Monday, June 04, 2007

Physics Q&A #2: The Fundamental Forces (part 2)

(Note: I have some diagrams I want to add in, but I don't have access to them on this computer. I'll put them in when I get home from work.)

Welcome back to the concluding part of this 3-part Physics Q&A. If you haven't already, I recommend you go back and read the first two parts of this entry. If you haven't read them, you'll likely be quite lost.

This time, we're going to tackle the two most complicated forces: The strong and weak nuclear forces. Of these two, the strong is the simpler one, so let's start there.

The Strong Nuclear Force

While electromagnetism works off of the electric charge of particles, the strong nuclear force works off of color charge. Of all the existing particles, only quarks and gluons have color charge, so these are the only particles that participate in strong nuclear interactions. A few brief notes on color charge:

  • Color is conserved in all interactions

  • All quarks have one of three colors: red, blue, and green

  • All anti-quarks have one of the opposite three colors: anti-red, anti-blue, and anti-green

  • Gluons have eight possible color charges (and one ninth theoretical charge that we've never observed). All of these are linear combinations of the typical quark and anti-quark charges, such as red-antiblue or red-antired + blue-antiblue

  • Different colors attract, like colors can't interact with each other

  • Only color-neutral particles can actually exist in stable states

The reason only color-neutral particles can exist is a bit complicated, but it has to do with symmetry. Essentially, any observable particles must be what are known as "color-singlets" (due to theory on symmetry and Lie Groups I won't get into here), which means that any color-swapping we perform on the gluons that make it up must result back in the same particle. Since we could do swapping such as Red <-> Blue or Blue <-> Green, any particle that shows any imbalance in color at all wouldn't be a singlet. This leaves only color-neutral combinations being allowed.

So, let's get down to how gluons and quarks interact, which gives us the fundamental nature of the strong nuclear force. The strong nuclear force has three possible vertices for interaction. The first and most important one happens when a quark goes along and emits a gluon. Since gluons must carry some color and color is conserved, this means that the quark must change color at the vertex. So for instance, we could start off with a red quark, which emits a red-antiblue gluon and becomes a blue quark. The other two vertices don't matter as much here, but for completeness sake, one of them is where a gluon emits another gluon, and the other is where two gluons directly interact (respectively, a vertex of three gluons and a vertex of four gluons).

Now, let's use this to try to put together a particle. First, let's start off with a baryon, which is made up of one red quark, one blue quark, and one green quark. A possible interaction here is for the red quark to emit a red-antiblue gluon and become blue, and then for the blue quark to absorb this gluon and become red. This leaves us with a color-neutral quark like we started with, so the interaction can and will occur, pulling the red and blue (now blue and red) quarks together. Of course, the third quark will also have to get pulled towards the other two to keep the baryon from splitting apart, so there will be interactions with it as well.

The other type of particle we can make is a meson, which consists of a quark bonded to an antiquark. For instance, let's say we start off with a red quark and an antired antiquark. The red quark can emit a red-antiblue gluon and become blue, and then the antired quark can absorb this gluon and become antiblue, leaving us with a blue-antiblue meson. This can then happen again, switching over to green-antigreen or back to red-antired.

However, there's a little quirk here. Red and antired don't actually cancel out with each other, and so don't actually qualify as color-neutral. So how is it that mesons exist at all? The trick here is that gluons undergo tons of these interactions and cycle through all the possible color combinations very rapidly. In fact, they can't really be described as oscillating but instead in a superposition of quantum states representing the possible color combinations. This means that at any given time, the "actual" color of a meson is red-antired + blue-antiblue + green-antigreen, and all of these do add up to neutral.

Before moving on to the weak force, there's one more quirk with the strong force I'd like to address: Why does it have limited range? Gluons, like photons, are massless and so have infinite lifetime, so why can't they travel out far?

The answer to this is complicated, but it starts with the fact that gluons also carry color charge, and since the second vertex which I mentioned briefly allows gluons to emit or absorb other gluons, then two gluons with different colors can attract each other. In general, you won't just have one gluon being exchanged between two quarks at a time; you'll have many. And all these gluons attract each other, compressing down into what's known as a "flux tube" between the two quarks. Any other gluons that are emitted will also be caught by this flux tube and will then travel over to the other quark.

