Warped Passages - Lisa Randall [170]
The anarchic principle and the many undesirable interactions that quantum mechanics will induce tell us that some new concepts must enter into any model of physics that underlies the Standard Model if this model is to have a chance of being correct. One reason that symmetries are so important is that they are the only natural way in a four-dimensional world to guarantee that unwanted interactions do not occur. Symmetries essentially provide an extra rule about which interactions can conceivably happen. You can readily understand this phenomenon with the help of an analogy.
Suppose that you prepare six table settings, but you have to prepare them so that all six settings are the same. That is, your settings permit a symmetry transformation that interchanges every pair of settings. Without such a symmetry, you could in principle have given one person two forks, another three, and someone else a pair of chopsticks. But with the symmetry constraints, you can only make settings in which all six people have the same number of forks, knives, spoons, and chopsticks—you could never give one person two knives and another person three.
Similarly, symmetries tell you that not all interactions can occur. Even if many of the particles interact, quantum contributions generally won’t produce interactions that violate a symmetry if the classical interactions preserve that symmetry. If you don’t start with symmetry-violating interactions, you won’t ever generate any (aside from the rare known anomalies mentioned in Chapter 14), even when you include all possible interactions involving virtual particles. By imposing symmetry on your table settings, you will always end up with identical settings, no matter how many changes you make, such as adding grapefruit spoons or steak knives. Similarly, interactions that are inconsistent with a symmetry will not be induced, even when quantum mechanical effects are taken into account. If a symmetry weren’t already violated in the classical theory, there would be no path that a particle could take that could induce a symmetry-violating interaction.
Until recently, physicists thought that symmetries were the only way to avoid the anarchic principle. But as Raman and I saw, once we’d eaten enough ice cream, separated branes are another way. A crucial reason why extra dimensions initially appeared so promising to me is that they suggested a reason, apart from symmetry, that restricted or unusual types of interactions could be natural. Sequestering unwanted particles can prevent unwanted interactions because they won’t generally occur between particles that are separated on different branes.
Particles on different branes don’t interact strongly because interactions are always local—only particles in the same place interact directly. Sequestered particles can make contact with particles on other branes, but only if there are interacting particles that can travel from one brane to the other. Like Ike on the Jailbrane, particles on different branes have only restricted means of communication with each other because they have no options apart from invoking an intermediary. Even if such indirect interactions do occur, they are often extremely small, since intermediary particles in the bulk, particularly ones with mass, only rarely travel long distances.
This suppression of interactions between particles sequestered in different places would be similar to the suppression of international information in a country, which I’ll call Xenophobia, where the government carefully controls the borders and the media. In Xenophobia, information not provided locally could be acquired only from foreign visitors who manage to enter, or from newspapers or books that get smuggled in.
Similarly, separated branes provide a platform from which to evade the anarchic principle, thereby doubling the set of tools at nature’s disposal for guaranteeing the absence