Why Does E=mc2_ - Brian Cox [79]
FIGURE 16
Feynman did a little more than just introduce the diagrams. He associated a mathematical rule with each vertex, and the rules are derived directly from the master equation. The rules multiply together in composite diagrams and allow physicists to calculate the likelihood that the process corresponding to a particular diagram will actually happen. For example, when two electrons encounter each other, the simplest diagram we can draw is as illustrated in Figure 16(a). We say the electrons scatter via the exchange of a photon. This diagram is built up by sewing together two electron-photon vertices. You should think of the two electrons heading in from the left, scattering off each other as a result of the photon exchange, and then heading out to the right. Actually, we have sneaked in another rule here. Namely, you are allowed to flip a particle to an antiparticle (and vice versa) provided you make it into an incoming particle. Figure 16(b) shows another possible way of sewing together the vertices. It is a little more fancy than the other figure, but again it corresponds to a possible way that the two electrons can interact. A moment’s thought should convince you that there are an infinite number of possible diagrams. They all represent different ways that two electrons can scatter, but fortunately for those of us who have to calculate what is going on, some diagrams are more important than others. In fact, the rule is very easy to state: Generally speaking, the most important diagrams are the ones with the fewest vertices. So in the case of a pair of electrons, the diagram in Figure 16(a) is the most important one, because it has only two vertices. That means we can get a pretty good understanding of what happens by calculating only this diagram using Feynman’s rules. It is delightful that what pops out of the math is the physics of how two electrically charged particles interact with each other, as discovered by Faraday and Maxwell. But now we can claim to have a much better understanding of the origin of this physics—we derived it starting from gauge symmetry. Calculations using Feynman’s rules also give us much more than just another way to understand nineteenth-century physics. Even when two electrons interact, we can compute corrections to Maxwell’s predictions—small corrections that improve upon his equations in that they agree better with the experimental data. So the master equation is breaking new ground. We really are just scratching the surface here. As we stressed, the Standard Model describes everything we know about the way particles interact with each other and it is a complete theory of the strong, weak, and electromagnetic forces, even succeeding in unifying two of them. Only gravity is excluded from this ambitious scheme to understand how everything in the universe interacts with everything else.
FIGURE 17
But we need to stay on message. How do Feynman’s rules, which summarize the essential content of the Standard Model, dictate the ways in which we can destroy mass and convert it into energy? How can we use them to help us best exploit E = mc 2 ? First let us recall an important result from Chapter 5—light is made up of massless particles. In other words, photons do not have any mass. Now there is an interesting diagram we can draw—it is shown in Figure 17. An electron