The Universe_Leading Scientists Explore the Origin, Mysteries, and Future of the Cosmos

by John Brockman

  The Dirac equation is a more complicated case. Dirac was moved by broad theoretical imperatives. He wanted to make the existing equation for quantum mechanical behavior of electrons—that’s the Schrödinger equation—consistent with special relativity. To do that, he invented a new equation—the Dirac equation—that seemed very strange and problematic, yet undeniably beautiful, when he first found it. That strange equation turned out to require vastly new interpretations of all the symbols in it, interpretations that weren’t anticipated. It led to the prediction of antimatter and the beginnings of quantum field theory. This was another revolution that was, in a sense, conceptually driven. On the other hand, what gave Dirac and others confidence that his equation was on the right track was that it predicted corrections to the behavior of electrons in hydrogen atoms that were very specific and agreed with precision measurements. This support forced them to stick with it and find an interpretation to let it be true. So there was important empirical guidance and encouragement from the start.

  Our foundational work on QCD [quantum chromodynamics] falls in the same pattern. We were led to specific equations by theoretical considerations, but the equations seemed problematic. They were full of particles that aren’t observed—quarks and especially gluons—and didn’t contain any of the particles that are observed! We persisted with them nevertheless, because they explained a few precision measurements, and that persistence eventually paid off.

  In general, as physics has matured in the 20th century, we’ve realized more and more the power of mathematical considerations of consistency and symmetry to dictate the form of physical laws. We can do a lot with less experimental input. Nevertheless the ultimate standard must be getting experimental output: illuminating reality. How far can aesthetics take you? Should you let that be your main guide, or should you try to assemble and do justice to a lot of specific facts? Different people have different styles; some people try to use a lot of facts and extrapolate a little bit; other people try not to use any facts at all and construct a theory that’s so beautiful that it has to be right, and then fill in the facts later. I try to consider both possibilities and see which one is fruitful. What’s been fruitful for me is to take salient experimental facts that are somehow striking, or that seem anomalous—don’t really fit into our understanding of physics—and try to improve the equations to include just those facts.

  My reading of history is that even the greatest advances in physics, when you pick them apart, were always based on a firm empirical foundation and straightening out some anomalies between the existing theoretical framework and some known facts about the world. Certainly QCD was that way; when we developed asymptotic freedom to explain some behaviors of quarks—that they seem to not interact when they’re close together—it seemed inconsistent with quantum field theory, but we were able to push and find very specific quantum field theories in which that behavior was consistent, which essentially solved the problem of the strong interaction and has had many fruitful consequences. Axions also—similar thing—a little anomaly: There’s a quantity that happens to be very small in the world, but our theories don’t explain why it’s small. You can change the theories to make them a little more symmetrical—then we do get zero—but that has other consequences. The existence of these new particles rocks cosmology, and they might be the dark matter—I love that kind of thing.

  String theory is sort of the extreme of non-empirical physics. In fact, its historical origins were based on empirical observations but wrong ones. String theory was originally based on trying to explain the nature of the strong interactions, the fact that hadrons come in big families, and the idea was that they could be modeled as different states of strings that are spinning around or vibrating in different ways. That idea was highly developed in the late ’60s and early ’70s, but we put it out of business with QCD, which is a very different theory that turns out to be the correct theory of the strong interaction.

  But the mathematics that was developed around that wrong idea, amazingly, turned out to contain—if you do things just right, and tune it up—to contain a description of general relativity and at the same time obeys quantum mechanics. This had been one of the great conceptual challenges of 20th-century physics: to combine the two very different-seeming kinds of theories—quantum mechanics, our crowning achievement in understanding the microworld, and general relativity, which was abstracted from the behavior of space and time in the macroworld. Those theories are of a very different nature, and when you try to combine them you find it’s very difficult to make an entirely consistent union of the two. But these evolved string theories seem to do that.

  The problems that arise in making a quantum theory of gravity—unfortunately for theoretical physicists who want to focus on them—really only arise in thought experiments of a very high order: thought experiments involving particles of enormous energies, or the deep interior of black holes, or perhaps the earliest moments of the Big Bang, which we don’t understand very well. All remote from any practical, doable experiments. It’s hard to check the fundamental hypotheses of this kind of idea. The initial hope, when the so-called first string revolution occurred, in the mid-1980s, was that when you actually solved the equations of string theory, you’d find a more or less unique solution, or maybe a handful of solutions, and it would be clear that one of them described the real world.

  From these highly conceptual considerations of what it takes to make a theory of quantum gravity, you would be led “by the way” to things we can access and experiment, and it would describe reality. But as time went on, people found more and more solutions with all kinds of different properties, and that hope—that indirectly by addressing conceptual questions you’d be able to work your way down to description of concrete things about reality—has gotten more and more tenuous. That’s where it stands today.

