C, P, and T

[mmcirvin]

This is a nice result: B mesons and anti-B mesons (quark-antiquark pairs in which one member is either a bottom quark or an anti-bottom) decay at different rates, the largest difference between the interations of matter and those of antimatter yet measured. It's not exactly surprising—observing and measuring this predicted effect was a major goal of making lots of B mesons. But CP violation is a hard effect to measure and in some ways mysterious.

The abbreviation "CP" refers to two of three famous partial symmetries of nature: P, C, and T.

P is parity: symmetry under mirror reflections. The electromagnetic, gravitational, and strong interactions are all parity-symmetric. If you observe some physical process that involves these forces and then set up its mirror image, it will happen in exactly the same way (only mirror-reflected), and with the same conditional probabilities of outcomes. But the weak force involved in nuclear beta decay is not parity-symmetric, a fact that was suggested by Yang and Lee and observed by Chien-Shiung Wu's team in the fifties. If you have a cobalt nucleus (or a weakly unstable particle of many other types) that gives off an electron in beta decay, the electron's exit route has preferred orientations relative to the nucleus's spin axis, such that the mirror image of the same process does not have the same probability. (Yang and Lee got the Nobel Prize; Wu didn't, an injustice that particle experimentalist Melissa Franklin never lets her students forget.)

C is charge conjugation: the replacement of particles with their antiparticles. Again, everything but the weak force seems to be C-symmetric, but weak interactions are fairly enthusiastically C-asymmetric. If you take some weak decay and replace all the matter with antimatter and vice versa, it won't go the same way with the same conditional probabilities.

However, even weak interactions are very close to being CP-symmetric. That is, if you replace the particles with their antiparticles and set up the mirror-image configuration in space, the process will go the same way, or very nearly so.

T is time reversal: the symmetry in conditional probability between some process, and the same thing running backwards. Mind you, T doesn't say anything about whether the initial condition itself is as likely in both cases; it's about conditional probability. Like CP, T seems to be almost but not quite a symmetry of the weak interactions, as well as a symmetry of everything else.

(Pedantic note: Actually, there are exotic theorized effects in the strong interactions that ought to also cause tiny CP and T violations. That is a whole other weird story that I won't go into here, especially since I have mostly forgotten about it. Sidney Coleman's book Aspects of Symmetry has a good treatment, if I recall correctly. But in practice you need to look at the weak interactions to see them.)

What seems to be an absolute symmetry, as far as anyone knows, is CPT: charge conjugation, parity, and time reversal. That is: Having observed the conditional probability for a given process, you replace the particles with antiparticles, take the mirror image of the spatial configuration, and look for the whole thing running in reverse with what was the final configuration evolving into what was the original one, and you'll find that the conditional probability is always the same.

It's possible to prove that any quantum theory that obeys the theory of relativity has to obey CPT as well. CPT essentially corresponds to turning a Feynman diagram upside down, which shouldn't affect the associated quantum probability calculations, so theories that lend themselves to Feynman diagrams will tend to obey it. CPT implies, among other things, that particles and their antiparticles must always have the same mass. So it becomes very interesting to make precise measurements of the masses of particles and antiparticles: it's a precision test of relativity! Since CPT is an exact symmetry, it follows that CP violation and T violation must go hand in hand.

Now, an interesting thing about CP violation is that it might be able to cause an imbalance of matter over antimatter, such as we see in the world around us (and for which there are no other good explanations). Andrei Sakharov (yeah, the same guy) once figured out what it would take to produce a matter-antimatter imbalance from previously equal abundances. He said you needed C and CP violation, a thermodynamic inequilibrium, and violation of baryon number conservation (another interesting partial symmetry of nature). All these things existed in the early universe, but it appears that there's not enough observed CP violation to explain the imbalance we see. This story is not yet finished.

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