Knocking on Heaven's Door: How Physics and Scientific Thinking Illuminate the Universe and the Modern World - Lisa Randall (2011)



In February 2007, the Nobel Prize—winning theoretical physicist Murray Gell-Mann spoke at the elite TED conference in California, where innovators working in science, technology, literature, entertainment, and other forefront arenas gather once a year to present new developments and insights about a wide variety of subjects. Murray’s crowd-pleasing talk, which was rewarded with a standing ovation, was on the topic of truth and beauty in science. The basic premise of the talk can best be summarized with his words, which echo those of John Keats: “Truth is beauty and beauty is truth.”

Gell-Mann had good reasons to believe his grand statement. He had made some of his most significant Nobel Prize—winning discoveries about quarks by searching for an underlying principle that could elegantly organize the seemingly random set of data that experiments had discovered in the 1960s. In Murray’s experience, the search for beauty—or at least simplicity—had also led to truth.

No one in the audience disputed his claim. After all, most people love the idea that beauty and truth go together and that the search for one will more often than not reveal the other. But I confess that I have always found this assumption a little slippery. Although everyone would love to believe that beauty is at the heart of great scientific theories, and that the truth will always be aesthetically satisfying, beauty is at least in part a subjective criterion that will never be a reliable arbiter of truth.

The basic problem with the identification of truth and beauty is that it does not always hold—it holds only when it does. If truth and beauty were equivalent, the words “ugly truth” would never have entered our vocabulary. Even though those words weren’t specifically directed toward science, observations about the world are not always beautiful. Darwin’s colleague Thomas Huxley nicely summarized the sentiment when he said “science is organized common sense where many a beautiful theory was killed by an ugly fact.”59

To make matters more difficult, physicists have to allow for the disconcerting observation that the universe and its elements are not entirely beautiful. We observe a plethora of messy phenomena and a zoo of particles that we’d like to understand. Ideally, physicists would love to find a simple theory capable of explaining all such observations that uses only a spare set of rules and the fewest possible fundamental ingredients. But even when searching for a simple, elegant, unifying theory—one that can be used to predict the result of any particle physics experiment—we know that even if we find it, we would need many further steps to connect it to our world.

The universe is complex. New ingredients and principles are generally needed before we can connect a simple, spare formulation to the more complicated surrounding world. Those additional ingredients might destroy the beauty present in the initial proposed formulation, much as earmarks all too often interfere with a congressional bill’s initial idealistic legislation.

Given the potential pitfalls, how do we go about trying to go beyond what we know? How do we try to interpret as-yet-unexplained phenomena? This chapter is about the idea of beauty and the role of aesthetic criteria in science, and the advantages and disadvantages of beauty as a guide. It also introduces model building, which uses a bottom-up approach to science, while paying attention to aesthetic criteria in attempts to guess what comes next.


I recently spoke with an artist who humorously remarked how one of the great ironies of modern science is that today’s researchers seem more likely than contemporary artists to present beauty as their goal. Of course, artists haven’t abandoned aesthetic criteria, but they are at least as likely to talk about discovery and invention when discussing their work. Scientists cherish those other attributes too, but they simultaneously strive to find the elegant theories they often find most compelling.

Yet despite the value many scientists place on elegance, they can have divergent notions about what is simple and beautiful. Just as you and your neighbor might violently disagree over the artistic merits of a contemporary artist such as Damien Hirst, different scientists find distinct aspects of science satisfying.

Together with like-minded researchers, I prefer to search for underlying principles that illuminate connections among superficially disparate observed phenomena. Most of my string theory colleagues study specific solvable theories in which they use difficult mathematical formulations to tackle toy problems (problems not necessarily relevant to any real physical setup) that might only later find applications to observable physical phenomena. Other physicists prefer to focus only on theories with a concise elegant formalism that generate many experimental predictions which they can systematically calculate. And others simply like computing.

Interesting principles, advanced mathematics, and complicated numerical simulations are all part of physics. Most scientists value all of them, but we choose our priorities according to what we find most pleasing or most likely to lead to scientific advances. In reality, we often also choose our approach according to which method best suits our unique inclinations and talents.

