If you bring a small magnet near some iron, the iron gets magnetized and you end up with a more powerful magnet. Something similar happens with Yang-Mills theories. If I have some particle with a Yang-Mills charge, say, a quark, then quarks and antiquarks can pop out of the vacuum around the charge and screen it, as happens in electromagnetism. But gluons can also pop out of the vacuum, and since they act like little magnets, they tend to align themselves along the direction of the field produced by the original quark. This increases the strength of the field, which in turn induces more gluons to pop out of the vacuum, which further increases the field, and so on.
As a result, the deeper into the virtual gluon cloud you penetrate—i.e., the closer you get to the quark—the weaker the field will look. Ultimately, as you bring two quarks closer together, the interaction will get so weak that they will begin to act as if they are not interacting at all, the characteristic of asymptotic freedom.
I used gluons and quarks as labels here, but the discovery of asymptotic freedom did not point uniquely to any specific Yang-Mills theory. However, Gross and Wilczek recognized the natural candidate was the Yang-Mills theory that Greenberg and others had posited was necessary for Gell-Mann’s quark hypothesis to explain the observed nature of elementary particles. In this theory each quark carries one of three different types of charges, which are labeled, for lack of better names, by colors, say, red, green, or blue. Because of this nomenclature Gell-Mann coined a name for this Yang-Mills theory: quantum chromodynamics (QCD), the quantum theory of colored charges, in analogy to quantum electrodynamics, the quantum theory of electric charges.
Gross and Wilczek posited, based on the observational arguments in favor of such a symmetry associated with quarks, that quantum chromodynamics was the correct gauge theory of the strong interaction of quarks.
The remarkable idea of asymptotic freedom got an equally remarkable experimental boost within a year or so of these theoretical developments. Experiments at SLAC and at another accelerator in Brookhaven, Long Island, made the striking and unexpected discovery of a new massive elementary particle that appeared as if it might be made up of a new quark—indeed, the so-called charmed quark that had been predicted by Glashow and friends four years earlier.
But this new discovery was peculiar, because the new particle lived far longer than one might imagine based on the measured lifetime of unstable lighter strongly interacting particles. As the experimentalists who discovered this new particle said, observing it was like wandering in the jungle and finding a new species of humans who lived not up to one hundred, but up to ten thousand years.
Had the discovery been made even five years earlier, it would have seemed inexplicable. But in this case, fortune favored the prepared mind. Tom Appelquist and David Politzer, both at Harvard at the time, quickly realized that if asymptotic freedom was indeed a property of the strong interaction, then one could show that the interactions governing more massive quarks would be less strong than the interactions governing the lighter, more familiar quarks. Interactions that are less strong would mean particles decay less quickly. What would otherwise have been a mystery was in this case a verification of the new idea of asymptotic freedom. Everything seemed to be fitting into place.
Except for one pretty big thing. If the theory of quantum chromodynamics was a theory of the interactions of quarks and gluons, where were the quarks and gluons? How come none had ever been seen in an experiment?
Asymptotic freedom provides a key clue. If the strength of the strong interaction gets weaker the closer one gets to a quark, then conversely it should get stronger and stronger the farther one is away from the quark. Imagine, then, what happens if I have a quark and an antiquark that are bound together by the strong interaction and I try to pull them apart. As I try to pull them apart, I need more and more energy because the strength of the attraction between them grows with distance. Eventually so much energy becomes stored in the fields surrounding the quarks that it becomes energetically favorable instead for a new quark-antiquark pair to pop out of the vacuum and then for each to become bound to one of the original particles. The process is shown schematically below.
It would be like stretching a rubber band. Eventually the band will snap into two pieces instead of stretching forever. Each piece in this case would then represent a new bound quark-antiquark pair.
What would this mean for experiments? Well, if I accelerate a particle such as an electron and it collides with a quark inside a proton, it will kick the quark out of the proton. But as the quark begins to exit the proton, the interactions of the quark with the remaining quarks will increase, and it will eventually be energetically favored for virtual quark-antiquark pairs to pop out of the vacuum and bind to both the ejected quark and the other quarks as well. This means that one will create a shower of strongly interacting particles, such as protons or neutrons or pions or so on, moving along the direction of the original ejected quark, and similarly a shower of strongly interacting particles recoiling in the direction of motion of the original remaining quarks left over from the proton. One will never see the quarks themselves.
Similarly, if a particle collides with a quark, in recoiling sometimes the quark will emit a gluon before it binds with an antiquark popping out of the vacuum. Then since gluons interact with each other as well as with quarks, the new gluon might emit more gluons. The gluons in turn will be surrounded by new quarks that pop out of the vacuum, creating new strongly interacting particles moving along the direction of each original gluon. In this case one would expect in some cases to see not a single shower moving in the direction of the original quark, but several showers, corresponding to each new gluon that is emitted along the way.
