How Does Spontaneous Symmetry Breaking Explain Particle Masses?

[Sumo]

I often have this problem when reading physics books (the kind I can understand) where, because I'm only in High school math, the author explains only in analogies, and the analogies sometimes don't make logical sense.

I'm reading Steven Weinberg's "Dreams of a Final Theory" and I got to the part where he describes spontaneous symmetry breaking. He says that the equations for the electron and neutrino fields (for example) are symmetrical, interchangable. But the solutions to the equations are not symmetrical, as he says "electrons and W and Z particles have mass, but neutrinos and photons do not." He explains this by saying that where you can mix up the fields you get multiple possible solutions (ex. a solution where an up quark has a higher mass than down, must also have a solution where down is higher than up). He then says "the difference between the two solutions would be simply a matter of which quark we chose to call up and down. Nature as we know it represents one solution of all the equations of the standard model." And then he goes on by how physics predicts a Higgs particle to explain this breaking.

But I'm not so sure this is true, given his description. It seems as though he just gave the answer. The equations can give either an electron with the properties we observe or with those of a neutrino because if it has the properties of a neutrino then we call it a neutrino. Nature is not one solution, but all of them, and that's why we have both electrons and neutrinos. It doesn't seem so far fetched to imagine that an electron and a neutrino are aspects of the same thing.

Obviously I'm misunderstanding him. If someone could explain how.

 

[Physics Monkey]

"Nature is not one solution, but all of them, and that's why we have both electrons and neutrinos."

Here is your problem, nature really does choose just one solution. Just think about the chair that you're sitting in right now, there isn't any reason why it should face one way or the other. All the directions are the same as far as the atoms that make up the chair are concerned, but the chair still faces in just one direction, that's symmetry breaking. Ferromagnetic domains do point in just one direction, one generator of the electroweak gauge group does remain unbroken by the Higgs, and so on. The fact of the matter is that nature does pick just one vacuum and that is the world we see at low energies. The fact that you call the massive particle an "electron" is irrelevant, the key is really that nature has got to have a massive particle no matter what you call it. Of course, electrons and neutrinos are "aspects of the same thing" in some very real sense. They form an SU(2) doublet in the standard model, and in the early universe before the Higgs acquired a vacuum expectation value, they were rather more similar than they appear now.