Warped Passages (37 page)

But actual renormalization group calculations are even more clever, since they add up the contributions of friends talking to one another as well. A better analogy for the contributions due to virtual particles resembles the paths of a message as it goes through a big bureaucracy. If a person at the top of the hierarchy sends a message, it will go through directly. But someone lower down in the hierarchy might have to have his messages vetted by his bosses. If someone at an even lower level sends a message, it might first have to circulate through even more layers of red tape before ultimately reaching its destination. In that case, at each level bureaucrats would send the message around before sending it on to successively higher levels. Only after the message finally reached the upper echelons would it be released. The message that emerged in this case would generally not be the original; instead, it would be the one that was filtered through this many-layered bureaucracy.

If you think of virtual particles as bureaucrats, and a higher-level bureaucrat as corresponding to a virtual particle with higher energy, a high-level message would get directly communicated, whereas the lower-level ones would pass through many stages. The quantum mechanical vacuum is the “bureaucracy” a photon encounters. Each interaction is vetted through intermediate virtual particles with less and less energy. As in a bureaucracy, there can be diversions at all levels (or distances). Some of the paths will bypass the “bureaucratic” detours imposed by virtual particles, and some will involve virtual particles that travel over ever-increasing distances. The shorter-distance
(higher-energy) communication encounters fewer virtual processes than those that occur at larger distances.

However, there is a notable difference between virtual processes and a bureaucracy. In a bureaucracy, any one particular message takes one particular path, no matter how complicated that path. Quantum mechanics, on the other hand, says there can be many paths. And it insists that the net strength of an interaction is the sum of the contribution from all the possible paths that could occur.

Consider a photon traveling from one charged particle to another. Because it can turn into virtual electron-positron pairs en route (see Figure 60), quantum mechanics tells us that sometimes it will. And the paths with virtual electrons and positrons influence the efficacy with which the photon communicates the electromagnetic force.

Figure 60.
Virtual correction to electron-positron scattering. Reading from left to right: an electron and a positron annihilate into a photon, which in turn splits into a virtual electron-positron pair, which then annihilate back into a photon, which in turn converts to an electron and positron. The intermediate virtual electron and positron thereby affect the strength of the electromagnetic force.

And this is not the only quantum mechanical process that can occur. Virtual electrons and positrons can themselves emit photons, which can turn into other virtual particles, and so on. The distance between the two charged particles that exchange the photon determines how many such interactions the messenger photon will have with particles
in the vacuum, and how large an impact the interactions will have. The strength of the electromagnetic force is the net result of the many paths the photon takes when all possible bureaucratic detours—quantum mechanical processes in which virtual particles might participate over long or short distances—are taken into account. Because the number of virtual particles that a photon will encounter depends on the distance it travels, the photon’s interaction strength depends on the distance between the charged objects with which it interacts.

When all the contributions from all possible paths are added together, the calculation shows that the vacuum dilutes the message that the photon carries from the electron. The intuitive explanation for the dilution of the electromagnetic interaction is that opposite charges attract and like charges repel, and therefore, on average, virtual positrons are closer to an electron than are virtual electrons. The charges from the virtual particles therefore weaken the full impact of the initial electron’s electric force. Quantum mechanical effects
screen
the electric charge. Electric charge screening means that the strength of the interaction between a photon and an electron decreases with distance.

The true electric force at long distances appears to be smaller than the classical short-distance electric force because a photon that communicates a force over short distances more frequently takes a path that doesn’t involve virtual particles. A photon that travels a short distance wouldn’t have to travel through a big, weakening cloud of virtual particles, as the photon that was communicating a force far away would have to do.

Not just the photon, but all force-carrying gauge bosons interact with virtual particles en route to their destination. Virtual particle pairs, the particle and its antiparticle, spontaneously erupt from and get absorbed by the vacuum, affecting the net strength of an interaction. These virtual particles temporarily waylay the gauge boson transmitting the force and change its overall interaction strength. Calculations show that the weak force’s strength, like electromagnetism’s, decreases with distance.

However, virtual particles don’t always put the brakes on interactions. Surprisingly, they can sometimes help them along. In the early 1970s, David Politzer, who was then a Harvard graduate student of
Sidney Coleman (who suggested the problem), and separately David Gross and his then student, Frank Wilczek, who were both at Princeton, as well as Gerard ’t Hooft in Holland, did calculations that demonstrated that the strong force behaves in precisely the opposite way from the electric force. Rather than screening the strong force at long distances and thereby making it weaker, virtual particles actually enhance the interactions of the gluons (the particles that communicate the strong force)—so much so that the strong force at long distances deserves its name. Gross, Politzer, and Wilczek won the 2004 Nobel Prize for Physics for their critical insight into the strong force.

The key to this phenomenon is the gluons themselves. One big difference between gluons and photons is that gluons interact with one another. A gluon can enter an interaction region and turn into a pair of virtual gluons which then influence the force’s strength. These virtual gluons, like all virtual particles, exist only momentarily. But their effects pile up as you increase the distance, until the strong force is indeed extraordinarily strong. And the result of a calculation is that virtual gluons dramatically enhance the strong force’s strength at larger particle separations. The strong force is much stronger when particles are well separated than when they are close together.

