However, before we plunge into these subjects, this chapter will take a brief journey inside matter in order to set the physical stage. And because understanding where we’re heading also requires some familiarity with the types of reasoning that today’s theorists employ, we’ll consider the theoretical approaches that are critical to more recent developments.
At first I thought “the fundamental things apply” was a clever choice of song quote. But on further reflection the words sounded so much like physics that I decided to check that my memory wasn’t playing tricks on me, as sometimes happens with song lyrics—even those you think are burnt into your head. I was rather surprised (and amused) when I discovered that the song was more rooted in physics
than I had ever imagined. I certainly hadn’t realized that the “time going by” was supposed to be the fourth dimension!
Physical insights can work like this discovery; small clues sometimes reveal unanticipated connections. When you’re lucky, what you find is better than what you were looking for—but you have to be looking in the right place. In physics, once you discover relationships, even by following tenuous leads, you look for meaning in the way you think best. That might involve educated guesses or it might involve trying to deduce the mathematical consequences of a theory you think you trust.
In the next section we’ll consider the modern methods used to pursue such clues: model building—my forte—and the alternative approach to fundamental high-energy physics, namely, string theory. String theorists try to derive universal predictions from a definite theory, whereas model builders try to find ways to solve particular physical problems and then to build up theories from these starting points. Model builders and string theorists both seek more comprehensive theories with more explanatory power. They aim to answer similar questions, but they approach them in different ways. Research sometimes involves educated guesses, as with model building, and sometimes it involves deducing logical consequences of the ultimate theory you already believe to be correct, as with the string theory approach. We’ll soon see that the recent research on extra dimensions successfully combines elements of both methods.
Model Building
Although I was first drawn to math and science by the certainty they promised, today I find the unanswered questions and the unexpected connections at least as attractive. The principles contained in quantum mechanics, relativity, and the Standard Model stretch the imagination, but they barely scratch the surface of the remarkable ideas engrossing physicists today. We know that something new is required because of the deficiencies in existing ideas. Those shortfalls are harbingers of novel physical phenomena that should emerge when we do more precise experiments.
Particle physicists try to find the laws of nature that explain how elementary particles behave. These particles, and the physical laws they obey, are components of what physicists call a
theory
—a definite set of elements and principles with rules and equations for predicting how those elements interact. When I speak about theories in this book, I’ll be using the word in this sense; I won’t mean “rough speculations”, as in more colloquial usage.
Ideally, physicists would love to find a theory capable of explaining all observations, one that uses the sparest possible set of rules and the fewest possible fundamental ingredients. The ultimate goal for some physicists is a simple, elegant, unifying theory—one that can be used to predict the result of any particle physics experiment.
The quest for such a unifying theory is an ambitious—some might say audacious—task. Yet in some respects it mirrors the search for simplicity that began long ago. In ancient Greece, Plato imagined perfect forms, such as geometric shapes and ideal beings, that earthly objects only approximate. Aristotle also believed in ideal forms, but he thought that only observations can reveal the ideals that physical objects resemble. Religions also often postulate a more perfect or more unified state that is removed from, but somehow connected to, reality. The story of the fall from the Garden of Eden supposes an idealized prior world. Although the questions and methods of modern physics are very different from those of our ancestors, physicists, too, are seeking a simpler universe, not in philosophy or religion but in the fundamental ingredients that constitute our world.
However, there is an obvious impediment to finding an elegant theory that we can connect to our world: when we look around us, we see very little of the simplicity that such a theory should embody. The problem is that the world is complex. It takes a lot of work to connect a simple, spare formulation to the more complicated real world. A unified theory, while being simple and elegant, must somehow accommodate enough structure for it to match observations. We would like to believe that there is a perspective from which everything is elegant and predictable. Yet the universe is not as pure, simple, and ordered as the theories with which we hope to describe it.
Particle physicists negotiate the terrain connecting theory to observations with two distinct methodologies. Some theorists follow a
“top-down” approach: they start with the theory they believe to be correct—for example, string theorists start with string theory—and try to derive its consequences so that they can connect it to the much more disordered world we observe. Model builders, on the other hand, follow a “bottom-up” approach: they try to deduce an underlying theory by making connections among observed elementary particles and their interactions. They search for clues in physical phenomena. They make models, which are sample theories that may or may not prove correct. Both approaches have their merits and their deficiencies, and the best route to progress is not always apparent.
The conflict between the two scientific approaches is interesting because it reflects two very different ways of doing science. This division is the latest incarnation of a long debate in science. Do you follow the Platonic approach, which tries to gain insights from more fundamental truth, or the Aristotelian approach, rooted in empirical observations? Do you take the top-down or the bottom-up route?
The choice could also be phrased as “Old Einstein vs. Young Einstein.” As a young man, Einstein rooted his work in experiments and physical reality. Even his so-called thought experiments were grounded in physical situations. Einstein changed his approach after learning the value of mathematics when he developed general relativity. He found that mathematical advances were crucial to completing his theory, which led him to use more theoretical methods later in his career. Looking to Einstein won’t resolve the issue, however. Despite his successful application of mathematics to general relativity, his later mathematical search for a unified theory never reached fruition.
