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.

• Received 2 June 2014

DOI:https://doi.org/10.1103/RevModPhys.87.165