Decoherence induced $CPT$ violation and entangled neutral mesons

We discuss two classes of semimicroscopic theoretical models of stochastic spacetime foam in quantum gravity and the associated effects on entangled states of neutral mesons, signalling an intrinsic breakdown of $CPT$ invariance. One class of models deals with a specific model of foam, initially constructed in the context of noncritical (Liouville) string theory, but viewed here in the more general context of effective quantum-gravity models. The relevant Hamiltonian perturbation, describing the interaction of the meson with the foam medium, consists of off-diagonal stochastic metric fluctuations, connecting distinct mass eigenstates (or the appropriate generalization thereof in the case of $K$-mesons), and it is proportional to the relevant momentum transfer (along the direction of motion of the meson pair). There are two kinds of $CPT$-violating effects in this case, which can be experimentally disentangled: one (termed “$\omega$-effect”) is associated with the failure of the indistinguishability between the neutral meson and its antiparticle, and affects certain symmetry properties of the initial state of the two-meson system; the second effect is generated by the time evolution of the system in the medium of the spacetime foam, and can result in time-dependent contributions of the $\omega$-effect type in the time profile of the two-meson state. Estimates of both effects are given, which show that, at least in certain models, such effects are not far from the sensitivity of experimental facilities available currently or in the near future. The other class of quantum-gravity models involves a medium of gravitational fluctuations which behaves like a “thermal bath”. In this model both of the above-mentioned intrinsic $CPT$ violation effects are not valid.