Read an Excerpt
Excerpt from Chapter 2:
The Standard Model
of Particle Physics
To better understand the reasons why we think supersymmetry will be discovered, and how it extends our present description of nature, we need to know a little about the main achievements of over two centuries of physics. Past study has led to the establishment of the Standard Model of particle physics, a complete description of the basic particles and forces that shape our world. In this chapter we will consider first the five forces and then the particles. The world we see is built entirely of three particles: the electron and two particles similar to the electron called quarks. There are more particles-antiparticles, neutrinos, more quarks and more particles like the electron, and Higgs bosons.
We understand why some of the additional particles exist, but not others. Then we will learn a little about Feynman diagrams, a way of picturing how particles interact (for practitioners it is also a way to calculate the behavior of particles). Next we consider a property of all particles called spin and how it leads to categorizing particles into two groups, bosons and fermions. We will see later that at a deeper level, supersymmetry merges these two categories. Last we look at reasons why the Standard Model is not expected to be the final stage of particle physics, even though it successfully describes phenomena and experiments.
When Gauguin painted "Where do we come from? What are we? Where are we going?" we knew only of the electrical, magnetic, and gravitational forces. There was controversy about whether atoms existed. The first particle to be discovered, the electron, had just been found. Radioactive decays of nuclei ("radioactivity") had just been noticed. These decays could not be explained by the known interactions, so physicists realized that another force was needed to describe nature's behavior. It was called the weak force, because its effects were rare and essentially never occurred when two interacting objects were separated by distances larger than an atom. In 1911 atoms were found to have a nucleus, and it was discovered that heavier nuclei have a number of protons in them. Because physicists knew that the repulsive electrical force pushed the protons apart, it became clear that yet another force-the nuclear force-must exist to bind the protons together into a stable nucleus. The effects of the nuclear force also can be felt only at tiny distances, no larger than a nucleus. Although Newton had correctly foreseen three centuries ago that there could be forces that had effects only at small distances, finding evidence for them took over two centuries.
These five forces (the electrical, magnetic, gravitational, weak, and nuclear forces) account for all we observe in nature. The interactions of particles with a "Higgs field" (more about this later, especially in Chapter 7) can be thought of as giving mass to the particles, so one can think of the Higgs interaction as an additional force. There may in a sense be other forces, but they are not relevant for the behavior of particles or for how particles combine to make up the world around us. (For completeness, let me mention two at this point. One is a force that recent evidence suggests causes the universe to expand more rapidly than it would if only the gravitational force affected its expansion. This force does not in any way affect the behavior of individual particles. For historical reasons it is called the cosmological constant. The other possible forces have effects only at extremely tiny distances far smaller than the size of a proton.) We will return to possible additional forces later briefly; the five known forces are the important ones for our purposes. Any others do not affect how our world works, though understanding them may be essential to achieve a complete picture of the laws of nature.
Ever since Charles-Augustin de Coulomb showed, over two hundred years ago, that the electrical and gravitational forces depend in the same way on the distance between interacting objects, and that therefore the formulas describing them have the same form, physicists have tried to unify our understanding of them. In the second half of the nineteenth century, using the work of Michael Faraday and others, James Clerk Maxwell succeeded in relating the electrical and magnetic forces, in the sense that electrical forces that vary in space or time generate magnetic forces, and vice versa. By the 1960s we knew of the five -forces, the electrical and magnetic ones being unified into electromagnetism. There was no theory at all of the weak and nuclear forces, only a few known regularities of their behavior. By the 1980s, however, the Standard Model had emerged and had been well tested. It was a complete description of the weak, electromagnetic, and strong (nuclear) forces, fully consistent with quantum theory and special relativity. The progress-over two decades was spectacular-in that short period, we went from a crude awareness of the weak and strong forces to their comprehensive description.
The picture of the electromagnetic force that emerges is that electrons, and any particles that have electric charge, interact by exchanging photons. The photons can carry energy between the electrons; two electrons can scatter off one another by exchanging a photon; and an electron and a proton bind by exchanging many photons, which provide an attractive force that keeps the electron and proton connected in a stable object, a hydrogen atom. All the forces work in a similar way. The gravitational force arises from the exchange of gravitons. The analogous particles for the weak interactions are called W and Z bosons, and for the strong force they are called gluons. In all these cases, we speak of the photon, W and Z bosons, and gravitons as "mediating" the forces. There is one more subtlety in connection with my use of the name strong force here. Because of the history, I cheated a little when I listed the nuclear force above. It turns out that the nuclear force between protons and neutrons that binds them into nuclei is not the fundamental force. Rather, the basic force is the strong force between quarks, and the nuclear force is a kind of residual effect after quarks are bound into protons and neutrons. We'll return to it after we describe the quarks.
MASS, DECAYS, AND QUANTA
Two frequently used words about particles that can be confusing are mass and decays. For our purposes, mass essentially means weight, and we don't need a more precise definition. Some particles, such as photons, don't have any mass. The masses of particles are measured mostly by bouncing particles off each other, since how much they bounce is related to how heavy they are.
