Abstract: Symmetry transformations have been proven a bedrock tool for understanding the nature of particle interactions, formulating, and testing fundamental theories. Based on the up to now unbroken CPT symmetry, the violation of the CP symmetry between matter and antimatter by weak interactions, discovered in the decay of kaons in 1964 and observed more recently in 2001 in B mesons, strongly suggests that the behavior of these particles under weak interactions must also be asymmetric under time reversal T. However, until recent years there has not been a direct detection of the expected time-reversal violation in the time evolution of any system. This Colloquium examines the field of time-reversal symmetry breaking in the fundamental laws of physics. For transitions, its observation requires an asymmetry with exchange of initial and final states. A discussion is given of the conceptual basis for such an exchange with unstable particles, using the quantum properties of Einstein-Podolsky-Rosen entanglement available at B meson factories combined with the decay as a filtering measurement. The method allows a clear-cut separation of different transitions between flavor and CP eigenstates in the decay of neutral B mesons. These ideas have been implemented for the experiment by the BABAR Collaboration at SLAC's B factory. The results, presented in 2012, prove beyond any doubt the violation of time-reversal invariance in the time evolution between these two states of the neutral B meson.

Abstract: We discuss the linearization of Einstein equations in the presence of a cosmological constant, by expanding the solution for the metric around a flat Minkowski space-time. We demonstrate that one can find consistent solutions to the linearized set of equations for the metric perturbations, in the Lorentz gauge, which are not spherically symmetric, but they rather exhibit a cylindrical symmetry. We find that the components of the gravitational field satisfying the appropriate Poisson equations have the property of ensuring that a scalar potential can be constructed, in which both contributions, from ordinary matter and Lambda > 0, are attractive. In addition, there is a novel tensor potential, induced by the pressure density, in which the effect of the cosmological constant is repulsive. We also linearize the Schwarzschild-de Sitter exact solution of Einstein's equations ( due to a generalization of Birkhoff's theorem) in the domain between the two horizons. We manage to transform it first to a gauge in which the 3-space metric is conformally flat and, then, make an additional coordinate transformation leading to the Lorentz gauge conditions. We compare our non-spherically symmetric solution with the linearized Schwarzschild-de Sitter metric, when the latter is transformed to the Lorentz gauge, and we find agreement. The resulting metric, however, does not acquire a proper Newtonian form in terms of the unique scalar potential that solves the corresponding Poisson equation. Nevertheless, our solution is stable, in the sense that the physical energy density is positive.

Abstract: Tests of the T, CP and CPT symmetries in the neutral kaon system are performed by the direct comparison of the probabilities of a kaon transition process to its symmetry-conjugate. The exchange of in and out states required for a genuine test involving an antiunitary transformation implied by time-reversal is implemented exploiting the entanglement of K0K0 pairs produced at a 0 -factory.A data sample collected by the KLOE experiment at DAONE corresponding to an integrated luminosity of about 1.7 fb-1 is analysed to study the At distributions of the 0 -> KSKL -> pi+pi- pi +/- e -/+ v and 0 -> KSKL -> pi +/- e -/+ v3 pi 0 processes, with At the difference of the kaon decay times. A comparison of the measured At distributions in the asymptotic region At ⠅ iS allows to test for the first time T and CPT symmetries in kaon transitions with a precision of few percent, and to observe CP violation with this novel method.