Fundamentals

by Frank Wilczek

  That bold strategy works amazingly well. If you accept the basic picture that most of the mass of an atom, and all of its positive electric charge, is concentrated in a small nucleus, and that the remainder consists of electrons, then Maxwell’s equations plus a quantum condition—this time, for the electron field—do the rest. Together they give us a model of atoms that is both precise and rich in consequences.

  How do we know it’s right? Atoms sing songs that bare their souls, in light. Allowing for a little poetic license, this phrase describes the art and science of spectroscopy.

  Spectroscopy

  Let’s begin at the beginning, with the photon* and electron fields. The photon field gave us, through its quantum condition, photons. Photons, being electrically neutral, do not influence one another directly.

  The electron field gives us, through its quantum condition, electrons. Electrons do influence one other, through electric forces. Because of that, we can’t build up all the excitations of the electron field simply by adding up the most basic ones independently. But when electrons are reasonably far apart, the energy involved in their interactions is much less than the energy tied up in their mass (that is, E = mc2), so they retain their integrity. In other words, the basic excitations of the electron field look like a bunch of little particles—electrons—that influence each other. That field-based ferment provides the usual starting point both for elementary science courses and for advanced chemistry and biology texts.

  To model an atom, we introduce the influence of a nucleus, and let it act among excitations of the electron field that contain enough electrons to balance the positive electric charge of that nucleus. Within that setup, the accurate equations for the electron field can get quite complicated, because we need to include both the influence of the nucleus on the electrons and the influence of the electrons on one another. This is the beginning of the long but inexhaustible story of atomic physics and chemistry, based on fundamentals. Many talented people spend their entire careers exploring parts of it.

  Our goal here, however, is both broader and more limited. We want to understand in a very general way what some of the most basic predictions of atomic physics look like, and how they connect to fundamentals. For that purpose, the central result of atomic physics is beautifully simple to state: By studying the colors of light that atoms emit, we can collect rich and detailed information about how they work.

  Here’s how that goes: An atom can exist in states with different total energy. The allowed energies form, because of the quantum condition, a pattern of discrete values. States with higher energy can decay into states with lower energy, by radiating a photon. The photon’s energy reads out the difference in energy between the initial and final atomic state energies. As Planck and Einstein taught us, the energy of a photon is related to its frequency—or, equivalently, its color. And that is something that is practical to measure.

  The array of colors that an atom emits is called its spectrum. The study of spectra is called spectroscopy. Spectroscopy is among the most powerful tools we have to communicate with Nature. It can be used to study not only electrically neutral atoms, but molecules, too, or atoms that are not electrically neutral (ions), or anything else that emits photons.

  In 1913, before quantum mechanics assumed its modern, mature form, Niels Bohr invented some rules to restrict the possible energies of hydrogen atoms. Bohr pulled his rules out of thin air, using inspired guesswork. They predicted a spectrum that agreed remarkably well with existing observations. This was not entirely surprising, since they were devised with those observations in mind. More impressive was that Bohr’s framework led to additional predictions, which all worked. When Einstein, attending a seminar, first learned of one notable confirmation, he was visibly moved, and said (referring to Bohr’s work), “Then it is one of the greatest discoveries.”

  Bohr’s swashbuckling success was enormously influential. It inspired people to look for more general, logically coherent quantum conditions. Today, we see Bohr’s rules, together with the Planck-Einstein relation, as the precursors of our modern quantum conditions.

  Einstein called Bohr’s work “the highest form of musicality in the sphere of thought.” Yet modern quantum mechanics, its descendant, is far more harmonious—and the resemblance of its equations to the equations that arise in music is uncanny.

  The equations for the electron field around a nucleus, specifically, resemble the equations for a gong constructed from a strange material. Within that metaphor, the spectrum of colors of light emitted by the atom corresponds to the spectrum of tones emitted by the gong. Both reflect their instruments’ stable patterns of vibration. But the spectra of atoms are not designed for musical purposes. They do not form the notes of any sensible scale. Especially when more than one electron is involved, the allowed patterns of vibration can become very intricate. Atomic spectra are perfectly definite, and in principle they can be calculated, but they are complicated.

  The disciplined complexity of spectra is a gift to human understanding. Since each distinct kind of atom emits a distinct pattern of light, atomic spectra form a kind of signature, or fingerprint. Thus, simply by looking—and paying careful attention to color!—we can discern the identity and study the behavior of atoms that are far removed from us in space and time. The cosmos becomes a giant, well-equipped chemistry lab. For that reason, spectroscopy is a mainstay of astrophysics and cosmology.

  Spectroscopy also allows us to test our fundamentals. Since—so far—our accurate theoretical calculations of these spectra, in the cases where we’ve managed to do them, agree with precise observations, we gain confidence that we’ve got the laws right. And since—so far—astronomers and chemists have seen the same set of atomic spectra everywhere and at every time they’ve looked, we conclude that the same laws operate upon the same basic materials everywhere in the universe and throughout its history.

