Needless to say, the similarities end there. Particle physics models
are guesses at alternative physical theories that might underlie the Standard Model. If you think of a unified theory as the summit of a mountain, model builders are trailblazers who are trying to find the path that connects the solid ground below, consisting of well-established physical theories, to the peak—the path that will ultimately tie new ideas together. Although model builders acknowledge the fascination of string theory and the possibility that it could turn out to be true, they are not as certain as string theorists that they know what theory they will find if they ever get to the top.
As we will see in Chapter 7, the Standard Model is a definite physical theory with a fixed set of particles and forces that reside in a four-dimensional world. Models that go beyond the Standard Model incorporate its ingredients and mimic its consequences at energies that have already been explored, but they also contain new forces, new particles, and new interactions that can be seen only at shorter distances. Physicists propose these models to address current puzzles. Models might suggest different behaviors for known or conjectured particles, behaviors determined by a new set of equations that follow from a model’s assumptions. Or they might suggest a new spatial setting, such as the ones we’ll explore with extra dimensions or branes.
Even when we fully understand a theory and its implications, that theory can be implemented in different ways, which might have different physical consequences for the real world in which we live. For example, even when we know how particles and forces interact in principle, we still need to know which particular particles and forces exist in the real world. Models allow us to sample the possibilities.
Different assumptions and physical concepts distinguish theories, as do the distance or energy scales at which a theory’s principles apply. Models are a way of getting at the heart of such distinguishing features. They let you explore a theory’s potential implications. If you think of a theory as general instructions for making a cake, a model would be a precise recipe. The theory would say to add sugar, but the model would specify whether to add half a cup or two cups. The theory would say that raisins are optional, but the model would tell you to be sensible and leave them out.
Model builders look at the unresolved aspects of the Standard Model and try to use known theoretical ingredients to address its
inadequacies. The model building approach is fueled by the instinct that the energies for which string theory makes definite predictions are too far away from those we can observe. Model builders try to see the big picture so they can find the pieces that could be relevant to our world.
We model builders pragmatically admit that we can’t derive everything at once. Instead of trying to derive string theory’s consequences, we try to figure out which ingredients of the underlying physical theory will explain known observations and reveal relationships among experimental discoveries. A model’s assumptions could be part of the ultimate underlying theory, or they might illuminate new relationships even before we understand their deeper theoretical underpinnings.
Physics always strives to predict the largest number of physical quantities from the smallest number of assumptions, but that doesn’t mean that we always manage to identify the most fundamental theories right away. Advances have often been made before everything was understood at the most fundamental level. For example, physicists understood the notions of temperature and pressure and employed them in thermodynamics and engine design long before anyone had explained these ideas at a more fundamental microscopic level as the result of the random motion of large numbers of atoms and molecules.
Because models relate to physical “phenomena,” (meaning experimental observations) model builders with stronger ties to experiment are sometimes called phenomenologists. “Phenomenology” is a poor choice of word, however. It does not do justice to data analysis, which in today’s complex scientific world is deeply embedded in theory. Model building is far more tied to interpretation and mathematical analysis than phenomenology, in the philosophical sense of the word, would suggest.
The best models do, however, have an invaluable feature. They yield definite predictions for physical phenomena, giving experimenters a way to verify or contradict a model’s claims. High-energy experiments are not merely searching for new particles—they are testing models and looking for clues to better ones. Any proposed particle physics model will involve new physical principles and new physical laws that apply at measurable energies. It will therefore predict new particles
and testable relationships among them. Finding these particles and measuring their properties can confirm or rule out proposed ideas. The goal of high-energy experiments is to shed light on underlying physical laws and the conceptual framework that gives them their explanatory power.
Only some models will prove correct, but models are the best way to investigate possibilities and build up a reservoir of compelling ingredients. And if string theory is right, we might eventually learn how some models follow as consequences of it, much as thermodynamics was rooted in atomic theory. However, for about a decade the two communities were sharply divided. As Albion Lawrence, a young string theorist from Brandeis University, commented recently when he and I were discussing this schism, “One of the tragedies is that string theory and model building were distinct intellectual subjects. Model builders and string theorists weren’t talking to each other for years. I always thought of string theory as the granddaddy of all models.”
Both string theorists and model builders are searching for a tractable, elegant route that connects theory to the observed world. Any theory will be truly compelling and likely to be correct only if this path, and not just the view from the top, manifests this elegance. Model builders, who start from the bottom, run the risk of many false starts, but string theorists, who start at the top, run the risk of finding themselves at the edge of a precipitous, isolated cliff, too remote for them to find their way back to base camp.
You might say that we are all searching for the language of the universe. But whereas string theorists focus on the inner logic of the grammar, model builders focus on the nouns and phrases that they think are most useful. If particle physicists were in Florence learning Italian, the model builders would know how to ask for lodging and acquire the vocabulary that would be essential to finding their way around, but they might talk funny and never fully comprehend the
Inferno
. String theorists, on the other hand, might aspire to grasp the subtleties of Italian literature—but run the risk of starving to death before learning how to ask for dinner!
Fortunately, things have now changed. These days, theory and low-energy phenomena bolster each other’s progress, and many of us
now think about string theory and experimentally oriented physics simultaneously. I have continued to follow the model building approach in my research, but I now also incorporate ideas from string theory. I think we’re ultimately most likely to make advances by combining the best of both methods.
