Miscellany

Just so we don’t get too uppity, keep in mind that the subject matter of the previous two posts might be completely discredited within a few years, due to the ceaseless efforts of the supernatural movement. (Link from Panda’s Thumb.)

Wow, with a title like that, I should just end the post right now; it’s going to be all downhill from there. You could make a lot of money from a book with a title like that. Or did Deepak Chopra already write it?

Okay, I’m delaying the inevitable. I was hoping today to write about quantum gravity, after once and for all explaining the mysteries of quantum mechanics in the previous post. But I carelessly brought up the issue of the interpretation of the theory, which deserves more nuanced discussion. Not that I’m qualified to give it. You can read something about the issues at Michael Nielsen’s blog (two posts).

But I would like to at least say some words about what I think the issue is, even if I don’t want to make a strong case for any particular resolution. There certainly is an “issue,” which may or may not be a “problem.”

Every scientific theory comes in two pieces: a formal structure, and an “interpretation” that maps this structure onto what we see. Usually the interpretation is perfectly obvious, and we don’t worry about it. But in quantum mechanics, what we see is not what there is, so we need to think more deeply. What is it that really happens when we do a measurement? For example, consider an unstable nucleus. Its wavefunction is a combination of two classical possibilities: the nucleus has already decayed, or it hasn’t. But when we observe it, we don’t see this superposition of possibilities; we see that it has either decayed or not. What really happens when we look at it? The Copenhagen interpretation says that the wavefunction collapses to the possibility that we have observed, while the many-worlds interpretation says that the observer+nucleus system evolves smoothly to a superposition of “nucleus decayed, observer saw decay” and “nucleus intact, observer did not see decay.”

The MW interpretation is nice because everything is smooth evolution obeying the laws of physics (in this case the Schrodinger equation). But it’s tricky because, since “I” actually do or do not see the nucleus decay, I need to identify “I” with a certain “branch of the wavefunction,” not with the entire wavefunction. This is hard to do, both technically and conceptually. (“What does “I” mean? How does this branching process take place?)

I’m in the camp that says it’s fair to call this a philosophy problem, not a physics problem. But it’s a perfectly legitimate philosophy problem, not a silly waste of time. Fortunately for physicists, we don’t need to know the answer to make progress on the questions we really care about. (Apparently, anyway; statements like that have a way of showing up in future textbooks as evidence of how misguided past generations were.)

The joint is jumping over at Peter Woit’s Blog, even though his is even newer than mine. (Blog statistics are just what academia needs: another quantitatively precise and wholly meaningless measure of worth.) I suspect it’s because Peter tends to say provocative and controversial things that people readily disagree with (about emotional topics like, say, string theory), whereas I am so sweetly reasonable that everyone cannot help but agree with everything I say.

Peter did ask a question to cosmologists that I didn’t get to, so I thought I should take a swing: “What is ‘string cosmology’?” If the response were to make any sense, I should explain something about string theory, which means explaining something about quantum gravity, which means explaining something about ‘quantum’ even without gravity. I don’t know how far we’ll get, but explaining quantum mechanics is a worthy goal in its own right.

Quantum mechanics (QM) is one of the top two most profound ideas in the history of physics. The other member of the top two is classical mechanics, the system developed by Galileo and Newton and their friends, which was eventually superseded by quantum mechanics. (The ordering of the top two is tricky, and there’s no consensus on number three.) Nevertheless, QM is consistently misrepresented (or even misunderstood) by professional physicists, and its basic ideas aren’t nearly as clear to people on the street as they should be.

Classical mechanics is simple. For any physical system (balls on a billiard table, planets moving around the sun, the whole universe) you tell me the “state” that the system is in at some time, and I can use the laws of physics to predict what the state will be at any other time. Specifying the state typically means specifying the positions and velocities of all the components. This kind of system is at the heart of the “clockwork universe” that came out of the Enlightenment.

Quantum mechanics came about in the early 20th century. Surprisingly, the description of classical mechanics in the previous paragraph also applies perfectly well to quantum mechanics: you tell me the state, I’ll use the laws of physics to evolve it forward in time (or backward, for that matter). The crucial difference lies in a feature so profound that it’s hard to conceptualize: in quantum mechanics, what you can see (the observable properties of the system) is related to, but not the same as, what there really is.