  My personal style in fundamental physics continues to be opportunistic: To look at the phenomena as they emerge and think about possibilities to beautify the equations that the equations themselves suggest. As I mentioned earlier, I certainly intend to push harder on ideas that I had a long time ago but that still seem promising and still haven’t been exhausted: in supersymmetry and axions and even in additional applications of QCD. I’m also always trying to think of new things. For example, I’ve been thinking about the new possibilities for phenomena that might be associated with this Higgs particle that probably will be discovered at the LHC. I realized something I’d been well aware of at some low level for a long time, but I think now I’ve realized its profound implications, which is that the Higgs particle uniquely opens a window into phenomena that no other particle within the standard model would be sensitive to. If you look at the mathematics of the standard model, you discover there are possibilities for hidden sectors—things that would interact very weakly with the kind of particles we’ve had access to so far but would interact powerfully with the Higgs particles. We’ll be opening that window. Very recently I’ve been trying to see if we can get inflation out of the standard model by having the Higgs particle interact in a slightly nonstandard way with gravity. That seems promising too.

  Most of my bright ideas will turn out to be wrong, but that’s OK. I have fun, and my ego is secure.

  In 1993, the Congress of the United States canceled the SSC project, the Superconducting Super Collider, which was under construction near Waxahachie, Texas. Many years of planning, many careers had been invested in that project, also more than $2 billion had already been put into the construction. All that came out of it was a tunnel from nowhere to nothing. Now it’s 2009, and a roughly equivalent machine, the Large Hadron Collider, will be coming into operation at CERN near Geneva. The United States has some part in that. It has invested half a billion dollars out of the $15 billion total. But it’s a machine that is in Europe, really built by the Europeans; there’s no doubt that they have contributed much more. Of course, the information that comes out will be shared by the entire scientific community. So
the end result, in terms of tangible knowledge, is the same. We avoided spending the extra money. Was that a clever thing to do?

  I don’t think so. Even in the narrowest economic perspective, I think it wasn’t a clever thing to do. Most of the work that went into this $15 billion was local, locally subcontracted within Europe. It went directly into the economies involved, and furthermore into dynamic sectors of the economy for high-tech industries involved in superconducting magnets, fancy cryogenic engineering, and civil engineering of great sophistication, and of course computer technology. All that know-how is going to pay off much more than the investment in the long run. But even if it weren’t the case that purely economically it was a good thing to do, the United States missed an opportunity for national greatness. A hundred or two hundred years from now, people will largely have forgotten about the various spats we got into, the so-called national greatness of imposing our will on foreigners, and they’ll remember the glorious expansion of human knowledge that’s going to happen at the LHC and the gigantic effort that went into getting it. As a nation, we don’t get many opportunities to show history our national greatness, and I think we really missed one there.

  Maybe we can recoup. The time is right for an assault on the process of aging. A lot of the basic biology is in place. We know what has to be done. The aging process itself is really the profound aspect of public health; eliminating major diseases, even big ones like cancer or heart disease, would increase life expectancy by only a few years. We really have to get to the root of the process.

  Another project on a grand scale would be to search systematically for life in the galaxy. We have tools in astronomy, we can design tools, to find distant planets that might be Earth-like, study their atmospheres, and see if there is evidence for life. It would be feasible, given a national investment of will and money, to survey the galaxy and see if there are additional Earth-like planets that are supporting life. We should think hard about doing things we’ll be proud to be remembered for, and think big.

  19

  Who Cares About Fireflies?

  Steven Strogatz

  Jacob Gould Schurman Professor of Applied Mathematics, Cornell University; author, The Joy of X

  INTRODUCTION by Alan Alda

  Actor, writer, director; host of PBS program Brains on Trial; author, Things I Overheard While Talking to Myself

  Steve Strogatz has worked all his life studying something that some people thought didn’t exist while others thought was too obvious to mention. It’s found in that subtle region—the haze on the horizon—that smart people, it seems, have always been intrigued by. He saw something there, and went and looked closer. What drew him on was a pattern in nature that showed, surprisingly, that an enormous number of things sync up spontaneously.

  His research covered a wide range of phenomena, from sleep patterns to heart rhythms to the synchronous pulse of Asian fireflies. And in his 2003 book, Sync, he drew all these strands (and many others) together in a way that has the shock of the new. Even though we may see the moon every night (perhaps not realizing it’s an example of sync) it’s hard not to be surprised at the number of things around us—and in us—that must (or must not) sync up for things to go right.

  I’ve known Steve about thirteen years. We met when I called him on the phone, wondering if he’d even take my call. I had read an article of his in Scientific American about coupled oscillators. From his first description of Huygens’ discovery that pendulum clocks would sync up if they could sense each other’s vibrations, I was fascinated, and I hoped he’d tell me more about it. He was surprisingly generous in the face of my hungry, naïve curiosity and we’ve been friends ever since.