  QUANTUM CHROMODYNAMICS (QCD)

  The wonderful results of atomic modeling and spectroscopy take off from the bold assumption that atoms have tiny nuclei that contain all of their positive electric charge and almost all of their mass. Following that success, the next item on the fundamental physics agenda, logically, was to understand those nuclei. It launched an exploration that dominated research in physics over much of the twentieth century, and was full of surprising discoveries and twists and turns. Here, so that we can get right to fundamentals, I will pass lightly over almost all of that history. If you’d like to learn more about the early history of nuclear physics and its unanticipated, world-changing spin-offs, I highly recommend the book The Making of the Atomic Bomb by Richard Rhodes.

  The central discovery in nuclear physics, prior to quantum chromodynamics, was that it is useful to model atomic nuclei starting with protons and neutrons as ingredients. But some new force had to act among those ingredients, to hold the nucleus together, since electrical repulsion among the protons wants to blow it apart, and gravity is far too weak. People called this new force the strong force, and they set out to understand it. When people investigated the behavior of protons and neutrons with that goal in mind, however, things got very messy very quickly. Decisive progress occurred only after they looked inside protons.

  Inside Protons

  To look inside protons, physicists follow a similar strategy to the ones they used earlier to study the interiors of atoms—scattering experiments, à la Geiger and Marsden, which we discussed earlier, but with different kinds of beams and with an added refinement. They expose the subject of our attention to a beam of particles, watch to see how those particles get deflected, and from that observed pattern of effects work backward to the structure that causes them.

  The crucial refinement is that one must study not only how much the beam particles (which in the pioneering experiments were electrons) get deflected, but also how much energy they lose. That extra information allows us to get resolution in time as well as in space. It
allows us, after a lot of image processing, to get snapshots of proton interiors. It’s important to get snapshots, it turns out, because inside protons things are moving fast. Long exposures—which in this context mean exposures longer than a millionth of a billionth of a billionth of a second—show only a blur.

  Freedom and Confinement

  Pictures of proton interiors revealed several surprises. They showed, first of all, that protons contain smaller particles, including quarks. Quarks had previously been used by scientists as a theoretical tool for organizing observations about strongly interacting particles, but their physical existence was widely doubted. Even one of their inventors, Murray Gell-Mann, expressed doubts. He compared his quarks to the veal in a French recipe, where “a piece of pheasant meat is cooked between two slices of veal, which are then discarded.”

  (The other inventor of quarks, George Zweig, took them much more literally. He spent many years trying to devise ways to detect isolated quarks, outside of protons. Those attempts never panned out, and now we know—or think we know—that they were doomed to failure.)

  Skepticism about the existence of quarks was not unreasonable before their observation, because they have some unprecedented properties and behaviors. For one thing, their electric charge is a fraction of an electron’s. Fractional charges had never been encountered before. For another, quarks are never found in isolation, but only within protons and other strongly interacting particles (so-called hadrons).

  The latter behavior, called “confinement,” continued to be puzzling, even after the quark-revealing snapshots of protons came to light. Inside the proton, it appeared, quarks hardly affected one another’s behavior. Yet ultimately the forces between them must prevent any from escaping.

  My first mature research in physics, done as a graduate student with my adviser, David Gross, addressed that problem. We wanted to find a theory that explained that paradoxical behavior of quarks but retained the “sacred principles” of locality, relativity, and quantum theory.

  Thus, we hunted for a theory based on quantum fields that leads to forces between particles that are powerfully attractive when the particles are far apart but grow feeble as the particles come together. In everyday life we can manufacture such forces from rubber bands. But rubber bands are not quantum fields. Getting quantum fields to act like rubber bands is not so easy.

  After a brief but intense struggle, we found a theory that does the job. It is the theory called quantum chromodynamics, or QCD. At first, the evidence for our theory was very tenuous. But over time, as people performed experiments at higher energies and used computers to solve more problems, the evidence began to accumulate and solidify. By now, almost fifty years later, it is mountainous.

  It has been a transcendent gift to experience each step on a path leading from vague aspirations and puzzlement through disciplined exploration, glimmers of enlightenment, calculations, testable predictions, and finally, at journey’s end, to shared truths about physical reality. David Gross and I received the Nobel Prize for our work in 2004. We shared it with David Politzer, who did related calculations independently.

  Mass from Energy: m = E/c2

  Now I’ll discuss one of QCD’s most striking applications. QCD explains the origin of most of our mass.

  Einstein’s famous formula E = mc2 expresses the energy latent in an object at rest, due to its mass. Since energy is conserved, we can use that formula to calculate how much energy is liberated when a particle breaks up or decays into particles of smaller mass. This formula gets used in that way when we trace how energy from Earth’s radioactivity moves continents (plate tectonics), for example, or how nuclear burning powers stars.

