Lecture notes

Foundations of Unitary Quantum  Mechanics

These are rudimentary notes on developments in quantum mechanics, designed for both undergraduate and graduate levels. I introduce theories of unitary quantum mechanics with a focus on Bohmian and Everettian mechanics. Although physicists occasionally express antagonism towards philosophy, I contend that many debates over quantum mechanics interpretations could be mitigated if the participants' operational philosophy of science were explicitly articulated. Consequently, I state the realist philosophy of science underpinning these notes. This allows for a discussion on the conflation between Einstein and Bell locality. I follow with the connection between Bohmian and Everettian mechanics, revealing that non-locality in Bohmian mechanics arises from the particles. Everettian mechanics, which corresponds to the pilot wave, exhibits Einstein locality. The principles of locality and completeness in quantum mechanics are known but are seldom presented didactically. Thus, I seized the opportunity to offer an introduction to Everettian mechanics using both the Schrödinger and the Heisenberg pictures, where in the latter, locality and completeness are explicit. Contrary to orthodox interpretations that suggest measurement interactions alter the quantum system, in unitary quantum mechanics, these interactions instead modify the measurer. In some flavors of many-worlds interpretations, the splitting is presented as if the entire universe splits. However, the Heisenberg picture shows that the dynamics of multiplicity is local. Differentiation of foliations only occurs in space-like connected regions, whose characteristic length scale is set by the nature of the interactions. Lastly, the notes conclude with a concise overview of decoherence. The contents of the lectures are not original, but perhaps provide a didactic iteration on a subject that has not yet percolated the community.

Foundations of Unitary Quantum Mechanics © 2024 by David Möckli is licensed under CC BY 4.0. To view a copy of this license, visit https://creativecommons.org/licenses/by/4.0/. 

Feedback Welcome

I am continuously improving these lecture notes. Therefore, I welcome any comments you may have. Please feel free to reach out to me at mockli@ufrgs.br.