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By Root 810 0

Glashow, Abdus Salam and Weinberg received the Nobel Prize in 1979, is no less than the Standard Model of particle physics. The idea is simple enough – empty space is not empty, and this leads to zig-zagging and therefore mass. But clearly we have some more explaining to do. How can it be that empty space is jammed full of Higgs particles – wouldn’t we notice this in our everyday lives, and how did this strange state of affairs come about in the first place? It certainly sounds like a rather extravagant proposition. We have also not explained how it can be that some particles (like photons) have no mass while others (like W bosons and top quarks) weigh in with masses comparable to that of an atom of silver or gold.

The second question is easier to answer than the first, at least superficially. Particles only ever interact with each other through a branching rule and Higgs particles are no different in that regard. The branching rule for a top quark includes the possibility that it can couple to a Higgs particle, and the corresponding shrinking of the clock (remember all branching rules come with a shrinking factor) is much less than it is in the case of the lighter quarks. That is ‘why’ a top quark is so much heavier than an up quark. This doesn’t explain why the branching rule is what it is, of course. The current answer to that is the disappointing ‘because it is’. It’s on the same footing as the question ‘Why are there three generations of particles?’ or ‘Why is gravity so weak?’ Similarly, photons do not have any branching rule that couples them to Higgs particles and as a result they do not interact with them. This, in turn, means that they do not zig-zag and have no mass. Although we have passed the buck to some extent, this does feel like some kind of an explanation, and it is certainly true that if we can detect Higgs particles at the LHC and check that they couple to the other particles in this manner then we can legitimately claim to have gained a rather thrilling insight into the way Nature works.

The first of our outstanding questions is a little trickier to explain – namely, how can it be that empty space is full of Higgs particles? To get warmed up, we need to be very clear about one thing: quantum physics implies that there is no such thing as empty space. In fact, what we call ‘empty space’ is really a seething maelstrom of subatomic particles and there is no way to sweep them away and clean it up. Once we realize that, it becomes much less of an intellectual challenge to accept that empty space might be full of Higgs particles. But let’s take one step at a time.

You might imagine a tiny region of deep outer space, a lonely corner of the Universe millions of light years from a galaxy. As time passes it is impossible to prevent particles from appearing and then disappearing out of nothing. Why? It is because the process of the creation and annihilation of particle–anti-particle pairs is allowed by the rules. An example can be found in the lower diagram in Figure 10.5: imagine stripping away everything except for the electron loop – the diagram then corresponds to an electron–positron pair spontaneously appearing from nothing and then disappearing back into nothing. Because drawing a loop does not violate any of the rules of QED we must acknowledge that it is a real possibility; remember, everything that can happen does happen. This particular possibility is just one of an infinite number of ways that empty space can fizz and pop, and because we live in a quantum universe the correct thing to do is to add all the possibilities together. The vacuum, in other words, has an incredibly rich structure, made up out of all the possible ways that particles can pop in and out of existence.

That last paragraph introduced the idea that the vacuum is not empty, but we painted a rather democratic picture in which all of the elementary particles play a role. What is it about the Higgs particle that makes it special? If the vacuum were nothing other than a seething broth of matter–antimatter creation and annihilation,