  Steve has that quality, like Richard Feynman’s, of not only wanting to make every complex thought clear to the average person but, also like Feynman, of actually knowing how. When we were working on the Broadway play QED, by Peter Parnell, in which I played Feynman, it’s no surprise that we asked Steve to advise us on the physics in the piece.

  Please let me introduce you to Steven Strogatz, professor of applied mathematics at Cornell University: my pal, Steve.

  Who Cares About Fireflies?

  The story of how I got interested in cycles goes back to an epiphany in high school. I was taking a standard freshman science course, Science I, and the first day we were asked to measure the length of the hall. We were told to get down on our hands and knees, put down rulers, and figure out how long the corridor was. I remember thinking to myself, “If this is what science is, it’s pretty pointless,” and came away with the feeling that science was boring and dusty.

  Fortunately I took to the second experiment a little better. The teacher, Mr. diCurcio, said, “I want you to figure out a rule about this pendulum.” He handed each of us a little toy pendulum with a retractable bob. You could make it a little bit longer or shorter in clicks in discrete steps. We were each handed a stopwatch and told to let the pendulum swing ten times, and then click, measure how long it takes for ten swings, and then click again, repeating the measurement after making the pendulum a little bit longer. The point was to see how the length of the pendulum determines how long it takes to make ten swings. The experiment was supposed to teach us about graph paper and how to make a relationship between one variable and another, but as I was dutifully plotting the length of time the pendulum took to swing ten times versus its length it occurred to me, after about the fourth or fifth dot, that a pattern was starting to emerge. These dots were falling on a particular curve I recognized because I’d seen it in my algebra class. It was a parabola, the same shape that water makes coming out of a fountain.

  I remember having an enveloping sensation of fear. It was not a happy feeling but an awestruck feeling. It was as if this pendulum knew algebra. What was the connection between the parabolas in algebra class and the motion of this pendulum? There it was on the graph paper. It was a moment that struck me, and was my first sense that the phrase “law of nature” meant something. I suddenly knew what people were talking about when they said there could be order in the universe and that, more to the point, you couldn’t see it unless you knew math. It was an epiphany that I’ve never really recovered from.

  A later experiment in the same class dealt with the phenomenon called resonance. The experiment was to fill a long tube with water up to a certain height, and the rest would contain air. Then you struck a tuning fork above the open end. The tuning fork vibrates at a known frequency—440 cycles per second, the A above Middle C—and the experiment was to raise or lower the water column until it reached the point where a tremendous booming sound would come out. The small sound of the tuning fork would be greatly amplified when the water column was just the right height, indicating that you had achieved resonance. The theory was that the conditions for resonance occur when you have a quarter-wavelength of a sound wave in the open end of the tube, and the point was that by knowing the frequency of the sound wave and measuring the length of the air, you could, sitting there in your high school, derive the speed of sound.

  I remember at the time not really understanding the experiment so well, but Mr. diCurcio scolded me and said, “Steve, this is an important experiment, because this is not just about the speed of sound. You have to realize that resonance is what holds atoms together.” Again, that gave me that chilling feeling, since I thought I was just measuring the speed of sound, or playing with water in a column, but from diCurcio’s point of view this humble water column was a window into the structure of matter. Seeing that resonance could apply to something as ineffable as atomic structure—what makes this table in front of me solid—I was just struck with the unity of nature again, and the idea that these principles were so transcendent that they could apply to everything from sound waves to atoms.

  The unity of nature shouldn’t be exaggerated, since this is certainly not to claim that everything is the same—but there are certain threads that reappear. Resonance is an idea that we can use to understand vibrations of
bridges and to think about atomic structure and sound waves, and the same mathematics applies over and over again in different versions.

  There’s one other story about Mr. diCurcio that I like. At one time I was reading a biography of Einstein, and diCurcio treated me like I was a full-grown scientist—at thirteen or fourteen. I mentioned to him that Einstein was struck as a young high school student by Maxwell’s equations, the laws of electricity and magnetism, and that they made a deep impression on him. I said I couldn’t wait until I was old enough, or knew enough math, to know what Maxwell’s equations were and to understand them. This being a boarding school, we used to have family-style dinner sometimes, and so he and I were sitting around a big table with several other kids, his two daughters, and his wife, and he was serving mashed potatoes. As soon as I said I would love to see Maxwell’s equations sometime, he put down the mashed potatoes and said, “Would you like to see them right now?” And I said, “Yeah, fine.” He started writing on a napkin these very cryptic symbols, upside-down triangles and E’s and B’s and crosses and dots and mumbled, in what sounded like speaking in tongues, “The curl of a curl is grad div minus del squared . . . and from this we can get the wave equation . . . and now we see electricity and magnetism, and can explain what light is.” It was one of these awesome moments, and I looked at my teacher in a new way. Here was Mr. diCurcio, not just a high school teacher but someone who knew Maxwell’s equations off the top of his head. It gave me the sense that there was no limit to what I could learn from this man.