So, for a single particle, classical mechanics tells us that it has a position and a velocity. The lesson of quantum mechanics is sometimes garbled into the idea that “we can’t be perfectly certain where the particle is or how fast it is moving.” The truth is more profound: there is no such thing as “where the particle is,” or “how fast it is moving.” Instead, there is something called the wavefunction that describes the state of the system. The wavefunction answers the question, “when we observe the system, what is the probability we will observe it to have a given position or velocity?” In classical mechanics we can observe anything we want about the state, but in quantum mechanics we can’t, we can only predict probabilities for what might happen when we make an observation.

What actually happens when we make an observation is the source of great philosophical angst. The old “Copenhagen interpretation” held that the wave function changed instantaneously and non-locally, into a state that was concentrated around the result of our observation. The newer (but still pretty venerable) “many-worlds interpretation” says that we the observers are also described by wave functions, and the measurement process mixes up our wave function with that of the thing we’re looking at in such a way that we only ever experience unique outcomes for observations, even though everything is evolving smoothly. As crazy as it sounds, many working physicists buy into the many-worlds theory (and, like approval for gay marriage, there is a significant demographic slant, in which younger people are more open).

Quantum mechanics is not so much a theory as it is a framework in which we can propose all sorts of specific theories. The most empirically successful are quantum field theories, in which the elements of our physical reality are fields defined on spacetime (quantities that take on values at every point, like an electric field). In quantum field theories, the actual field values are one of these unobservable things; what we can actually see is discrete excitations of the fields that we call “particles.” Quantum field theory successfully describes every experiment ever performed and every phenomenon ever observed, with one glaring exception: gravity. For a force that is so important, it’s truly embarrassing that we can’t fit it into our favorite framework. That’s why so many physicists think that the search for a consistent quantum theory of gravity is so interesting and vital.

P.S. (When reading Peter’s most recent post, please keep in mind the date posted.)

This quarter I don’t get to moonlight in the humanities; I actually have to teach a physics course. But it’s a fun one: Spacetime and Black Holes, an introduction to general relativity for undergraduates. GR is Einstein’s theory of gravity; it can be summed up in the simple statement “Gravity is the curvature of spacetime.” It plays a crucial role in understanding black holes and neutron stars, the big bang and the accelerating universe, gravitational waves, and every attempt to quantize gravity.

Teaching GR to undergraduates is still unusual; at many places it isn’t even a core graduate course. (Of course, these days they’re teaching undergraduates string theory.) For a long time GR was somewhat outside the main action of physics, since our experiments didn’t probe into regimes where it was important. That’s certainly changed in recent years. GR also has something of a reputation for being difficult, which is quite untrue; it’s intrinsically very straightforward, but the relevant mathematics (tensor analysis, differential geometry) is just so different than that used in other areas of physics that it seems like a big investment to learn.

This quarter I’ll be using Jim Hartle’s new book, which is a fantastically useful text. He approaches the subject with a physics-first attitude that allows the student to get to the fun parts without spending months learning formalism. (If they want to do that, they should take the graduate course and buy my book.) We just state without demonstration what the spacetime around a star or black hole looks like, and then dive right in to understanding its features. I’ve never actually taught it this way before, so it’s something of an experiment. The worry is that the students will fear that they’re getting a watered-down version of the true story, which really isn’t the case. By the end they’ll get the whole shootin’ match. If I would just quit blogging and write my lecture, anyway.

The Bush administration is zealous about so many nutty things it’s hard to keep track. Missile defense (“Star Wars” and its ilk) is one of them I had almost forgotten about. Apparently they hope to spend over $10 billion per year to develop a defense that doesn’t work against an enemy that doesn’t really exist.

Physicists have long known that the missile-defense plans are mostly scams; they are wildly optimistic, overhyped, undertested, and usually misrepresented. It’s just hard to shoot down a bullet with another bullet; and when the incoming bullet can use countermeasures, it’s practically impossible. Now a group of generals and admirals is saying the same thing: this is a colossal waste of money, let’s spend that money doing something useful like, say, protecting against terrorism. The military experts have an uphill battle; they don’t appreciate that the administration finds the battle against terror kind of boring, and is easily distracted by shiny objects.

Tomorrow Brian Greene will be visiting Chicago as part of a book tour. Brian is an accomplished string theorist, but best known as the author of the popular book The Elegant Universe, which last year was made into a NOVA special by PBS. Brian’s new book is The Fabric of the Cosmos, which I have bought but not yet had a chance to look at, although I’m sure it’s quite good. (Full disclosure: I know Brian a little bit, and my name even appears [misspelled] in the acknowledgments section of his book.) One of the reasons his books sell so many copies is that he really puts a fantastic amount of work into explaining recondite physics ideas in a way anyone can understand.

