Khalfin’s theorem and a proposed test of time-reversal invariance

A theorem closely related to one stated by Khalfin requires that, if the (time-dependent) rate for transitions a→b is a constant multiple of the rate for the inverse transitions b→a, the only possible value of that constant is unity, viz., reciprocity must hold. We consider a more general situation in which the two rates can be approximately, although not exactly, proportional. The application of similar arguments to the corresponding generalized situation shows that an earlier prediction of departure from reciprocity in ${\mathit{K}}^{0\rightleftarrows }$K${\mathrm{¯}}^0$ transitions is not endangered by the theorem.