The reason the electromagnetic force gets weaker with distance is that fewer photons emitted are going in the right direction to interact with the other particle (think of shooting a laser in a random direction with a target a close distance away. If you move farther from the target, its profile is smaller and you have a lower chance of hitting it). However, due to the effects of the flux tube, all gluons get pulled into the right direction so the number that interact doesn't decrease with distance, and the force stays the same.

So, shouldn't this imply that the force should be unbound rather than bound, if it doesn't decrease with distance? At first it seems so. The problem has to do with energy. Pulling quarks apart takes a ton of energy, and particles want to go to states with less energy. Eventually, you'll pull the two quarks so far apart that they'll find other quarks closer than each other and latch onto them instead (quarks only mate in pairs or triplets), emitting some energy and getting pulled in. Even if you had a perfect vaccuum, you're pumping a lot of energy into this pair by pulling them apart, and this is likely to result in pair production before long, giving two new quarks for each to attach to. So although the force could work at a large distance, it won't.

The Weak Nuclear Force

And finally, onto the last and most complicated of the fundamental forces. Part of its complication is that it further breaks down into two other types of interactions: Charged Weak interactions, which exchange a lot of properties between properties, and Weak Neutral interactions, which exchange only spin and momentum. Don't ask me about the adjective order; I didn't come up with it. Of these two, Weak Neutral interactions are a fair bit simpler and can sometimes actually act like a simple force, so I'll talk about them first.

Weak Neutral interactions are mediated by the Z boson, which is chargeless, high mass (so it decays rapidly and the force is short-range), and has a spin of 1. The allowed interactions are when a lepton or quark emits or absorbs a Z. The particle's type and charge are unchanged, but it gives some of its spin and momentum to the Z, which could then pass it on to another particle or decay into a particle-antiparticle pair.

This type of interaction is responsible for electron-neutrino scattering, which is where an electron and neutrino get deflected off of each other. Since neutrinos are chargeless, they can't be affected through the electromagnetic force, and since we do see this type of interaction in the lab, we know that Weak Neutral interactions are occuring.

And now, we get on to Charged Weak interactions. These interactions are mediated by W bosons, which are spin 1 and high mass like the Z, but unlike it have an electric charge of +1 or -1 and an isospin of +1 or -1 (respectively). As you may recall from my last post, isospin is a property that differentiates electrons from their neutrinos and the negatively-charged quarks from the positively charged ones.

The primary vertex for a Charged Weak interaction has some lepton or quark emitting or absorbing a W+ or W-. Since charge and isospin are conserved, this causes it to flip over to its counterpart in the same generation. For instance, an electron (charge -1, isospin -1/2) could come along and emit a W- (charge -1, isospin -1) and turn into an electron neutrino (charge 0, isospin +1/2). This W could then decay or it interact with another particle.

One common example of a Charged Weak interaction is Beta Decay, in which a neutron turns into a proton, an electron, and an electron-antineutrino. The neutron is made up of two Down quarks and an Up quark, while the proton is made up of one Down quark and two Up quarks. In the reaction, first, one of the neutron's Down quarks (charge -1/3, isospin -1/2) emits a W- (charge -1, isospin -1) and turns into an up quark (charge 2/3, isospin +1/2). Now we have a proton and a W-. Since the W- is unstable, it quickly decays. Its favored method of decay at these energies is into an electron (charge -1, isospin -1/2) and an electron-antineutrino (charge 0, isospin -1/2), so this is what we see happening. One simple variant on this reaction is that instead of an antineutrino coming out at the end, one comes into the system at the beginning and triggers the decay.

Now, you might be wondering how exactly this serves to work as a force (since it's grouped into the four fundamental forces). The simple answer is, it doesn't. Calling these "forces" is just bad terminology, and careful particle physicists use the term "interaction" to describe them all. It might seem weird that this never acts like a force, but let me remind you that the other interactions don't always act like forces either. For instance, in an electromagnetic interaction you can have an electron and a positron annihilate each other into a pair of photons. No forciness here, just a change in the types of particles. This is just the case for Charged Weak interactions, except Charged Weak ones don't have any options that leave the reactants and products unchanged.

So that's it for this overly-long answer to a question no one asked. If you have any questions on this or future questions you'd like me to address, leave a note in the comments.

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