There is a well-known correspondence between invariance under transformation and conservation laws (Noether's theorem). For example, invariance of a physical system under spatial translation leads to conservation of momentum; invariance under rotation leads to conservation of angular momentum; invariance under time evolution leads to conservation of energy, and so on. Each of these transformations is continuous.
There are also three discrete symmetry transformations:
and invariance under these transformations also leads to the concept of a conserved quantity. For example, the parity of an energy state in an atom is a conserved quantity provided only the electromagnetic interaction is considered. (In the language of quantum mechanics, this is because the parity operator commutes with the electromagnetic Hamiltonian.) Conservation of parity leads to the usual selection rules for radiative transition between the atomic energy states.
- charge conjugation, particle -> antiparticle
- parity, r -> -r (left hand to right hand)
- time reversal, t -> -t
Physicists used to believe that the four fundamental forces we observe in nature - gravity, electromagnetism, and the strong and weak nuclear forces - all conserved the C, P and T symmetries. But in 1957 experiments with radioactive nuclei showed that the weak interaction does not conserve parity; that is, it gives rise to processes that are fundamentally handed. (In quantum mechanics, this means that the parity operator and the electroweak Hamiltonian do not commute, or equivalently that the weak interaction mixes electromagnetic pure parity eigenstates.) Further, in 1963 experiments on kaon decay showed that the combined CP symmetry was also not conserved. However, there are quite general reasons for believing that the combined symmetry of CPT is conserved. This means that CP violation also implies T-violation.
Experiments to study the symmetry properties of physical systems can set limits on the degree to which the discrete symmetries such as P, CP, and CPT are conserved. These limits constitute direct information about the basic character of the fundamental interactions. In particular, experiments in atomic physics can be exquisitely sensitive to tiny departures from symmetry, and can contribute important information about the fundamental forces in the low-energy limit.
Normally, the weak interaction is ignored in atomic physics, because it is so much weaker than the electromagnetic interaction. However, the valence electrons of an atom can experience the weak interaction: the neutral vector boson Z0 can be exchanged between a nucleon and a valence electron, provided the electron wavefunction has a non-zero amplitude at the nucleus since the exchange is effectively a point interaction. This means that the parity-violating character of the weak interaction can be observed in the atom as a whole. Precise measurements of atomic parity non-conservation provide an important low-energy test of the electroweak Standard Model, complementary to particle physics experiments at high energies.
Since parity is not conserved within the atom, the atom is chiral or handed. For example, this can be seen by plotting the probability current density for a given atomic state; the picture shows the 2p1/2 state of hydrogen, where the effect of the weak interaction has been artificially increased to make the pitch of the helix visible. This picture is obtained using expressions given in Hegstrom et al, Am.J.Phys. 56 1086 (1988). Click on the image to see an animation and more details.
In order for an elementary particle, atom or molecule to possess a permanent electric dipole moment (EDM), time-reversal symmetry must be violated, and through the CPT theorem CP must be violated as well. CP violation was discovered in 1964, but it has been observed only in the decays of the neutral K mesons - and no EDM has yet been found. Experiments to search for an EDM began many decades ago, and are expected to continue with increasing precision well into the future. In the past, EDM experiments played a crucial role in eliminating theories put forward to explain the K system, because the theories usually predicted too large a dipole moment. The currently accepted Standard Model of Particle Physics predicts unobservably small dipole moments. Therefore, EDM experiments are an ideal probe for new physics beyond the Standard Model, such as supersymmetry, in which the natural size of EDMs of neutrons, atoms and molecules lies within a detectable range.