Warped Passages - Lisa Randall [169]
Nonetheless, the idea we started with, sequestering to prevent unwanted interactions in supersymmetric theories, seemed to me as if it had to be right. Nothing in four dimensions worked in a sufficiently compelling way, and extra dimensions seemed to have all the necessary ingredients for a successful model. However, it was not until the end of the summer that Raman and I understood sequestering and its consequences for supersymmetry breaking well enough to finally see eye to eye and converge on its merits.
Naturalness and Sequestering
The reason that sequestering could be important is that it is a way to prevent the problems caused by the anarchic principle, the unofficial rule that says that in four-dimensional quantum field theory, anything that can happen will happen. The problem with the anarchic principle is that theories end up predicting interactions and relationships among masses that are not seen in nature. Even interactions that don’t occur in a classical theory (the one without quantum mechanics taken into account) will occur once virtual particles are included; virtual particle interactions induce all possible interactions.
Here’s an analogy that illustrates why. Suppose you told Athena that it would snow tomorrow, and Athena then told Ike. Even though you had no direct communication with Ike, your communication would nonetheless influence what Ike would wear the next day—he would put on a parka because of your virtual advice.
Similarly, if a particle interacts with a virtual particle, and that virtual particle interacts in turn with a third particle, the net effect is that the first and the third particles interact. The anarchic principle tells us that processes involving virtual particles are bound to occur, even if they don’t happen classically. And those processes often induce unwanted interactions.
Many of the problems in particle physics theories stem from the anarchic principle. For example, the quantum contributions to the Higgs particle’s mass that result from virtual particles are the root of the hierarchy problem. Any path that the Higgs particle takes can be temporarily interrupted by heavy particles, and these interventions increase the Higgs particle’s mass.
We saw another example involving the anarchic principle in Chapter 11. In most theories with broken supersymmetry, virtual particles induce unwanted interactions—interactions that we know from experiments do not take place. Those interactions would change the identity of the known quarks and leptons. Such flavor-changing interactions either don’t occur in nature or occur very rarely. If we want a theory to work, we must somehow eliminate these interactions—which the anarchic principle tells us will arise.
Virtual particles don’t necessarily lead to these unwanted predictions. The theory won’t predict these unwanted interactions in the unlikely event that there are enormous cancellations between the classical and quantum mechanical contributions to a physical quantity. Even though the classical and quantum contributions would individually be much too big, the two together could conceivably add up to an acceptable prediction. But this way of getting around the problem is almost certainly a stopgap measure substituting for a true solution. None of us really believe that such precise, accidental cancellations are the fundamental explanation for the absence of certain interactions. We grudgingly employ the fortuitous cancellations as a crutch so that we can ignore these problems and proceed to investigate other aspects of our theories.
Physicists believe that interactions are absent from a theory only if the interactions were eliminated in a way that fits the physicists’ notion of what’s natural. In the everyday world, the word “natural” refers to things that happen spontaneously, without human intervention. But for particle physicists, “natural”