Not only do current views of beauty vary. As is also true with art, attitudes evolve over time. Murray Gell-Mann’s own specialty, quantum chromodynamics, presents an excellent case in point.

Gell-Mann’s conjecture about the strong nuclear force was based on a brilliant insight about how the many particles that were constantly being discovered in the 1960s could be organized into sensible patterns that would explain their abundance and types. He hypothesized the existence of more basic elementary particles known as quarks, which he suggested carry a new type of charge. The strong nuclear force would then influence any object that carried the conjectured charge, and cause quarks to bind together to form neutral objects—much as the electric force binds electrons with charged nuclei to form neutral atoms. If true, all the particles being discovered could be interpreted as bound states of these quarks—aggregate objects that have no net charge.

Gell-Mann realized that if there were three different types of quarks, each of which carried a distinct color charge, many such combinations of neutral bound states would form. And these many combinations could (and did) correspond to the plethora of particles that were being found. Gell-Mann thereby had found a beautiful explanation for what seemed like an inexplicable mess of particles.

However, when Murray—as well as the physicist (and later neurobiologist) George Zweig—first proposed this idea, people didn’t even believe it was a proper scientific theory. The reason is somewhat technical but interesting. Particle physics calculations rely on particles not interacting when they are far apart, so that we can compute the finite effects of the interactions that occur when they are close together. With this assumption, any interaction can be entirely captured by the local forces that apply when the interacting particles are in close proximity.

The force that Gell-Mann had conjectured, on the other hand, was stronger when particles were farther apart. That meant that quarks would always interact, even when very distant. According to the then-reigning criteria, Gell-Mann’s guess didn’t even correspond to a true theory that could be used for reliable calculations. Because quarks always interact, even their so-called asymptotic states—the states involving quarks that are far away from everything else—are very complicated. In an apparent concession to ugliness, the asymptotic states they postulated weren’t the simple particles you’d like to see in a calculable theory.

Initially, no one knew how to organize calculations among these complicated strongly bound states. However, today’s physicists think quite oppositely about the strong force. We now understand it much better than we did when the idea was first proposed. David Gross, David Politzer, and Frank Wilczek won the Nobel Prize for what they called “asymptotic freedom.” According to their calculations, the force is strong only at low energies. At high energies, the strong force is not much more powerful than other forces, and calculations work just as they should. In fact, some physicists today think theories such as the strong force, which become much weaker at high energies, are the onlywell-defined theories, since the interaction strength won’t grow to infinite strength at high energy as it might otherwise do.

Gell-Mann’s theory of the strong force is an interesting example of the interplay between aesthetic and scientific criteria. Simplicity was his initial guide. But hard scientific calculations and theoretical insights were necessary before everyone could agree on the beauty of his suggestion.

This, of course, isn’t the only example. Many of our most trusted theories have aspects so superficially ugly and uncompelling that even respected and well-established scientists rejected them initially. Quantum field theory, which combines quantum mechanics and special relativity, underlies all of particle physics. Yet the Nobel Prize—winning Italian scientist Enrico Fermi (among others) rejected it at first. For him, the problem was that although quantum field theory formalizes and systematizes all calculations and makes many correct predictions, it involves calculaional techniques that even some of today’s physicists view as baroque. Various aspects of the theory are quite beautiful and lead to remarkable insights. Other features we just have to put up with, even though we aren’t so enamored with all their intricacies.

This story has repeated itself many times since. Beauty is often agreed on only a posteriori. Weak interactions violate parity symmetry. This means that particles spinning to the left interact differently from those spinning to the right. The breaking of such a fundamental symmetry as left-right equivalence seems innately disturbing and unattractive. Yet this very asymmetry is what is responsible for the range of masses we see in the world, which is in turn necessary for structure and life. It was considered ugly at first, yet now we know it is essential. Although perhaps ugly in itself, parity symmetry breaking leads to beautiful explanations of more complicated phenomena essential to all the matter we see.

Beauty is not absolute. An idea might appeal to its creator but be cumbersome or messy from someone else’s perspective. Sometimes I’ll be quite taken with the beauty of a conjecture I’ve come up with largely because I know of all the other ideas people had thought of before that hadn’t worked. But being better than what came before doesn’t guarantee beauty. Having made my share of models that satisfied this criterion, but were nonetheless met with skepticism and confusion from colleagues who were less familiar with the topic my model addressed, I now think a better criterion for a good idea might be that even someone who never studied the problem can recognize its appeal.

