Parity

Parity involves a transformation that changes the algebraic sign of the coordinate system. Parity is an important idea in quantum mechanics because the wavefunctions which represent particles can behave in different ways upon transformation of the coordinate system which describes them. Under the parity transformation:

The parity transformation changes a right-handed coordinate system into a left-handed one or vice versa. Two applications of the parity transformation restores the coordinate system to its original state.

It is a reasonable presupposition that nature should not care whether its coordinate system is right-handed or left-handed, but surprisingly, that turns out not to be so. In a famous experiment by C. S. Wu, the non-conservation of parity in beta decay was demonstrated.

Non-conservation of Parity

The electromagnetic and strong interactions are invariant under the parity transformation. It was a reasonable assumption that this was just the way nature behaved, oblivious to whether the coordinate system was right-handed or left-handed. But for several years physicists had puzzled over the decay of the neutral kaons, which had equal mass but decayed to products of opposite parity. In 1956, T. D. Lee and C. N. Yang predicted the nonconservation of parity in the weak interaction. Their prediction was quickly tested when C. S. Wu and collaborators studied the beta decay of Cobalt-60 in 1957. 电磁相互作用和强相互作用在宇称变换下是不变的。人们合理地认为这正是自然的行为方式，对坐标系是右手法则还是左手法则并不在意。但几年来，物理学家们一直困惑于中性K介子的衰变，这些介子具有相等的质量，但衰变产物具有相反的宇称。1956年，T. D. Lee和C. N. Yang预言了弱相互作用中宇称不守恒。他们的预言在1957年很快得到了验证，当时C. S. Wu及其合作者研究了钴-60的β衰变。 By lowering the temperature of cobalt atoms to about 0.01K, Wu was able to "polarize" the nuclear spins along the direction of an applied magnetic field. The directions of the emitted electrons were then measured. Equal numbers of electrons should be emitted parallel and antiparallel to the magnetic field if parity is conserved, but they found that more electrons were emitted in the direction opposite to the magnetic field and therefore opposite to the nuclear spin. 通过将钴原子的温度降低到约0.01K，吴能够使核自旋沿外加磁场方向极化。然后测量了发射电子的方向。如果宇称守恒，沿磁场方向和反方向应有相等数量的电子被发射，但实验发现更多电子是沿与磁场相反的方向发射的，即与核自旋方向相反。

This and subsequent experiments have consistently shown that a neutrino always has its intrinsic angular momentum (spin) pointed in the direction opposite its velocity. It is called a left-handed particle as a result. Anti-neutrinos have their spins parallel to their velocity and are therefore right-handed particles. Therefore we say that the neutrino has an intrinsic chirality.

The idea that nature at a very fundamental level can tell the difference between "left-handed" and "right-handed" systems is a radical one. It was thought for a time that the combination of the parity operation (=P) and "charge conjugation" (changing each particle into its antiparticle = C) was an inviolate conservation law (CP invariance). But the study of the Kaon decay in 1964 showed a violation of CP. If you add time reversal (=T) to the picture, then it appears that the combination of all three leaves the system indistinguishable from the original (CPT invariance).