We discuss the concepts and methodology to implement an experiment probing directly Time Reversal (T) non-invariance, without any experimental connection to CP violation, by the exchange of 'in' and 'out' states. The idea relies on the B0-antiB0 entanglement and decay time information available at B factories. The flavor or CP tag of the state of the still living neutral meson by the first decay of its orthogonal partner overcomes the problem of irreversibility for unstable systems, which prevents direct tests of T with incoherent particle states. T violation in the time evolution between the two decays means experimentally a difference between the intensities for the time-ordered (l^+ X, J/psi K_S) and (J/psi K_L, l^- X) decays, and three other independent asymmetries. The proposed strategy has been applied to simulated data samples of similar size and features to those currently available, from which we estimate the significance of the expected discovery to reach many standard deviations.