Warped Passages - Lisa Randall [112]
Figure 59. A real physical photon can turn into a virtual electron and a virtual positron, which can then turn back into a photon. This is illustrated with a Feynman diagram on the right and schematically on the left.
Why Interaction Strength Depends on Distance
The strengths of the forces we know about depend on the energies and distances involved in particle interactions, and virtual particles play a part in that dependence. For example, the strength of the electromagnetic force is smaller when two electrons are further apart. (Remember, this quantum mechanical decrease is over and above the classical distance dependence of electromagnetism.) The consequences of virtual particles and the distance dependence of forces is real; theoretical predictions and experiments match extremely well.
The reason that the quantities of an effective theory—the strength of forces or interactions, for example—depend on the energies and the separations of the particles involved follows from a feature of quantum field theory that the physicist Jonathan Flynn jokingly called the anarchic principle.* The anarchic principle follows from quantum mechanics, which tells us that all particle interactions that can happen will happen. In quantum field theory, everything that is not forbidden will occur.
I’ll call each separate process by which a particular group of physical particles interacts a path. A path may or may not involve virtual particles. When it does, I’ll call that path a quantum contribution. Quantum mechanics tells us that all possible paths contribute to the net strength of an interaction. For example, physical particles can turn into virtual particles, which can interact with each other and then turn back into other physical particles. In such a process, the original physical particles might reemerge or they might turn into different physical particles. Even though the virtual particles wouldn’t last long enough for us to observe them directly, they would nonetheless affect the way real observable particles interacted with one another.
Trying to prevent virtual particles from facilitating an interaction would be like telling certain of your friends a secret and hoping it won’t reach another friend. You know that sooner or later, some of the “intermediate virtual” friends will betray your confidence and relay the message to that other friend. Even if you already told that friend your secret, the fact that your virtual friends will discuss it with him as well will affect his opinion on the subject, too. In fact, his opinion will be the net result of everyone he has talked to.
Not only direct interactions between physical particles, but also indirect interactions—those that involve virtual particles—play a role in communicating forces. Just as your friend’s opinion is affected by everyone who talks to him, the net interaction between particles is the sum of all possible contributions, including those from virtual particles. And because the importance of virtual particles depends on the distances involved, the strengths of forces depend on distance.
The renormalization group tells us precisely how to calculate the impact of virtual particles in any interaction. All of the effects of intermediate virtual particles are added together, and this either strengthens or impedes the strength of a gauge boson’s interactions.
Indirect interactions play a more important role when interacting particles are further apart. A greater distance is analogous to telling your secret to more “virtual” friends. Although you can’t be sure that any single friend will betray your confidence, the more friends you tell, the more likely