Non-Linearity and Quantum Mechanics: Quest for a Rogue Wave Mechanics

We address the following question: Can a non-linear correction to the Schroedinger equation solve the measurement problem? This problem has a long history (Einstein, de Broglie, Bialynicki-Birula and Mycielski, Ghirardi-Rimini-Weber, Pearle, Weinberg, Diosi, Penrose, ...). However, we have a new take on this issue, based on rogue waves, which are now best understood in terms of the so-called nonlinear Schroedinger equations. Our goal is to explain the spontaneous localization in terms of rare and uncontrollable occurrences of singularities in the solutions of the non-linear quantum dynamics (Quantum Rogue Waves). The aim is to propose answers to fundamental and important questions such as the measurement problem, the wave-particle duality, the role of non-linearity and its natural connection to gravity. The main project activity is the research on quantum rogue waves and it involves the four of us (Samuel Colin, Thomas Durt, Ralph Willox and Howard Wiseman). In order to carry this research, three of us (S Colin, T Durt and R Willox) each plan to travel twice to meet and work together. We (SC, TD and RW) already wrote an article on the subject together (submitted for publication) and expect to produce at least two more articles. In the end, it is our hope to suggest new experimental tests that might reveal the existence of non-linear corrections to the Schroedinger equation.