Compared with electric charge screening, the increase of the strong force with distance is a very counterintuitive result. How can it be that an interaction gets stronger when particles are further apart? Most interactions subside over distance. We would really need a calculation to show this, but there are examples in the world of such behavior.

For example, if someone sends a message through a bureaucracy whose importance some middle manager doesn’t understand, the middle manager might blow up what should have been an ordinary memo into a critically important directive. Once the middle manager modified the message, it would have a far greater impact than if the original author had communicated it directly.

The Trojan War is another example in which long-distance forces were more powerful than those at short distances. According to the
Iliad
, the Trojan War began when the Trojan prince Paris decided to run off with Helen, the wife of the Spartan king Menelaus. Had Menelaus and Paris fought over Helen mano a mano before Paris and
Helen absconded to Troy, the war between the Greeks and the Trojans would have ended before it mushroomed into an epic. Once Menelaus and Paris were far apart, they interacted with many others and created the strong forces that participated in the very powerful Greek-Trojan interactions.

Though surprising, the growth of strong interactions with distance is sufficient to explain all the distinctive properties of the strong force. It explains why the strong force is powerful enough to keep quarks bound up into protons and neutrons, and quarks trapped inside jets—the strong force grows at long distance to the point where a particle that experiences the strong force cannot be separated overly far from other strongly interacting particles. Fundamental strongly interacting particles such as quarks are never found in isolation.

A well-separated quark and an antiquark would store an enormous amount of energy, so much so that it would be more energy-efficient to create additional physical quarks and antiquarks in between than to let them remain isolated. If you were to try to pull the quark and antiquark further apart, new quarks and antiquarks would be created from the vacuum. Just as in Boston traffic, where you can never be more than a car-length behind the car in front of you without a car coming in from the next lane, those new quarks and antiquarks would hover near the original ones so that no single quark or antiquark would become any more isolated than when it started—some other quark or antiquark is always nearby.

Because the strong force at large distances is so strong that it doesn’t allow strongly interacting particles to be isolated from one another, particles that are charged under the strong force are always surrounded by other charged particles in strong-force-neutral combinations. The consequence is that we never see isolated quarks. We only see strongly bound hadrons and jets.

Grand Unification

The results of the previous section tell us about the distance dependence of the strong, weak, and electromagnetic forces.
²¹
In 1974, Georgi and Glashow made the bold suggestion that these three forces
change with distance and energy in such a way that they unify into a single force at high energy. They called their theory a GUT, short for
Grand Unified Theory
. Whereas the strong force symmetry interchanges three colors of quarks (as discussed in Chapter 7) and the weak force symmetry interchanges different particle pairs, the GUT force symmetry acts on and interchanges all types of Standard Model particles, quarks and leptons.
²²

According to Georgi and Glashow’s Grand Unified Theory, early in the evolution of the universe, when the temperature and energy were extremely high—the temperature was higher than one hundred trillion trillion degrees kelvin, and the energy was higher than one thousand trillion GeV—the strength of each of the three forces was the same as that of the others and the three nongravitational forces fused into a single one, “The Force.”

As the universe evolved, the temperature dropped and the unified force split into three distinct forces, each with its own distinct energy dependence, through which they evolved into the three nongravitational forces we know today. Although the forces began as a single force, they ended up with very different interaction strengths at low energies because of the different influences that virtual particles had on each of them.

The three forces would be like identical triplets who developed from a single fertilized egg, but matured into three rather different individuals. One triplet might now be a punk rocker with dyed, spiked hair, one a marine with a crewcut, and one an artist with a long ponytail. They would nonetheless share the same DNA, and when they were babies would have been pretty much indistinguishable.

In the early universe, the three forces would also have been indistinguishable. But they would have split apart through spontaneous symmetry breaking. Just as the Higgs mechanism broke electroweak symmetry and left only electromagnetism unbroken, it would also break the GUT symmetry and leave the three separate forces that we witness today.

A single interaction strength at high energy is a prerequisite for a Grand Unified Theory. That means that the three lines representing interaction strength as a function of energy must all intersect at a single energy. But we already know how the strengths of the three
nongravitational forces change with energy. And because quantum mechanics tells us that large distance is interchangeable with low energy and that short distance is interchangeable with high energy,
^*
the results of the previous section can be interpreted equally well in terms of energy. At low energies the electromagnetic and weak forces are less powerful than the strong force, but they strengthen at higher energies, whereas the strong force weakens.

In other words, the strengths of the three nongravitational forces are becoming more comparable at high energies. They might even be converging to a single strength. This would mean that the three lines representing interaction strength as a function of energy intersect at high energies.

Two lines meeting at a single point is not such an exciting result—it is bound to happen when the lines approach each other. But three lines meeting at a point is either a strong coincidence or evidence of something more meaningful. If the forces do converge, their single interaction strength could be an indication that there is only a single type of force at high energy—in which case we would have a unified theory.