The reverse is sometimes true as well—good ideas are rejected because their inventors consider them too ugly. Max Planck didn’t believe in photons, which he thought to be an unpleasant concept, even though he initiated the train of logic that led to their conjecture. Einstein thought the expanding universe that followed from his equations of general relativity couldn’t be true, in part because it contradicted his aesthetic and philosophical predispositions. Neither of these ideas might have seemed the most beautiful at the time, but the laws of physics and the universe in which they applied didn’t really care.


Given the evolving and uncertain nature of beauty, it’s worth considering some of the features that might make an idea or an image objectively beautiful in a way that has some universal appeal. Perhaps the most basic question about aesthetic criteria is whether humans even have any universal criteria for what is beautiful—in any context—be it art or science.

No one yet knows the answer. Beauty, after all, involves taste, and taste can be a subjective criterion. Nonetheless, I find it hard to believe that humans don’t share some common aesthetic criteria. I often notice a striking uniformity in people’s opinions about which piece of art in a given exhibit is the best or even which exhibits people choose to go see. Of course this doesn’t prove anything since we all share a time and place. Beliefs about beauty are difficult to isolate from the specific cultural context or time period in which they originate so it’s difficult to isolate innate from learned values or judgments. In some extreme cases, people might all agree that something looks nice or appears unpleasant. And in some rare instances, everyone might agree on the beauty of an idea. But even in those few cases, people don’t necessarily agree about all the details.

Even so, some aesthetic criteria do appear to be universal. Any beginning art class will teach about balance. Michelangelo’s David in the Accademia Gallery in Florence exemplifies this principle. David stands gracefully. He’s never going to tip over or fall apart. People search for balance and harmony where they can find it. Art, religion, and science all promise people the opportunity to access these qualities. But of course balance might also be simply an organizing principle. Art is also fascinating when it defies our notions of balance, as we see in early Richard Serra sculptures. (See Figure 47.)


FIGURE 47 ] These early Richard Serra sculptures illustrate that sometimes art is more interesting when it appears to be slightly off balance. (Copyright © 2011 by Richard Serra/Artists Rights Society [ARS], New York.)

Symmetry is also often considered essential to beauty, and art and architecture frequently exhibit the order that it generates. Something has symmetry if you can change it—for example, by rotating it, reflecting it in a mirror, or interchanging its parts—so that the transformed system is indistinguishable from the initial one. Symmetry’s harmoniousness is probably one reason that religious symbols often have it on display. The Christian cross, the Jewish star, the dharma wheel of Buddhism, and the crescent of Islam are all examples and are illustrated in Figure 48.


FIGURE 48 ] Religious symbols frequently embody symmetries.

More expansively, Islamic art, which forbids representation and relies on geometric forms, is notable for its use of symmetry. The Taj Mahal in India is a magnificent example. I haven’t spoken to anyone who’s visited the Taj Mahal and wasn’t taken with its masterful orderliness, shape, and symmetry. The Alhambra in southern Spain, which also incorporates Moorish art and its interesting symmetry patterns, may be one of the most beautiful buildings still standing today.


FIGURE 49 ] The architecture of the Chartres Cathedral and the ceiling of the Sistine Chapel both embody symmetry.

Recent art, such as the work of Ellsworth Kelly or Bridget Riley, exhibits symmetry explicitly and geometrically. Gothic or Renaissance art and architecture—see the Chartres Cathedral and the roof of the Sistine Chapel, for example—exquisitely exploited symmetry as well. (See Figure 49.)

However, art is often most beautiful when it is not completely symmetrical. Japanese art is notable for its elegance, but also for the well-defined breaking of symmetry. Japanese paintings and silk screens have a clear orientation that draws one’s eye across the pictures as one can see in Figure 50.


FIGURE 50 ] Japanese art is interesting in part because of its asymmetry.

