In a paper in arXiv Giulia Marcucci and Claudio Conti report on the mathematical structures of the so-called Time Asymmetric Quantum Mechanics. This theory predicts that time-travel is not possible and explain evidences as the Big Bang or the decay of unstable particles. The authors argue that possible shaping of the initial state of a system may furnish a road to validate these fascinating developments in quantum mechanics. The work also follows the experimental evidence of the quantization of the decays rates.

The picture above shows a pictorial representation of the Gelfand triplet, the phase space of the Time Asymmetric Quantum Mechanics