, but I would attribute it more to the general lack of lyrics. If a song's got words, I can use those to provide a memory hook (even if the title isn't actually in the song), but instrumental pieces are a little more slippery.
It's also vastly more difficult to ask other people for the names of instrumental pieces. If a song has lyrics, you can refer to them without having to turn a title request into performance art: "What's the name of that song, the up-tempo pop-punk one that goes into 'Crimson and Clover' at the end?" (Answer: "A Praise Chorus.") With classical music, you're forced to sing the tune, or, worse, try to translate it into ASCII, which is just hopeless.
Titles, descriptive or otherwise, are no real help. Mike lists the pieces excerpted for Fantasia:
The Nutcracker, The Sorcerer's Apprentice, The Rite of Spring, Night on Bald Mountain, Ave Maria, Dance of the Hours, Toccata and Fugue in D Minor, and Beethoven's Symphony no. 6 (Pastoral)
and claims this as evidence of the innate superiority of descriptive titles. The problem is, while they do have titles rather than numbers, I still couldn't begin to match title to music for most of those. I've heard all those pieces dozens of times, I'm sure, but to the extent that I could identify any of them, it's because they were in Fantasia, and have become associated with the images. In much the same way that "Ride of the Valkyries" is inextricably bound up with either "Apocalypse Now" or "Kill the Wabbit"...
(There was a great SNL bit some years back with Jeremy Irons narrating a commercial for "Looney Tunes Classics," a collection of great classical works associated with Warner Brothers cartoons. Sadly, the transcript isn't available, but in Goggling to try to find it, I found a list of arts grants that included:
"Tunes and 'Toons," Harvard Pops Orchestra, Thomas Lue '01: $300 OFA Grant for the performance of classical music made famous by cartoons. The first half of the program will feature performances of The Barber of Seville, Largo al Factotum, the Loony Tunes Overture, and other cartoon music. The second half will feature the orchestral accompaniment to the Bugs Bunny cartoon, What's Opera Doc?
Once again, comedy is ahead of the curve...)
But then, I'm no great fan of classical music. I often regret this, as it removes a huge range of conversation topics with faculty colleagues-- most of whom are only dimly aware of the last thirty-odd years of popular music. I try to get past this every now and again, but run into the same two problems every time: 1) I don't really know where to start, given the huge range of music, and the vast number of duplicate recordings, and 2) Whenever I just flip on the classical channel on the radio or digital cable, I make it through about ten minutes before I decide I really want to be doing something else.
As a highly educated person, I feel vaguely guilty about this. There are hundreds of years worth of classical composition out there, on themes spanning the whole of human experience, while I have an obsessive knowledge of the last forty-odd years worth of songs about sex, drugs, cars, and people having sex in cars while on drugs. It doesn't help that there's a long tradition of linkage between science and math and classical music (Goedel, Escher Bach being the best-known example)-- I feel sort of like I'm letting the side down by not enjoying Bach and Mozart more.
Then again, most classical music (that I've heard) just bores me to tears. I'll probably make a few more attempts at it, but ultimately, life's just too short to spend trying to learn to like something out of a vague sense of obligation.