Quantum Foundations: Measurements, Contextuality, and Classicality

Systems with non-Hermitian Hamiltonians, especially PT-symmetric systems, have been proposed in both fundamental physics and as effective descriptions of systems. This has led to some controversies, such as whether PT-symmetric theories are new physical theories or equivalent to standard quantum theory. These controversies have mainly been approached from a mathematical point of view within orthodox quantum theory. However, one of the lessons of quantum foundations is that which aspects of the theory can be independently varied depends on the interpretation of quantum theory. Therefore, looking at PT-symmetric quantum theory from the point of view of different interpretations may yield new ways of understanding the theory and may provide a means of experimentally separating interpretations that are equivalent in standard quantum mechanics. In this work, we begin this study by showing how some of the conceptual problems of PT-symmetric theories can be resolved in the pilot-wave approach to quantum theory.