Conservation Laws

Sorry for the delay in postings guys. Busy week this past week. Anyway, I had most of another post done Tuesday, but decided it was getting too technical without some more background. So, here's more background!

If you've taken a high-school level chemistry or physics class, you hopefully touched on some basic conservation laws. The ones you've most likely seen before are conservation of mass (if we put 2 grams in, we get 2 grams out), conservation of energy (energy can neither be created nor destroyed), conservation of charge (if we start with +2 charge, we can end with a +3 charge, so long as there's a -1 charge to balance our net charge back to +2), and conservation of momentum (speedy thing go in, speedy thing come out).
Physics respects most of these conservation laws. So far as we can tell, the net charge of the universe is constant and the net momentum of the universe is constant. However, with Einstein's famous equation, conservation of mass and conservation of energy goes right out the window. Mass is just another form of energy, so we can get rid of some energy to make some mass, and we can get rid of some mass to make some energy. Thus, we have conservation of mass-energy, rather than conservation of mass or energy. And that's what's important for particle physics.
When an acclerator collides two beams of really energetic particles, what we're trying to do is take advantage of the lots of energy and relatively small net momentum of the collision. Physics predicts that any process that conserves both energy and momentum and all the other conservation laws has a probability of occuring. So, if we slam together two energetic protons travelling in opposite directions, we have a lot of energy that can become mass, and not a whole lot of momentum requiring it to travel in a given direction. We get to see heavier particles that decay really quickly because we're throwing enough mass-energy together to make the new particles.
However, these aren't the only conservation laws physicists follow. We also have conservation of a lot of things like charge. So, remember that matter is made up of quarks and leptons (electrons, muons, tau leptons, and the neutrinos). In particle physics, we have to conserve not only mass-energy and momentum, but also quark and lepton number. If we start with 3 quarks, we have to end with 3 quarks. This could be 10 quarks and 7 antiquarks, or it could be 4 quarks and an antiquark. It all depends on how much energy we have to make particles with. We also have to conserve lepton number, so when we make a lepton, we have to also make an anti-lepton. If we make an electron, we have to make a positron (the electron's positively charged antiparticle). If we make a muon, we also make an anti-muon.
In general, lepton family number is also conserved. So the number of electrons and electron neutrinos is constant, the number of muons and muon neutrinos is constant, and the number of tau leptons and tau neutrinos is constant. However, there are specific processes that can violate the family conservation. Lepton number must always be conserved, lepton family number can occasionally not be conserved.
In much the same way, some composite particles (particles with a substructure) have a charm value or a strangeness value associated with them. In interactions involving the strong force and the electromagnetic force, this charm and strangeness is conserved, and is a result of the charm and strange quarks, respectively. In interactions involving the weak force, charm and strangeness can be violated. Thus, when we collide two protons in a collider, the immediate collision has to conserve the number of charm and strange quarks. After some small amount of time passes, the resulting particles can decay using the weak force, and we lose the conservation of charm and strangeness. This ability of the weak force to violate some conservation laws is key, as it's what allows the neutron to decay into a proton, an electron, and an anti-electron neutrino.
So, to wrap up: physicists make use of a lot of conservation laws to figure out how matter has to behave. Some of these 'laws' are stricter than others. In most interactions, conservation laws hold firm. In the rare few that violate conservation, their effects are extraordinarily important. So conservation laws, they're cool.