Lecture notes: Foundations of Unitary Quantum Mechanics

These lecture notes are motivated by recent developments in the foundations of unitary quantum theory and are designed for both undergraduate and graduate students. They introduce theories of unitary quantum mechanics with a realistic bias, focusing on Bohmian and Everettian mechanics. This framework allows for a discussion of the distinction between Einstein locality and Bell locality, which are often conflated but are fundamentally different. The connection between Bohmian and Everettian mechanics is explored, revealing that non-locality in Bohmian mechanics arises from the particles, while Everettian mechanics — associated with the pilot wave — preserves Einstein locality. While the principles of locality and completeness in quantum mechanics are well-known, they are rarely presented in a didactic manner. To address this, I offer an introduction to Everettian mechanics using both the Schrödinger and Heisenberg pictures. In the Heisenberg picture, locality and completeness become explicit. Contrary to orthodox interpretations, which suggest that measurement interactions alter the quantum system, unitary quantum mechanics asserts that these interactions modify the measurer instead. In some versions of many-worlds interpretations, the splitting of worlds is described as if the entire universe undergoes meiosis. However, the Heisenberg picture clarifies that the dynamics of multiplicity are local. Differentiation of foliations occurs only in space-like separated regions, with a characteristic length scale determined by the nature of the interactions. Using the local-realistic bias, I also discuss quantum agents and a recent no-go theorem by Frauchiger and Renner. The notes conclude with a concise overview of decoherence. While the material covered in these lectures is not original, it offers a didactic perspective on a subject that has yet to fully permeate the broader community. These notes are a work in progress.