Time-reversal invariance and magnetic fields

As pointed out above, the Wigner surmise and the analysis of statistical distributions require a careful study of which quantum numbers are exact, i.e. which rules a system must obey precisely. A rule which has not been considered so far is time-reversal invariance, which applies when a system evolves backwards in time in precisely the same way as it evolved forward, i.e. when the sign of time can be changed without affecting the basic equations. 

Not all systems are time-reversal invariant. In particular, time-reversal invariance is broken by an external magnetic field. This is most easily understood by considering the physical difference between natural rotation and Faraday rotation in naturally occurring rotation (in a crystal or a sugar solution) the plane of polarisation of the radiation comes back onto itself when the light beam is reflected backwards along the same path. This does not occur in Faraday rotation, where the angle of rotation continues to accumulate for the reflected beam. In fact, the Faraday effect is 

---