The reaction of professional scientists to popularization is an interesting and disturbing one. You would think that scientists would be overjoyed when someone with talent and charisma takes the time to explain their work to a wider audience. It’s at the very least good for the field, and one could argue that it’s the entire point of research in areas like cosmology and fundamental physics that are far removed from any imagined technological application. The reason we are paid to think about string theory and dark energy is because people are generally curious about the deep questions from which they originate, and it only makes sense that we would make an effort to tell people what we’ve found.

I vividly remember an incident in a California bookstore soon after the Elegant Universe TV special, late last year. There was a big pile of copies of Brian’s book, and the pile was noticed by a boy who couldn’t have been more than ten years old. He exclaimed to his mother, standing nearby:

“Mom, mom, look, it’s the Elegant Universe book! We’ve got to get this for Dad!”

“Sure. What is the book about, anyway?”

“It’s about string theory! He’ll love it!”

Any professional physicist should be thrilled to think that ten-year-olds are getting excited about science this way.

But two things get in the way: jealousy and dignity. The jealousy is obvious; researchers don’t necessarily like it when they see their colleagues spend time in the spotlight. They could imagine themselves there, or wonder why their research isn’t featured more prominently. I’ve heard extremely famous scientists complain about the NOVA series in ways that were couched in generalities, but amounted to whining about the lack of credit given to them (or their close friends). In academia, of course, attribution of credit for work that you’ve done is the coin of the realm, and scientists naively expect that the same standards should hold in popular media. So anyone who seems to be appearing in newspapers and TV more often than they should tends to rile up their colleagues, who can respond in remarkably petty ways.

The dignity issue is trickier. Effective pedagogy sometimes calls for dramatic flourishes, or for whiz-bang special effects, or for highlighting aspects of science that might not be most important to the scientists themselves. Stooping to such levels can elicit disdain from your colleagues, often quite explicitly. I remember a workshop on dealing with the media at a meeting of Packard Fellows, supposedly some of the best young scientists around. When asked what concerns they had, a large number said they wouldn’t think of talking to journalists, for fear that their senior colleagues would think they weren’t serious scientists. It’s part of a self-destructive attitude that scientists are going to have to get over if they want to continue to ask for public money, not to mention fulfill their obligation to share their discoveries with the wider world.

I just noticed that the amazon.com page for The Fabric of Spacetime says that six different people recommended The Privileged Planet as additional reading. A brief glance reveals that this book is ridiculous intelligent-design propaganda. Obviously someone had the bright idea of using amazon.com recommendations as a way of leading the unwary away from evil secular physics and toward the light.

P.S.: This blog owes its title indirectly to the Elegant Universe. The idea was, only a string theorist could think that our universe was “elegant,” and only because they never went out and actually looked at it. Get it?

I finally had a chance to see The Fog of War, the Errol Morris documentary about Robert McNamara, Secretary of Defense during the Kennedy and (much of the) Johnson administrations. It was a great film, the kind you could talk about endlessly. I’ll try not to do that, but a few things are irresistible.

First, the obvious parallels with our current mess in Iraq. McNamara was Defense Secretary during the escalation of the Vietnam war, so the connections are inevitable (and have been commented to death already). One does wonder what Rumsfeld would make of the movie. The most unbelievable moment to me was the account of a 1995 meeting between McNamara and the former Vietnamese foreign minister, to discuss what lessons could be learned. The minister explained to McNamara that the conflict was a civil war, that they were historic enemies of the Chinese, and that the US could not have “won” because the Vietnamese were fighting against a colonial power and would never give up. Amazingly, McNamara claimed to be shocked by these revelations (in 1995!). Cluelessness about the culture we are interfering with must be one of the most common themes of US intervention. That’s the one very obvious connection to the Iraq adventure, which in many ways is a very different story.

Second, although Vietnam dominated the movie, the opening bit about the Cuban Missile Crisis was the most gripping. Given the insanity on all sides, it’s miraculous that the world escaped without a full-blown nuclear war. McNamara quotes Castro as saying that if the US had invaded, he would have launched all the nuclear weapons on the island, knowing full well that the consequence would have been complete annihilation of Cuba. He also quotes our very own Gen. Curtis LeMay, who thought we should quickly launch an all-out pre-emptive strike against the Soviet Union before they could catch up to our nuclear arsenal. As I said, miraculous.