Nearly all particles are unstable and decay into others. The word decay has a technical meaning in physics-one particle disappears, typically turning into two or three others. A major difference between the way decay is used in physics and its use in everyday life or biology is that the particles that characterize the final state are not in any sense already in the decaying particle. The initial particle really disappears, and the final particles appear. The photons that make up the light we see provide an example: The photons emitted from a light bulb when it is turned on are not particles that were in the bulb just waiting to come out, and photons that enter our eyes after bouncing off an object are absorbed by the molecules in our eyes and disappear. All particles can be created or absorbed in interactions with other particles. Most particles were created during the Big Bang, and particles can be created in collisions, e.g., at colliding-beam accelerators. Which particles can appear or disappear in any interaction is not arbitrary but is, rather, fully determined by the interactions described by the Standard Model (and its extensions such as supersymmetry).
Two constraints keep a few particles from decaying. First, the total amount of energy in any process must not change-we say energy is conserved. Imagine a decaying particle at rest; its energy is just its mass. That mass is divided into the sum of masses of the particles created in its decay, plus some energy of motion of those particles. Since energy can't appear from nothing, the particles created in the decay must be lighter than the decaying particle. Second, most particles carry some charge (electric charge and some similar charges associated with other forces). Charges are also conserved-the total amount of charge can't change in a process. Because of these two constraints, several of the lighter particles (electrons, for example) do not decay. Whenever basic particles are able to decay, the decay is typically rapid, occurring in a tiny fraction of a second.
Electromagnetic waves carry energy from antennas to our radios and from light bulbs to our eyes. One of the things quantum theory has taught us is that the energy is carried in little chunks (or quanta), photons. Any electric charge sets up an electric field around itself, and when that charge oscillates (say, in an antenna), it radiates the electromagnetic wave or the photons. We have also learned that there is a gravitational field associated with mass, and there are other fields associated with matter-with electrons and other particles. All the particles can be thought of as the quanta of the fields. In this book we won't make any technical use of such ideas, but every time we speak of some kind of field, we will associate quanta and therefore particles with it, and vice versa.
THE PARTICLES: DO WE REALLY KNOW THE FUNDAMENTAL CONSTITUENTS OF MATTER?
When viewed from the particle side, the Standard Model is remarkable. What are we made of? What happens if we keep cutting an apple, or a person, into smaller and smaller pieces? Do we reach a smallest piece? What could it be? What are the stars made of? Everyone has wondered about such questions. The answer is that everything we see in the universe, from the smallest cell to flowers to people to stars, is made of three kinds of matter particles, bound together by gluons and photons. When we get to big objects such as planets and stars, gravity binds too. The three matter particles are the familiar electron and two particles similar to the electron called quarks, the up quark and the down quark. Up and down do have a technical meaning, but it's not important here. All of the basic particles carry various amounts of charges, electric charge and weak charge and strong charge. The weak and strong charges are somewhat like electric charge, but because they have no effects outside atoms, they are not familiar to us in everyday life. The main difference between electrons and quarks is that the quarks carry the strong charge, so they interact via exchanging gluons, whereas electrons do not interact with gluons at all. Electrons and quarks all have electric charges and masses (weights) in different amounts. Sometimes electrons are denoted by e, up quarks by u, and down quarks by d.
How do these seeds form our world? The quarks bind together to make neutrons and protons, neutrons having an up quark and two down quarks, protons having two up quarks and one down quark. The quarks interact via the strong force, mediated by gluon exchange. The edges of protons and neutrons are not sharp-gluons range outward a little before they are brought back by the attractive force of the quarks. Gluons that are a little outside the proton and neutron in turn exert an attractive force felt by other protons and neutrons; this residual strong force is the nuclear force that binds the protons and neutrons into nuclei. The nuclear force is strong enough to hold together many nuclei, with from 1 to 92 protons and varying numbers of neutrons. The electrical repulsion felt by one proton (due to all the other protons in the nucleus) increases as the number of protons increases, and with more than 92 protons the nucleus becomes unstable. This is why there are only 92 naturally occurring chemical elements. The electromagnetic force, mediated by photons, binds electrons to nuclei to make atoms, the atoms of the chemical elements. Outside an atom there is a residual electromagnetic force (analogous to the residual strong force outside protons and neutrons described earlier in this paragraph) that binds atoms into molecules. Atoms and molecules build up rocks, cells, and all of the world around us. All of the marvelous complexity and color and structure of our world arises from these simple foundations.
Always in the past when objects were studied at smaller distances, they turned out to have structure. The atoms of the 92 chemical elements were not the atoms invented by the Greeks as the basic indestructible units of matter, because they turned out to have a nucleus surrounded by electrons. The nucleus turned out to be made of protons and neutrons. Protons and neutrons themselves turned out to be made of quarks bound by gluons. Why, then, do we think that the electrons and quarks are the true Greek "atoms" and that despite a history of smaller and smaller units, the progression stops with them? There are three kinds of reasons that lead most particle theorists to think we have finally reached the end of the line.
The first reason, significant but less important than the others, is that investigators have tried by many means to determine whether electrons, quarks, W bosons, and gluons show any evidence of structure, and they have not found any. These experiments have probed perhaps 10,000 times further than it took to see structure in the past, but electrons and quarks continue to behave as point-like objects with no parts.
The second reason is that always before, the prevailing theory (that of atoms or nuclei or protons) did not agree with experiment or even make sense unless these objects had structure at smaller distances, but the Standard Model is different. Because the Standard Model is a quantum theory, it is possible to ask how the forces behave at smaller and smaller distances and to do calculations to answer the question. Suppose that the basic particles were indeed point-like. How strong would the forces be if we could examine them not just down to almost 10-" meter, where experiments can presently be done, but at a million million times smaller distances? The calculations show that in the Standard Model, all the interactions become weaker at smaller distances. The Standard Model does not lead to...