  It is a beautiful thing that the logic of the formula can also be read in the opposite direction, to produce mass from pure energy: m = E/c2. This is, in fact, how most of the mass of protons and neutrons—and thus the mass of human beings and the objects of everyday life—emerges.

  Inside protons we have quarks and gluons.* Quarks have very small masses, and gluons have zero mass. But inside protons they are moving around very fast, and thus they carry energy. All that energy adds up. When the accumulated energy is packaged into an object that is at rest overall, such as the proton as a whole, then that object has the mass m = E/c2. This accounts for almost all of the mass of protons and neutrons, as a product of pure energy. Almost all of the mass of human beings, in turn, arises from the mass of the protons and neutrons they contain. Mystics, especially in the Chinese tradition, often speak of chi, a universal energy that flows through creation, and they try to cultivate their inner chi. QCD teaches us that we come by it naturally.

  One of my earliest childhood memories is a of small notebook I kept when I was first learning about relativity, on the one hand, and algebra, on the other. I didn’t really understand either subject, but I thought that if I worked at it, I might discover something wonderful, like E = mc2. I had m = E/c2 in that notebook. Little did I know . . .

  GRAVITY (GENERAL RELATIVITY)

  Newton’s Coincidence

  Newton’s theory of gravity, based on the simple force law we described previously, went from success to success for more than two hundred years. From the beginning, though, it contained a striking, unexplained coincidence—actually, an infinite number of coincidences. According to Newton’s laws of motion, the force exerted on a body equals the body’s mass times the acceleration that the force induces. On the other hand, according to Newton’s law of gravity, the force exerted on a body is also proportional to that body’s mass. Putting those two laws together, we see that the body’s mass cancels. Gravity, in other words, provides a universal source of acceleration, the same for every object it acts upon.

  There are two distinctive kinds of mass in Newton’s theory. In one context, inertial mass governs a body’s response to forces in general. In another context, gravitational mass governs the gravitational force that a body feels or exerts.* There is nothing in the theory’s logical structure which requires that inertial mass and gravitational mass are proportional. The theory would still function perfectly well if that were not the case. One could imagine, for instance, that the ratio of inertial to gravitational mass might depend on a body’s chemical composition. Newton’s theory left the never-failing proportionality of inertial and gravitational mass or, equivalently, the universality of gravitational acceleration, as an unexplained coincidence.

  Responsive Space-Time

  Einstein put forward his theory of gravity, the general theory of relativity, in 1915. It explains Newton’s coincidence in an astonishing and deeply satisfying way. It also fulfills Newton’s aspiration for a theory of gravity based on local action, by bringing gravity within the same field-based framework as electromagnetism.

  If we don’t insist on mathematical details—and here, of course, we won’t—then we can portray the majestic logic of general relativity in ten broad strokes:

  A universal truth should have a universal explanation.

  Therefore, the “coincidence” that gravity will impart the same acceleration to any body that occupies a given position at a given time, regardless of the body’s properties, should be foundational.

  Thus, gravitational acceleration should reflect a property of space-time.

  One property that space-time can have is curvature.*

  The curvature of space-time affects the motion of bodies moving in space-time. Bodies that move “as straight as possible” might nevertheless fail to move in a straight line.

  In space-time, a straight line represents motion at a constant velocity. Deviation from straight-line motion, therefore, represents acceleration.

  Combining points 5 and 6, we see a way to achieve point 3: Gravity reflects space-time curvature.

  Since curvature can vary from place to place, and in time, it defines a field.

  To have a theo
ry of gravity, we need to have an equation that connects the curvature field of space-time to the influence of matter. Indeed, as Newton taught us, matter can exert gravity.

  Newton’s law of gravity suggests that the crucial property of matter, in exerting gravity, is its mass. It suggests, more specifically, that space-time curvature, which encodes gravity, should be proportional to mass. That suggestion is on the right track. It must be refined in order to get a precise equation, but the necessary refinement, once you have special relativity, is a matter of technique. (As I mentioned earlier, the main refinement is to recognize that all forms of energy, and not only mass-energy, exert gravity.)

  John Wheeler, the poet of relativity, summed it up this way: “Space-time tells matter how to move; matter tells space-time how to bend.”

  THE WEAK FORCE

  Natural Alchemy

  The weak force neither binds things together nor moves things around. Its importance lies in its power to transform. Its transformative power, leveraged by its very weakness, gives it a unique, central role in the evolution of the universe. The weak force supplies a kind of cosmic storage battery, allowing for the slow release of cosmic energy.

  In getting acquainted with the weak force, the process of neutron decay is a good place to start. It is one of the simplest weak force processes, and also one of the most important. Isolated neutrons decay with a half-life of a little over ten minutes, almost always into a proton, an electron, and an antineutrino. (Antineutrinos are the antiparticles of neutrinos.) Since neutrons and protons are much heavier than the other particles, another perspective on neutron decay can be illuminating. We can think of it as the conversion of neutrons into protons, with release of energy.