Because quantum chromodynamics is a specific, well-defined theory, one can predict the rate at which quarks will emit gluons, and the rate at which one would see a single shower, or jet as it is called, kicked out when an electron collides with a proton or neutron, and the rate at which one would see two showers, and so on. Eventually, when accelerators became powerful enough to observe all these processes, the observed rates agreed well with the predictions of the theory.
There is every reason to believe that this picture of free quarks and gluons quickly getting bound to new quarks and antiquarks so that one would never observe a free quark or gluon is valid. This is called Confinement because quarks and gluons are always confined inside strongly interacting particles such as protons and neutrons and can never break free from them without getting confined in newly created strongly interacting particles.
Since the actual process by which the quarks get confined occurs as the forces become stronger and stronger when the quark moves farther and farther away from its original companions, the standard calculations of quantum field theory, which are valid when the interactions are not too strong, break down. So this picture, validated by experiment, cannot be fully confirmed by tractable calculations at the moment.
Will we ever derive the necessary mathematical tools to analytically demonstrate from first principles that confinement is indeed a mathematical property of quantum chromodynamics? This is the million-dollar question, literally. The Clay Mathematics Institute has announced a million-dollar prize for a rigorous mathematical proof that quantum chromodynamics does not allow free quarks or gluons to be produced. While no claimants to the prize have yet come forward, we nevertheless have strong indirect support of this idea, coming not only from experimental observations, but also from numerical simulations that closely approximate the complicated interactions in quantum chromodynamics. This is heartening, if not definitive. We still have to confirm that it is some property of the theory and not of the computer simulation. However, for physicists, if not mathematicians, this seems pretty convincing.
One final bit of direct evidence that QCD is correct came from a realm where exact calculations can be done. Because quarks are not completely free at short distances, I earlier mentioned that there should be calculable corrections to exotic s
caling phenomena observed in the high-energy collisions of electrons off protons and neutrons, as originally observed at SLAC. Perfect scaling would require completely noninteracting particles. The corrections that one could calculate in quantum chromodynamics would only be observable in experiments that were far more sensitive than those originally performed at SLAC. It took the development of new, higher-energy accelerators to probe them. After thirty years or so, enough evidence was in so that comparison of theoretical predictions and experiment agreed at the 1 percent level, and quantum chromodynamics as the theory of the strong interaction was finally verified in a precise and detailed way.
Gross, Wilczek, and Politzer were finally awarded the Nobel Prize in 2004 for their discovery of asymptotic freedom. The experimentalists who had first discovered scaling at SLAC, which was the key observation that set theorists off in the right direction, were awarded the Nobel Prize much earlier, in 1990. And the experimentalists who discovered the charmed quark in 1974 won the Nobel Prize two years later, in 1976.
But the biggest prize of all, as Richard Feynman has said, is not the recognition by a medal or a cash award, or even the praise one gets from colleagues or the public, but the prize of actually learning something new about nature.
• • •
In this sense the 1970s were perhaps the richest decade in the twentieth century, if not in the entire history of physics. In 1970 we understood only one force in nature completely as a quantum theory, namely quantum electrodynamics. By 1979 we had developed and experimentally verified perhaps the greatest theoretical edifice yet created by human minds, the Standard Model of particle physics, describing precisely three of the four known forces in nature. The effort spanned the entire history of modern science, from Galileo’s investigations of the nature of moving bodies, through Newton’s discovery of the laws of motion, through the experimental and theoretical investigations of the nature of electromagnetism, through Einstein’s unification of space and time, through the discoveries of the nucleus, quantum mechanics, protons, neutrons, and the discovery of the weak and strong forces themselves.
But the most remarkable characteristic of all in this long march toward the light is how different the fundamental nature of reality is from the shadows of reality that we experience every day, and in particular how the fundamental quantities that appear to govern our existence are not fundamental at all.
Making up the heart of observed matter are particles that had never been directly observed and, if we are correct, will never be directly observable—quarks and gluons. The properties of forces that govern the interactions of these particles—and also the particles that have formed the basis of modern experimental physics for more than a century, electrons—are also, on a fundamental level, completely different from the properties we directly observe and on which we depend for our existence. The strong interaction between protons and neutrons is only a long-distance remnant of the underlying force between quarks, whose fundamental properties are masked by the complicated interactions within the nucleus. The weak interaction and the electromagnetic interaction, which could not be more different on the surface—one is short-range, while the other is long-range, and one appears thousands of times weaker than the other—are in fact intimately related and reflect different facets of a single whole.
That whole is hidden from us because of the accident of nature we call spontaneous symmetry breaking, which distinguishes the two weak and electromagnetic interactions in the world of our experience and hides their true nature. More than that, the properties of the particles that produce the characteristics of the beautiful world we observe around us are only possible because, after the accident of spontaneous symmetry breaking, just one particle in nature—the photon—remains massless. If symmetry breaking had never occurred so that underlying symmetries of the forces governing matter were manifest—which in turn would mean that the particles conveying the weak force would also be massless, as would most of the particles that make us up—essentially nothing we see in the universe today, from galaxies to stars, to planets, to people, to birds and bees, to scientists and politicians, would ever have formed.