Albion points out that “the distinction is becoming fuzzy again, catalyzed in large part by the study of extra dimensions. People are talking to each other.” The communities are no longer so rigidly defined, and there is more common ground. There has been a renewed convergence of purpose and ideas. Both scientifically and socially, there are now strong overlaps between model builders and string theorists.
One of the beautiful aspects of the extra-dimensional theories I will describe is that ideas from both camps converged to produce them. String theory’s extra dimensions might be a nuisance, but they might also prove to be an opportunity for finding new ways of addressing old problems. We can certainly ask where the extra dimensions are, and why we haven’t seen them. But we might also ask whether these unseen dimensions could have any import in our world. These dimensions might help explain underlying relationships that are relevant to observed phenomena. Model builders relish the challenge of connecting notions such as extra dimensions to observable quantities such as relations among particle masses. And, if we’re lucky, the insights based on extra-dimensional models might successfully address one of the biggest problems facing string theory: its experimental inaccessibility. Model builders have used theoretical elements derived from string theory to attack questions in particle physics. And those models, including the ones that have extra dimensions, will have testable consequences.
When we investigate extra-dimensional models later on, we will see that the model building approach in conjunction with string theory has generated major new insights into particle physics, the evolution of the universe, gravity, and string theory. With the string theorist’s knowledge of grammar and the model builder’s vocabulary, the two together have begun to write quite a reasonable phrase book.
The Heart of Matter
Ultimately, the ideas we will consider encompass the entire universe. However, these ideas are rooted in particle physics and in string theory—theories that aspire to describe the smallest components of matter. So before setting out on our journey to the extreme theoretical territory these theories address, we’ll now take a brief trip into matter down to its smallest parts. On this guided tour of the atom, take note of matter’s basic building blocks and the sizes of the objects that different physical theories deal with. They should provide a few landmarks that you can use to orient yourself later on and help you to recognize the components with which each area of physics concerns itself.
The basic premise in most of physics is that elementary particles constitute the building blocks of matter. Peel away the layers, and inside you will always ultimately find elementary particles. Particle physicists study a universe in which these objects are the smallest elements. String theory takes this assumption one step further and postulates that those particles are the oscillations of elementary strings. But even string theorists believe that matter is composed of particles—the unbreakable entities at its core.
It might be difficult to believe that everything is composed of particles; they certainly are not evident to the naked eye. But that is because of the coarse resolving power of our senses, which cannot directly detect anything anywhere nearly as tiny as an atom. Nonetheless, even though we can’t directly view them, elementary particles are the elementary building blocks of matter. Just as the images on your computer or TV are composed of tiny dots, even though they present images that appear to be continuous, matter is composed of atoms, which are in turn composed of elementary particles. Physical objects around us appear to be continuous and uniform, but in reality they are not.
Before physicists could look inside matter and deduce its composition, they needed technological advances to create sensitive measuring instruments. But every time they developed more accurate technological tools,
structure
—more elementary constituents—
emerged. And every time physicists had access to tools that could probe still smaller sizes, they discovered yet more fundamental ingredients:
substructure
, constituents of the previously known structural elements.
The goal of particle physics is to discover matter’s most basic constituents and the most fundamental physical laws obeyed by those constituents. We study small distance scales because elementary particles interact at these scales, and it’s easier to disentangle fundamental forces. At large scales, the basic ingredients are bound into composite objects, which makes fundamental physical laws difficult to disentangle and therefore more obscure. Small distance scales are interesting because new principles and connections apply there.
Matter is not simply a Russian doll with smaller copies of similar entities inside. Smaller distances reveal truly novel phenomena. Even the workings of the human body—the heart and the circulation of the blood, for example—were badly misconstrued until scientists such as William Harvey cut people open in the 1600s and looked inside. Recent experiments have done the same thing with matter, exploring smaller distances where new worlds operate via more fundamental physical laws. And just as the blood’s circulation has important consequences for all human activity, the fundamental physical laws have important consequences for us on larger scales.
We now know that all matter is made up of
atoms
, which combine through chemical processes into
molecules
. Atoms are very small, about an angstrom, or one-hundredth of a millionth of a centimeter in size. But atoms are not fundamental: they consist of a central, positively charged
nucleus
which is surrounded by negatively charged
electrons
(see Figure 30). The nucleus is far smaller than the atom, occupying only about one hundred thousandth of the atom’s size. And the positively charged nucleus is itself composite: it is made from positively charged
protons
and neutral (uncharged)
neutrons
, collectively known as
nucleons
, which are not very much smaller than the nucleus in size. This was the picture of matter that scientists held before the 1960s, and is very likely the blueprint you learned about in school.
This template for the atom is correct, although, as we will see later, quantum mechanics gives a more interesting picture of an electron’s
orbits than any picture you can draw. But we now know that even the proton and neutron are not fundamental. Contrary to Gamow’s quote in the introduction, the proton and neutron contain substructure, more fundamental ingredients known as
quarks
. The proton contains two
up quarks
and one
down quark
, while the neutron contains two down quarks and one up quark (see Figure 31). These
quarks are bound together through a nuclear force known as the
strong force
. The electron, the other component of the atom, is different. So far as we can tell, it is fundamental: the electron cannot be divided into smaller particles and contains no substructure within.