Multi-agent epistemic paradoxes in physical theories

Abstract

The purpose of physical thought experiments is to explore the consistency of a physical theory behind it in all possible settings, including scenarios which can be regarded as hypothetical. Some of these scenarios involve agents who can reason based on a given theory, and are also modeled within the same theory; combining the conclusions made by individual agents leads to a logical paradox. This doctoral thesis explores such multi-agent paradoxes inn quantum theory and beyond, the constructions behind them, and their origins. We start with reviewing (in an intuitive way) older instances of paradoxes. In particular, we focus on the famous incompleteness results from mathematics, and outline their construction: the diagonalization theorem, which also happens to be the structure underlying epistemic self-referential paradoxes. We continue with a review of the history of thought experiments in quantum theory, discuss their importance for interpretations of quantum theory, and give an overview of resolutions that were proposed over the years. We proceed to present a software package framework allowing to model quantum thought experiments where agents reason about their knowledge and are also modeled within the theory, with several adaptable modules. Next, we explore other physical theories, such as generalized probabilistic theories, Spekkens' toy model, and the positive formalism of Oeckl, find examples of scenarios like those in quantum theory, and check in which ones a paradox is recovered. Subsequently, we present a more general framework to talk about multi-agent paradoxes in an arbitrary physical theory, and establish a link between paradoxes and contextuality. We also list some properties of paradoxes in quantum theory. Finally, we classify some ``escape strategies'' for avoiding multi-agent paradoxes in physical theories by analyzing the axioms governing agents' knowledge used in the derivation of inconsistencies. We conclude by pointing out future research directions.