Warped Passages - Lisa Randall [113]
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