Fundamental symmetries
There are a variety of symmetries in standard theories of subatomic particles. For instance, the fact that the three colors of quarks are identical can be considered a symmetry. But of all the symmetries, charge conjugation (C) and parity (P) stand out for their philosophical importance.
Charge conjugation is the symmetry of their being an identical antiparticle for every particle. If protons exist, an antiproton is expected to exist with exactly the same mass and other properties, only with opposite quantum numbers.
Parity is the symmetry that reflects the fact that reflecting the universe about a point or a plane should give a universe of equal physical validity. One consequence of parity is that using a left-hand rule instead of a right-hand rule should make no measurable difference. When we studied magnetic fields, the direction of the magnetic field depended on our choice of a right-handed convention. However, magnetic fields only manifest themselves through the forces felt by the charged particles through the magnetic field. The calculation of the force also hinged on a right-hand rule. The application of two right-hand rules would have given the same result as the application of two-left hand rules. Thus, physical phenomena were not biased in any way towards right or left-handed rules.
It was a shock when parity violation was observed in 1957. In this experiment a nucleus which would undergo beta decay was oriented with its spin along a magnetic field. Spin and angular momenta are also vectors whose direction is determined by the right-hand rule. The experimental result that violated parity conservation, was that the electrons from the beta decay flew off more often in the direction of the magnetic field than in the opposite direction. This result could be explained by the non-existence of right-handed neutrinos. Electrons can spin one way or the other, but apparently neutrinos spin only with a left-handed orientation relative to the direction of their velocity. Since left-handed neutrinos exist but no left-handed anti-neutrinos, this result also violates charge conjugation.
The symmetries are not violated as unfairly as it first seems. If one were to consider the equivalent experiment with antiparticles, the opposite result would occur. For all anti-neutrinos are right-handed in their spin. Thus the combination of the two symmetries (CP) did appear to be conserved. This symmetry states that for every left-handed particle there exists an equivalent right-handed anti-particle.
However, in the early 1960s CP violation was observed. This is a flat-out violation of the symmetry between particles and anti-particles. This violation is extremely small and is only observed in studies of neutral kaons, mesons with an anti-strange and a down quark, or one strange and one anti-down quark. An example of the violation is that a KL meson, which like a photon is its own antiparticle, decays more often to (e+ + n + p) than to the 3 corresponding anti-particles. The difference is only about a tenth of a percent, but it is a dramatic result nonetheless. More apparent evidence of CP violation is in the matter around us. There is more matter than anti-matter in the universe. Obviously, the equations that guided the formation of the universe must have violated the symmetry between matter and anti-matter at some stage. The nature of CP violation still carries a cloud of mystery.