As Einstein’s research demonstrated, there are different types of scientific truth and different ways of finding them. One is based in observations; this is how we learned about quasars and pulsars, for example. The other is based on abstract principles and logic: for example, Karl Schwarzschild first derived black holes as a mathematical consequence of general relativity. Ultimately, we would like these to converge—black holes have now been deduced from both the mathematical description of observations and from pure theory—but in the first phases of investigation, the advances we make based on the two types of truth are rarely the same. And in the case of string theory, the principles and equations are not nearly so well laid out as
are those of general relativity, making deriving its consequences that much harder.
When string theory first rose to prominence, it sharply divided the particle physics world. I was a graduate student in the mid-1980s when the “string revolution” first split the world of particle physics asunder. At that time, one community of physicists decided to devote themselves wholeheartedly to the ethereal, mathematical realm of string theory.
String theory’s basic premise is that strings—not particles—are the most fundamental objects of nature. The particles we observe in the world around us are mere consequences of strings: they arise from the different vibrational modes of an oscillating string, much as different musical notes arise from a vibrating violin string. String theory gained favor because physicists were looking for a theory that consistently includes quantum mechanics and general relativity and that can make predictions down to the tiniest conceivable distance scales. To many people, string theory looked like the most promising candidate.
However, another group of physicists decided to stay in touch with the relatively low-energy world that experiments could explore. I was at Harvard, and the particle physicists there—which included the excellent model builders Howard Georgi and Sheldon Glashow, along with many talented postdoctoral fellows and students, were among the stalwarts who continued with the model building approach.
Early on, the battles between the merits of the two opposing view-points—string theory and model building—were fierce, with each side claiming better footing on the road to truth. Model builders thought that string theorists were in mathematical dreamland, whereas string theorists thought that model builders were wasting their time and ignoring the truth.
Because of the many brilliant model builders at Harvard, and because I relished the challenges of model building, when I first entered the world of particle physics I stayed within that camp. String theory is a magnificent theory which has already led to profound mathematical and physical insights, and it might well contain the correct ingredients to ultimately describe nature. But finding the connection between string theory and the real world is a daunting task. The
problem is that string theory is defined at an energy scale that is about ten million billion times larger than those we can experimentally explore with our current instruments. We still don’t even know what will happen when the energy of particle colliders increases by a factor of ten!
An enormous theoretical gulf separates string theory, as it is currently understood, from predictions that describe our world. String theory’s equations describe objects that are so incredibly tiny and possess such extraordinarily high energy that any detectors we could imagine making with conceivable technologies would be unlikely ever to see them. Not only is it mathematically tremendously challenging to derive string theory’s consequences and predictions, it is not even always clear how to organize string theory’s ingredients and determine which mathematical problem to solve. It is too easy to get lost in a thicket of detail.
String theory can lead to a plethora of possible predictions at distances we actually see—the particles that are predicted depend on the as yet undetermined configuration of fundamental ingredients in the theory. Without some speculative assumptions, string theory looks like it contains more particles, more forces, and more dimensions than we see in our world. We need to know what separates the extra particles, forces, and dimensions from the visible ones. We don’t yet know what physical features, if any, favor one configuration over another, or even how to find a single manifestation of string theory that conforms to our world. We would have to be very lucky to extract all the correct physical principles that will make the predictions of string theory match what we see.
For example, string theory’s invisible extra dimensions have to be different from the three that we see. The gravity of string theory is more complex than the gravity we see around us—the force that caused Newton’s apple to fall on his head. Instead, string theory’s gravity operates in six or seven additional dimensions of space. Fascinating and remarkable as string theory is, puzzling features such as its extra dimensions obscure its connection to the visible universe. What distinguishes those extra dimensions from the visible ones? Why aren’t they all the same? Discovering how and why nature hides string theory’s extra dimensions would be a stunning achievement, making
it worthwhile to investigate all possible ways in which this might happen.
So far, however, all attempts to make string theory realistic have had something of the flavor of cosmetic surgery. In order to make its predictions conform to our world, theorists have to find ways to cut away the pieces that shouldn’t be there, removing particles and tucking dimensions demurely away. Although the resulting sets of particles come tantalizingly close to the correct set, you can nonetheless tell that they aren’t quite right. Elegance might well be the hallmark of a correct theory, but we can only really judge a theory’s beauty once we’ve fully understood all its implications. String theory is captivating at first, but ultimately string theorists have to address these fundamental problems.
When exploring mountainous territory without a map, you can rarely tell what the most direct route to your destination will turn out to be. In the world of ideas, as in complex terrain, the best path to follow is not always clear at the outset. Even if string theory does ultimately unify all the known forces and particles, we don’t yet know whether it contains a single peak representing a particular set of particles, forces, and interactions, or a more complicated landscape with many possible implications. If the paths were smooth, well-signposted grids, route-finding would be simple. But that is rarely the case.
So, the approach to advancing beyond the Standard Model that I will emphasize is model building. The term “model” might evoke a small-scale battleship or castle you built in your childhood. Or you might think of numerical simulations on a computer that are meant to reproduce known dynamics—how a population grows, for example, or how water moves in the ocean. Modeling in particle physics is not the same as either of these definitions. However, it’s not entirely different from the use of the word in magazines or fashion shows: models, both on runways
*
and in physics, demonstrate imaginative creations and come in a variety of shapes and forms. And the beautiful ones get all the attention.