A review of the experimental status of CPT invariance leads to two conclusions: (i) There is no hint of a CPT violation in the data. (ii) CPT invariance has not been probed with a quantitative sensitivity that greatly exceeds that achieved in studies of CP symmetry. I sketch some models where CPT violations could be implemented. Yet it is hard to see how those types of ansatz could generate observable effects in the transitions of neutral K mesons. On the other hand the quite special quantum aspects of the reaction φ → KL KS can be harnessed to probe quantum mechanics in novel ways by analyzing EPR like correlations of a kind that have not been studied before. Some comparisons are made with Weinberg's recent formulation of non-linear (though homogenous) quantum mechanics and with generalizations that can be obtained from Bohm's interpretation of quantum mechanics.