Hi all,
today Nuriya will tell us about her master's project. See below for title and abstract.
Best,
-joe
Title: Inadequacy of modal logic in quantum settings
Abstract: This is an article on quantum foundations and logic: we explore the extent to which the principles of classical modal logic can be applied to fully quantum settings. Modal logic models our reasoning in multi-agent problems, and allows us to solve puzzles like the muddy children paradox. The Frauchiger-Renner thought experiment highlighted fundamental problems in applying classical reasoning when quantum agents are involved; we take it as a guiding example to test the axioms of classical modal logic. In doing so, we find a problem in the original formulation of the theorem: a missing assumption about unitarity of evolution is necessary to derive a contradiction and prove the theorem. Adding this assumption clarifies how different interpretations of quantum theory fit in, i.e., which properties they violate. Finally, we show that most of the axioms of classical modal logic break down in quantum settings, and make suggestions to generalize them.