Simplicity is another and sometimes related criterion that might help when evaluating beauty. Some simplicity arises from symmetries, but underlying order can be present, even in the absence of manifest symmetry. Jackson Pollock pieces have an underlying simplicity in the density of paint, though the impression might first seem chaotic. Although the individual splashes of paint seem completely random, his most famous and successful pieces have a fairly uniform density of each color that enters the work.

Simplicity in art can frequently be deceptive. I once tried to sketch a few Matisse cutouts, his simplest works, which he created when he was old and frail. Yet when I tried to reproduce them, I realized that they weren’t so simple—at least not for my unskilled hand. Simple elements can embody more structure than we superficially observe.

In any case, beauty isn’t found only in simple basic forms. Some admired works of art, such as those of Raphael or Titian, involve rich complex canvases with many internal elements. After all, complete simplicity can be mind-numbing. When we look at art, we prefer something interesting that guides our eye. We want something simple enough to follow, but not so simple as to be boring. This seems to be how the world is constructed as well.


Aesthetic criteria are difficult to pin down. In science—as in art—there are unifying themes but no absolutes. Yet even though aesthetic criteria for science might be poorly defined, they are nonetheless useful and omnipresent. They help guide our research, even if they provide no guarantee of success or truth.

Aesthetic criteria that we apply to science resemble those that were just outlined for art. Symmetries certainly play an important role. They help us organize our calculations and often relate disparate phenomena. Interestingly as with art, symmetries are usually only approximate. The best scientific descriptions frequently respect the elegance of symmetric theories while incorporating the symmetry breaking necessary to make predictions about our world. The symmetry breaking enriches the ideas it encompasses, which thereby yield more explanatory power. And, as is often true for art, the theories that incorporate broken symmetries can be even more beautiful and interesting than those that are perfectly symmetrical.

The Higgs mechanism, which is responsible for elementary particle masses, is an excellent example. As will be explained in the following chapter, the Higgs mechanism very eloquently explains how the symmetries associated with the weak force can be slightly broken. We haven’t yet discovered the Higgs boson—the particle that would provide incontrovertible evidence that the idea is correct. But the theory is so beautiful and so uniquely satisfies criteria required by both experiments and theory that most physicists believe it is realized in nature.

Simplicity is another important subjective criterion for theoretical physicists. We have a deep-rooted belief that simple elements underlie the complicated phenomena we see. Such a search for simple basic elements of which all reality is composed or resembles began long ago. In ancient Greece, Plato imagined perfect forms—geometric shapes and ideal beings that objects on Earth only approximate. Aristotle, too, believed in ideal forms, but in his case, he thought that the ideals that physical objects approximate would be revealed only through observations. Religions also often postulate a more perfect or more unified state that is removed from, but somehow connected to, reality. Even the story of the fall from the Garden of Eden presupposes an idealized prior world. Although the questions and methods of modern physics are very different from those of our ancestors, many physicists, too, are seeking a simpler universe—not in philosophy or religion, but in the fundamental ingredients that constitute our world.

The search for underlying scientific truth often involves looking for simple elements from which we can construct the complex and rich phenomena we observe. Such research often involves trying to identify meaningful patterns or organizing principles. Only with a concise realization of simple and elegant ideas do most scientists expect a proposal to have the potential to be right. A starting point involving the fewest inputs has the further benefit that it promises the most predictive power. When particle physicists consider suggestions for what might lie at the heart of the Standard Model, we usually become skeptical when the realization of an idea becomes too cumbersome.

Again, as with art, physical theories can be simple in themselves, or they may be complex compositions made up of simple and predictable elements. The end point of course isn’t necessarily simple, even when the initial components—and perhaps even the rules themselves—are.

The most extreme version of such pursuits is the search for a unifying theory consisting of only a few simple elements obeying a small set of rules. This quest is an ambitious—some might say an audacious—task. Clearly an obvious impediment prevents us from readily finding an elegant theory that completely accounts for all observations: the world around us manifests only a fraction of the simplicity that such a theory should embody. A unified theory, while being simple and elegant, must somehow accommodate enough structure to match observations. We would like to believe in a single simple, elegant, and predictable theory that underlies all of physics. Yet the universe is not as pure, simple, and ordered as the theories. Even with an underlying unified description, a lot of research will be necessary to connect it to the fascinating and complex phenomena we see in our world.

