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and an antielectron bang into each other and annihilate to produce a single photon (for clarity we have labeled the electron e- and the positron e+). That is allowed by Feynman’s rules. This diagram is noteworthy because it represents a case whereby we started with some mass (an electron and a positron have some mass) and we end up with no mass at all (a photon). It is the ultimate matter-destruction process, and all of the initial energy locked away inside the mass of the electron and antielectron is liberated as the energy of a photon. There is a hitch, though. The annihilation into a single photon is disallowed by the rule that everything that happens must simultaneously satisfy the laws of energy and momentum conservation, and this particular process cannot do that (it is not entirely obvious and we won’t bother to prove it). It is a hitch that is easy to get around, though—make two photons. Figure 18 shows the relevant Feynman diagram—again, the initial mass is utterly destroyed and converted 100 percent into energy, in this case two photons. Processes like this played a very important role in the early history of the universe when matter and antimatter almost completely canceled themselves out by just such interactions. Today we see the remnant of that cancellation. Astronomers have observed that for every matter particle in the universe there are around 100 billion photons. In other words, for every 100 billion matter particles made just after the big bang, only one survived. The rest took the opportunity available to them, as pictured graphically in Feynman’s diagrams, to divest themselves of their mass and become photons.

In a very real sense, the stuff of the universe that makes up stars, planets, and people is only a tiny residue, left over after the grand annihilation of mass that took place early on in the universe’s history. It is very fortunate and almost miraculous that anything was left at all! To this day, we are not sure why that happened. The question “why is the universe not just filled with light and nothing else?” is still open-ended, and experiments around the world are geared up to help us figure out the answer. There is no shortage of clever ideas, but so far we have yet to find the decisive piece of experimental evidence, or proof that the theories are all wrong. The famous Russian dissident Andrei Sakharov carried out the pioneering work in this field. He was the first person to lay out the criteria that must be satisfied by any successful theory aiming to answer the question as to why there is any matter at all left over from the big bang.

FIGURE 18

We have learned that nature does have a mechanism for destroying mass, but unfortunately it is not very practical for use on Earth because we need a way of generating and storing antimatter—there is nowhere we can go to mine it and as far as we can tell, no lumps of it are lying around in outer space. As a fuel source it seems useless because there simply is no fuel. Antimatter can be created in the laboratory, but only by feeding in lots of energy in the first place. So although the process of matter-antimatter annihilation represents the ultimate mechanism for converting mass to energy, it is not going to help us solve the world’s energy crisis.

FIGURE 19

What about fusion, the process that powers the sun? How does that come about in the language of the Standard Model? The key is to focus our attention on the Feynman vertex involving a W particle. Figure 19 shows what is going on when a deuteron is manufactured from the fusion of two protons. Remember that protons are, to a good approximation, made up of three quarks: two up quarks and one down quark. The deuteron is made up of one proton and one neutron, and the neutron is again mainly made up of three quarks, but this time one up quark and two down quarks. The diagram shows how one of the protons can be converted into a neutron, and as you can see, the W particle is the key. One of the up quarks inside the proton has emitted a W particle and changed into a down quark as a result,