The Complex Structure of Quantum Mechanics

The project aims to advance our understanding of quantum mechanics, a notoriously puzzling theory, and the ways it differs from classical physics. It focuses on the mathematics used to formulate the theory—in particular, complex numbers—aiming to understand why complex numbers are so central to quantum mechanics as opposed to classical physics. The project will result in several research articles and presentations, provide mentoring opportunities for women working in foundations of physics, and yield a piece on pedagogy for teachers of introductory quantum mechanics courses. The project will advance the public's understanding of quantum mechanics and the mathematics required for it by producing a piece aimed at a general scientific audience, outlining the main ideas of the project while critically evaluating recent claims that complex numbers are truly essential to describing quantum physics. The PI will develop a new undergraduate course on the mathematical and conceptual foundations of quantum mechanics. This project in the philosophical foundations of physics addresses a question of longstanding interest and importance, asked by just about every famous physicist who has thought about the theory since its inception (including the likes of Schrödinger, Pauli, and Bohm), yet which still lacks an agreed-upon answer: are complex numbers essential to quantum mechanics, and if so, why? In classical physics, complex numbers are used as a dispensable calculational tool; in quantum mechanics, they seem to be playing a newly integral role. What is about quantum mechanics and the kinds of phenomena it describes that makes complex numbers so central to the theory? The project will show that an especially elucidating answer flows from distinctively quantum phenomena involving spin. This yields direct insight into the nature of quantum mechanical systems and the mathematics used to describe them, and helps elucidate how quantum mechanics differs from classical physics. It further yields insight into the nature of mathematically formulated scientific theories more generally, particularly the relationship between the mathematics used to formulate a theory and the nature of the world itself. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria. NSF Award ID: 2419293 | Program: 01002425DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Jill North | Institution: Rutgers University New Brunswick, NEW BRUNSWICK, NJ | Award Amount: $177,330 View on NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2419293 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2419293.html