Third, and perhaps the only point that hasn’t already been beaten to death, the movie rehearsed a tired critique of the concept of “rationality.” A common criticism of McNamara when he was Defense Secretary, which is trotted out essentially unmodified in the movie, is that he and his staff (the “best and the brightest”) were super-intelligent and supremely rational, yet continued to get us into all sorts of trouble. Clearly, we conclude, this rationality stuff isn’t all it’s cracked up to be. Well, rubbish. Rationality is never to blame for bad decisions, any more than arithmetic is to blame when you can’t pay your bills. Rationality can tell you how to achieve certain goals through certain actions. If the result turns out to be a mess, there are two possibilities: the goals weren’t the right ones, or your rationality was simply faulty. McNamara calls Castro “rational,” just before he relates the anecdote that Castro was willing to have Cuba be completely destroyed. Sorry, the mistake there is not an overzealous application of instrumental reason; it’s just being stupid. Rationality doesn’t tell you that preventing the fall of dominoes in Southeast Asia is worth any possible cost in human lives; your nonsensical value system is telling you that, and rationality simply allows you to implement this craziness efficiently.

I’m sure that, if the situation in the Middle East deteriorates (even further), pundits will point to Rumsfeld and his crew and accuse them of being too rational, not sensitive enough to human needs and foibles, as if those qualities were somehow in opposition. This history-repeating-itself thing grows tiresome awfully fast.

By popular demand, I am forced to reveal the recipe alluded to below for burnt caramel ice cream. I found this recipe on the web years ago, and had lost track of where it came from. But a quick googling led me to this page, which leads me to believe that the original source was a small book called Wild About Ice Cream by Sue Spitler. Which apparently costs $1.50, which is not as cheap as getting things for free on the web but is pretty good. Anyway:

BURNT CARAMEL ICE CREAM

=======================

(Yields: 1 Quart or 950 ml)

Ingredients:

————

1 C (190 g) granulated sugar

1 C (240 ml) hot water

4 eggs

1/2 C (40g) powdered sugar

2 C (450 ml) heavy cream

1 tsp vanilla extract

Instructions:

————-

Heat granulated sugar and 1/4 C (60 ml) of the water in a large skillet on medium high heat until the sugar melts and boils, stirring occasionally. (Water will essentially boil away.)

Boil until mixture is a dark brown; remove from heat. Gradually stir in remaining 3/4 C (180 ml) water.

Cool to room temperature and set aside.

Beat eggs in a medium bowl until thick and lemon colored; gradually beat in powdered sugar.

Stir in cream and vanilla; stir in the caramel mixture. Chill. Freeze in an ice cream machine according to manufacturers directions.

(Bonus tip from long experience: The secret to great home-made ice cream is to keep all the ingredients as cold as possible, at least just before you put them into the ice cream maker. That way the mixture will freeze quicker, preventing ice from crystallizing and giving you a smoother product. Not as rich as Toscannini’s, but surpassing anything outside the Boston area.)

Okay, so let’s say you’re in Chicago. You’re taking the El (the elevated train; in Chicago the weather is always perfect, so there’s no reason to put public transportation underground as in climates that aren’t as blessed as we are). You get off at some stop, and the question hits you: What blogs are nearby? You can get the answers from Paul Goyette’s Chicago blog map, organized by El stop. There are 131 blogs as of this writing, although I’m sure there are many more to be dug up and linked to.

Now let’s imagine instead that you’re morbidly curious about the political-donation habits of important people (or unimportant ones). Just check out the fundrace.org neighbor search. For example, the President’s dad has donated to his pride and joy, just as you would expect. Less obviously, someone by the name of Howard Dean has donated to Bush as well. Or maybe that makes perfect sense.

Bill Gates has donated to Bush, but leading string theorist Ed Witten has donated to Clark and Edwards, and he’s smarter. Not at picking winners, obviously, but you know what I mean.

(Game inspired by Wonkette.)

The Supreme Court is hearing arguments about the Pledge of Allegiance. I think that the “under God” bit is an unconstitutional travesty, but honestly I don’t care too much; there are more important battles to fight. But this did amuse me:

Newdow, 50, held his own under a barrage of fast-paced questions. Chief Justice William Rehnquist threatened to clear the courtroom if spectators applauded Newdow a second time.

Rehnquist had asked what the vote was when the U.S. Congress in 1954 added “under God” to the pledge. The law was an effort to distinguish America’s religious values and heritage from those of communism, which is atheistic.

Newdow replied the vote was unanimous. Rehnquist said that did not sound divisive to him. “That’s only because no atheist can get elected to public office,” Newdow answered, triggering the applause, a rare event in the high court.

The applause must have been good to hear. I’m glad that someone takes this seriously enough to devote some real effort to demonstrating the obvious.

Update: Amanda Butler at Crescat Sententia was in the courtroom for the oral arguments, and gives a detailed account of the proceedings.