Of course, we can go too far in these characterizations of beauty or simplicity. A standard joke among students in our science or math classes involves professors who repeatedly refer to well-understood phenomena as “trivial,” no matter how complex they might be. The professor already knows the answer and the underlying elements and logic very well, but this is not so true for the students sitting in class. In retrospect, after they have reduced the problem to simple pieces, it can become trivial to them, too. But they first have to discover how to do that.


In the end, just as in life, science doesn’t have just a single criterion for beauty. We merely have some intuitions—along with experimental constraints—that we use to guide our search for knowledge. Beauty—both in art and science—might have some objective aspects, but almost any application involves taste and subjectivity.

For scientists, however, there is one big difference. Ultimately experiments will decide which, if any, of our ideas are correct. Scientific advances might exploit aesthetic criteria, but true scientific progress also requires understanding, predicting, and analyzing data. No matter how beautiful a theory appears, it can still be wrong, in which case it must be thrown away. Even the most intellectually satisfying theory has to be abandoned if it doesn’t work in the real world.

Nonetheless, before we reach the higher energies or distant parameters needed to determine the correct physical descriptions, physicists have no choice but to employ aesthetic and theoretical considerations to guess what lies beyond the Standard Model. In this interim, with only limited data, we rely on existing puzzles coupled with taste and organizational criteria to point the way forward.

Ideally, we’d like to be able to work through the consequences of a variety of possibilities. Model building is the name of the approach we use to do this. My colleagues and I explore various particle physics models, which are guesses for physical theories that might underlie the Standard Model. Our goals are simple principles that organize the complicated phenomena that appear on more readily visible scales so that we can resolve current puzzles in our understanding.

Physics model builders take the effective theory viewpoint and the desire to understand smaller and smaller distance scales very much to heart. We follow a “bottom-up” approach that starts with what we know—both the phenomena we can explain and those we find puzzling—and attempt to deduce the underlying model that explains the connections among observed elementary particle properties and their interactions.

The term “model” might evoke a physical structure such as a small-scale version of a building used to display and explore its architecture. Or you might think of numerical simulations on a computer that calculate the consequences of known physical principles—such as climate modeling or models for the spread of contagious diseases.

Modeling in particle physics is very different from either of these definitions. Particle models do, however, share some of the flair of models in magazines or fashion shows. Models, both on runways and in physics, illustrate imaginative new ideas. And people initially flock toward the beautiful ones—or at least those that are more striking or surprising. But in the end, they are drawn toward the ones that show true promise.

Needless to say, the similarities end there.

Particle physics models are guesses for what might underlie the theories whose predictions have been already tested and that we understand. Aesthetic criteria are important in deciding which ideas are worth pursuing. But so are consistency and testability of the ideas. Models characterize different underlying physical ingredients and principles that apply at distances and sizes that are smaller than those which have yet been experimentally tested. With models, we can determine the essence and consequences of different theoretical assumptions.

Models are a means of extrapolating from what is known to create proposals for more comprehensive theories with greater explanatory power. They are sample proposals that may or may not prove correct once experiments allow us to delve into smaller distances or higher energies and test their underlying hypotheses and predictions.

Bear in mind that a “theory” is different from a “model.” By the word theory, I don’t mean rough speculations, as in more colloquial usage. The known particles and the known physical laws they obey are components of a theory—a definite set of elements and principles with rules and equations for predicting how the elements interact.

But even when we fully understand a theory and its implications, that same theory can be implemented in many different ways, and these will have different physical consequences in the real world. Models are a way of sampling these possibilities. We combine known physical principles and elements into candidate descriptions of reality.

If you think of a theory as a PowerPoint template, a model would be your particular presentation. The theory allows animations, but the model includes only those you need to make your point. The theory would say to have a title and some bullet points, but the model would contain exactly what you want to convey and will hopefully apply well to the task at hand.

The nature of model building in physics has changed according to the questions physicists have tried to answer. Physics always involves trying to predict the largest number of physical quantities from the smallest number of assumptions, but that doesn’t mean we manage to identify the most fundamental theories right away. Advances in physics are often made even before everything is understood at the most fundamental level.

