Foundations of Quantum Theory

Professors Caticha, Earle, Goyal, and Knuth

Quantum theory is perhaps the most empirically successful theory in the history of physics. In the eighty-five years since its creation, quantum theory has proved itself capable of accounting precisely for a vast range of physical phenomena such as the principles of chemical bonding and chemical reactions, the nuclear reactions that fuel the stars, and exotic phenomena like superconductivity.

Much of the modern technology that fuels our lives is underpinned by quantum theory. The transistor, the basis for the modern computer that underlies all information processing technology, requires quantum theory for its design and modeling. The same holds true for the laser and the light-emitting diode, which jointly provide the basis for optical communication networks and optical data storage. Yet more quantum technology, such as quantum computers and quantum cryptography, is waiting in the wings, promising to transform our lives still further.

But, since the beginning of its existence, quantum theory has been of great interest for quite another reason. Taken at face value, quantum theory challenges many of the key tenets of the mechanical conception of reality. That picture of reality, which was developed by Descartes, Galileo, and Newton (amongst others), underpinned the development of physics—what is now called classical physics—for approximately three hundred years.

The challenge posed by quantum theory is, at the minimum, to develop an intuition for the reality that it describes which is sufficient to be able to discover, explore, and harness the phenomena it encompasses. And, at best, to develop a conception of physical reality which takes quantum theory fully into account, to develop a conception which is as coherent and compelling as the mechanical conception of reality, and which is capable of guiding the further development of physics.

In our group, we are particularly interested in developing a deep understanding of quantum theory by reconstructing (deriving) the mathematical formalism of quantum theory from a set of compelling physical principles.  Our various approaches all draw heavily upon our parallel work in the foundations of inference, in particular our understanding of information theory.