Moreover, we have learned that even these particles that make us up are not all that exist in nature. The observed particles combine in simple groupings, or families. The up and down quarks make up protons and neutrons. Along with them one finds the electron, and its partner, the electron neutrino. Then, for reasons we still don’t understand, there is a heavier family, made up of the charm and strange quark on the one hand, and the muon and its neutrino on the other. And finally, as experiments have now confirmed over the past decade or two, there is a third family, made of two new types of quarks, called bottom and top, and an accompanying heavy version of the electron called the tau particle, along with its neutrino.
Beyond these particles, as I shall soon describe, we have every reason to expect that other elementary particles exist that have never been observed. While these particles, which we think make up the mysterious dark matter that dominates the mass of our galaxy and all observed galaxies, may be invisible to our telescopes, our observations and theories nevertheless suggest that galaxies and stars could never have formed without the existence of dark matter.
And at the heart of all of the forces governing the dynamical behavior of everything we can observe is a beautiful mathematical framework called gauge symmetry. All of the known forces, strong, weak, electromagnetic, and even gravity, possess this mathematical property, and for the three former examples, it is precisely this property that ensures that the theories make mathematical sense and that nasty quantum infinities disappear from all calculations of quantities that can be compared to experiment.
With the exception of electromagnetism, these other symmetries remain completely hidden from view. The gauge symmetry of the strong force is hidden because confinement presumably hides the fundamental particles that manifest this symmetry. The gauge symmetry of the weak force is not manifest in the world in which we live because it is spontaneously broken so that the W and Z particles become extremely massive.
• • •
The shadows on the wall of everyday life are truly merely shadows. In this sense, the greatest story every told, so far, has been slowly playing out over the more than two thousand years since Plato first imagined it in his analogy of the cave.
But as remarkable as this story is, two elephants remain in the room. Two protagonists in our tale could until recently have meant that the key aspects of the story comprised a mere fairy tale invented by theorists with overactive imaginations.
First, the W and Z particles, postulated in 1960 to explain the weak interaction, almost one hundred times more massive than protons and neutrons, were still mere theoretical postulates, even if the indirect evidence for their existence was overwhelming. More than this, an invisible field—the Higgs field—was predicted to permeate all of space, masking the true nature of reality and making our existence possible because it spontaneously breaks the symmetry between the weak and the electromagnetic interactions.
To celebrate a story that claims to describe how it is that we exist, but that also posits an invisible field permeating all of space, sounds suspiciously like a religious celebration, and not a scientific one. To truly ensure that our beliefs conform to the evidence of reality rather than how we would like reality to be, to keep science worthy of the name, we had to discover the Higgs field. Only then could we truly know if the significance of the features of our world that we hold so dear might be no greater than that of the features of one random ice crystal on a window. Or, more to the point, perhaps, no greater than the significance of the superconducting nature of wire in a laboratory versus the normal resistance of the wires in my computer.
The experimental effort to carry out this task was no easier than that in developing the theory itself. In many ways it was more daunting, taking more than fifty years and involving the most difficult fabrication of technology that humans have ever attempte
d.
Chapter 20
* * *
SPANKING THE VACUUM
If anyone slaps you on the right cheek, turn to him the other also.
—MATTHEW 5:39
As the 1970s ended, theorists were on top of the world, triumphant and exultant. With progress leading to the Standard Model so swift, what other new worlds were there to conquer? Dreams of a theory of everything, long dormant, began to rise again and not just in the dim recesses of the collective subconscious of theorists.
Still, the W and Z gauge particles had never actually been observed, and the challenge to directly observe them was pretty daunting. Their masses were precisely predicted in the theory at about ninety times the mass of the proton. The challenge to produce these particles comes from a simple bit of physics.
Einstein’s fundamental equation of relativity, E = mc2, tells us that we can convert energy into mass by accelerating particles to energies of many times their rest mass. We can then smash them into targets to see what comes out.
The problem is that the energy available to produce new particles by smashing other fast-moving particles into stationary targets is given by what is called the center-of-mass energy. For those undaunted by another formula, this turns out to be the square root of twice the product of the energy of the accelerated particle times the rest mass energy of the target particle. Imagine accelerating a particle to one hundred times the rest mass energy of the proton (which is about one gigaelectronvolt—GeV). In a collision with stationary protons in a target, the center-of-mass energy that is available to create new particles is then only about 14 GeV. This is just slightly greater than the center-of-mass energy available in the highest-energy particle accelerator in 1972.
The Greatest Story Ever Told—So Far Page 23