In the nineteenth century, physicists understood the notions of temperature and pressure and employed them in thermodynamics and engine design long before anyone could explain these ideas at a more fundamental microscopic level as the result of the random motion of large numbers of atoms and molecules. In the early twentieth century, physicists tried to make models to explain mass in terms of electromagnetic energy. Though these models were based on strongly shared beliefs on how those systems worked, those models proved wrong. A little later, Niels Bohr made a model of the atom to explain the emission spectra that people had observed. His model was soon superseded by the more comprehensive theory of quantum mechanics, which absorbed but also improved on Bohr’s core idea.

Model builders today try to determine what lies beyond the Standard Model of particle physics. Although currently referred to as the Standard Model because it has been well tested and is well understood, it was something of a guess as to how known observations might fit together at the time it was developed. Nonetheless, because the Standard Model implied predictions for how to test its premises, experiments could ultimately show it to be correct.

The Standard Model correctly accounts for all observations to date, but physicists are fairly confident that it is not complete. In particular, it leaves open the question of what are the precise particles and interactions—the elements of the Higgs sector—that are responsible for the masses of elementary particles and why it is that the particles in that sector have the particular masses that they do. Models that go beyond the Standard Model illuminate deeper potential interconnections and relationships that might address these questions. They involve specific choices of fundamental assumptions and physical concepts, as well as the distance or energy scales at which they might apply.

Much of my current research involves thinking about new models, as well as novel or more detailed search strategies that would otherwise miss new phenomena. I think about the models I originated but the full range of other possibilities as well. Particle physicists know the types of elements and rules that could be involved, such as particles, forces, and allowed interactions. But we don’t know precisely which of these ingredients enters the recipe for reality. By applying known theoretical ingredients, we attempt to identify the potentially simple underlying ideas that enter into what is an ultimately complex theory.

As important, models provide targets for experimental exploration, and suggestions for how particles will behave at smaller distances than physicists have experimentally studied so far. Measurements provide clues to help us distinguish among competing candidates. We don’t yet know what the new underlying theory is, but we can nonetheless characterize the possible deviations from the Standard Model. By thinking about candidate models for underlying reality and their consequences, we can predict what the LHC should reveal if the models turn out to be right. Our use of models admits the speculative nature of our ideas and recognizes the plethora of possibilities that might agree with existing data and explain as-yet-puzzling phenomena. Only some models will prove correct, but creating and understanding them is the best way to delineate the options and build up a reservoir of compelling ingredients.

Exploring models and their detailed consequences helps us establish what experimenters should search for—whatever might be out there. Models tell experimenters the interesting features that characterize new physical theories so that experimenters can test whether model builders have correctly identified the elements or the physical principles that guide the system’s relationships and interactions. Any model with new physical laws that apply at measurable energies should predict new particles and new relationships among them. Observing which particles emerge from collisions and the properties they have should help determine the type of particles that exist, their masses, and their interactions. Finding new particles or measuring different interactions will confirm or rule out models that have been proposed, and pave the way for better ones.

With enough data, experiments will determine which underlying model is the right one—at least at the level of precision, distance, and energy that we can study. The hope is that at the smallest distance scales that we can probe at LHC energies, the rules for the underlying theory will be simple enough to allow us to deduce and calculate the influence of the associated physical laws.

Physicists have lively discussions about which are the best models to study and what is the most useful way to account for them in experimental searches. I’ll frequently sit down with experimental colleagues and discuss with them how best to use models to guide their searches. Are benchmark points with specific parameters in particular models too specific? Is there a better way to cover all the possibilities?

LHC experiments are so challenging that without definite search targets, the results will be overwhelmed by Standard Model background. Experiments were designed and optimized with existing models in mind, but they are searching for more general possibilities as well. It is critical that experimenters are aware of a big range of models that span the possible new signatures that might emerge, since no one wants specific models to overly prejudice the searches.

Theorists and experimenters are working hard to make sure we don’t miss anything. We won’t know which, if any, of the different suggestions is correct until it is experimentally verified. Proposed models might be the correct description of reality, but even if they are not, they suggest interesting search strategies that tell us the distinguishing features of new as-yet-undiscovered matter. Hopes are the LHC will tell us the answers—no matter what they turn out to be—and we want to be prepared.