Douglas Lundholm
Twisted perspectives on quantum mechanics
Our understanding of the influence of geometry and topology in quantum systems has seen some rapid developments recently, with experimental confirmations of intermediate notions of quantum statistics and "anyons", as well as with the recent Nobel prize in physics, in which the deeper aspects of entanglement and non-locality are beginning to be fully appreciated. In this talk I aim to discuss some bridges between these developments using the general concepts of perspectives, twisting and vorticity. Namely, while "anyons" (intermediate exchange quantum statistics) are a consequence of the twisting of the phase of a wave function under particle exchange, and their corresponding exclusion statistics may be viewed as a resulting vorticity in the probabilities around the diagonals of the configuration space, also contextual systems and non-local entanglement quantum games may be understood from a more general twisting of probability distributions. As has been also emphasized by e.g. Mermin and Mansfield, such twisting may be illustrated geometrically using impossible figures such as in the artistic works of Escher, Penrose and Reutersvärd.
