Philip Goyal

Research Interests

The physical origin of the mathematical rules of quantum theory is obscure. Although this obscurity not a serious obstacle to the use of quantum theory in many applications, it hinders both the clear interpretation of the theory ("What is quantum theory is telling us about how nature works?"), and the application of the theory to novel physical domains ("Can we apply the rules of quantum theory without modification in such domains as quantum gravity? In any case, what latitude is there for making modifications to the quantum rules?").

One powerful way to elucidate the physical origin of the mathematical rules of quantum theory is to attempt to derive (or reconstruct) these rules a set of physical principles. Once this is done, one can more readily generate an interpretation that fits these physical principles (it is much easier to interpret a set of physical principles than a set of abstract mathematical statements), and assess the applicability of the quantum formalism in new physical domains.

My research has focussed on harnessing new ideas (particularly from quantum information) to formulate simple physical principles from which quantum theory can be reconstructed. I have developed two such reconstructions -- one of the finite-dimensional von Neumann-Dirac quantum rules, and (more recently) one of Feynman's rules. The latter reconstruction very directly shows that the origin of complex numbers in quantum theory rests on essentially the same key symmetries that algebraically characterise complex numbers in mathematics. In other words, complex numbers are natural in quantum theory and in mathematics for essentially the same reason.

I have also shown how to derive the correspondence rules of quantum theory (such as the canonical commutation relations) that are needed to apply the abstract quantum rules to specific physical systems of interest. The key idea I use is very simple: the predictions of the quantum model of a physical system must "on average" (suitably defined) agree with those of the classical model of the same system.

Positions Held

• 2004-7 Research Fellow, Cavendish Laboratory, Cambridge.

Recent Publications

• Goyal, P. Information-Geometric Reconstruction of Quantum Theory. Physical Review A 78, 052120 (2008)
• Why Quantum Theory is Complex, Philip Goyal, Kevin H. Knuth, John Skilling, arxiv: 0907.0909
• From Information Geometry to Quantum Theory, Philip Goyal, arxiv: 0805.2770
• An Information-Geometric Reconstruction of Quantum Theory, I: The Abstract Quantum Formalism, Philip Goyal, arxiv: 0805.2761
• An Information-Geometric Reconstruction of Quantum Theory, II: The Correspondence Rules of Quantum Theory, Philip Goyal, arxiv: 0805.2765

Seminars

• What is Quantum Theory telling us about how Nature works? CHESS Interactions Conference, Saskatoon.
• Why Quantum Theory is Complex. Bayesian Inference and Maximum Entropy Methods, Oxford, MS.
• PIRSA:09040062, Why Quantum Theory is Complex, 2009-08-11, Reconstructing Quantum Theory
• PIRSA:08120042, Introduction to Quantum Foundations, 2008-12-10, Young Researchers Conference 2008
• PIRSA:08110043, From Information Geometry to Quantum Theory, 2008-11-04, Quantum Foundations
• PIRSA:08090076, From Information Geometry to Quantum Theory , 2008-09-29, The Clock and the Quantum: Time and Quantum Foundations
• PIRSA:08030007, Foundations of Quantum Mechanics #6, 2008-02-28, New Horizons In Fundamental Physics
• PIRSA:08030003, Foundations of Quantum Mechanics #5, 2008-02-26, New Horizons In Fundamental Physics
• PIRSA:07010026, An Information-Theoretic Approach to Quantum Theory, 2007-01-22, Quantum Foundations