In article <D2020q.6GH@cs.dal.ca> you write:
a) One of the first things we learn, is that there are four interaction forces: weak, strong, EM, gravitational. I thought that I remembered reading in here, that many suspect that one of the forces is actually a redundancy of another, and that there are only three. Can anyone elaborate on this? I suppose it would be ideal if we could find that there was only one, giving everyone less to study :)
The electromagnetic and weak forces are not exactly unified, but are "mixed" with each other in the Glashow-Weinberg-Salam electroweak theory. There are two forces in the GWS theory with different gauge bosons; one has three gauge bosons often called W1, W2, and W3, and the other has a single gauge boson sometimes called B (not to be confused with the B meson, which is a thing made of quarks). The photon, quantum of the EM force, is a superposition of W3 and B states, and the Z is another superposition of the two; the W+ and W- are superpositions of the W1 and W2.
So the theory still has two independent coupling constants, for the W and B bosons. It would be nice if there were only one, nicer if we could unify them with the strong force (in a so-called Grand Unified Theory, or GUT), and nicer still if we got gravity in the bargain (such a theory is sometimes misleadingly called a Theory of Everything, or TOE; really it would just be a Theory of All Basic Particle Interactions). Nobody knows whether this is really a fruitful approach, but there are some indications that some GUT, at least, might work (there are some that we know don't work, but they're tantalizingly close to working, and others seem consistent with known data but are fairly untested).
b) Do we know anything about the distribution of quarks, say in the structure of the proton? I suppose we can't, no more than we could say anything about the position of an electron, since it is technically a wave-function.
It is possible to say some things about the structure of the wave function, though. It's a hairy and arcane subject, but scattering data have yielded fair determinations of what are called "parton distribution functions," which are related to how, on average, the quarks and gluons ("partons") are distributed within a proton or neutron.
However, I thought that a scattering experiment of the late 60's that identified the existance of the quark, described them as point particles... Or was that simple point charges? In any case, is there no way to understand more about the relationship of th quarks inside of the proton?
There is a distinction to be made between the pointlike nature of a particle and the spread-out nature of its wave function. Electrons seem pointlike, in the sense that the interaction between the electron field and the photon field, for instance, is local: the vertex in a Feynman diagram involves interactions where both are at the same point, to the best of our knowledge. But the electrons and photons can still be smeared out over space, in which case the interaction can take place wherever both wavefunctions are locally nonzero.
Quarks seem to be like this too (though there are many complications from the haze of virtual particles that surrounds everything, and some would argue that the distinction between pointlike and non-pointlike particles has less to it than meets the eye). The pointlike nature of the quarks, among other things, was basically deduced by looking at how the scattering probability varies with energy of scattered electrons; this has a specific behavior, corresponding to what was seen, if the particles have no visible extension or internal structure on the scale of the wavelengths involved.
We have the decay of a muon into a virtual gauge boson and a muon neutrino, and the gauge boson further decays into the electron and electron anti-neutrino. Am I to understand that the virtual gauge boson decays simultaneously with the muon? From the diagram, you can consider it a spatial or temporal represenation, and it seems that the gauge boson decays afterwards, but textbooks lead me to believe otherwise.
One beautiful thing about a Feynman diagram is that it encompasses all of these possibilities. When you calculate the decay rate from this diagram you actually do something equivalent to integrating over situations in which the gauge boson decays after emerging from the muon or simultaneously, as well as situations in which the virtual gauge boson is created out of the vacuum along with the electron and antineutrino and is absorbed by the muon later!
Certainly, you would think that experimental evidence would show that the two decays are either simultaneous, or not... Assuming the decays are simultaneous, why is the boson required at all? To fulfill conservation?
Since the W boson is so massive, probability amplitude is strongly peaked around situations in which the W exists for a very short time and does not stray far. In practice the decays are effectively simultaneous. Indeed, the first good theory of beta decay (Fermi's) had no W boson in it; there was just one vertex with four lines coming out of it. However, it was realized early on that something more had to be going on, because in Fermi's theory certain scattering probabilities (such as that for scattering of a muon and a muon antineutrino into an electron and an electron antineutrino) increased without limit as energies increased, and eventually exceeded 1, a nonsensical result. (The requirement that probabilities not exceed 1 is sometimes called the "unitarity bound.")
The W solves this problem essentially because of the peculiar behavior of virtual particles. They can possess combinations of energy and momentum not normally allowed by the laws of motion, but with a small probability amplitude that decreases as the combination gets further into the classically forbidden region ("further off shell," in particle physics argot). The increase in scattering probability that violated the unitarity bound in the Fermi theory is tempered by a decreasing factor that comes from the W going further and further off shell after total energy exceeds the W mass. The W is also far off shell in the low-energy situation of ordinary beta decay, which, in the GWS model, is why weak interactions happen at such a slow rate compared to other kinds.
The W was actually first proposed long before Glashow, Weinberg, and Salam put the electroweak theory together, but it took a set of powerful new concepts (the combination of gauge theory and spontaneous symmetry breaking) to create a consistent and realistic theory with a W in it. And, of course, the W's existence is now confirmed quite directly in experiments; W particles can be made in large accelerators, and they have a mass of 80 GeV.