Quantum Theory from Complementarity, and its Implications Speaker(s): Philip Goyal
Abstract: Complex numbers are an intrinsic part of the mathematical formalism of quantum theory, and are perhaps its most mysterious feature. In this talk, we show how it is possible to derive the complex nature of the quantum formalism directly from the assumption that a pair of real numbers is associated with each sequence of measurement outcomes, and that the probability of this sequence is a realvalued function of this number pair. By making use of elementary symmetry and consistency conditions, and without assuming that these real number pairs have any other algebraic structure, we show that these pairs must be manipulated according to the rules of complex arithmetic. We demonstrate that these complex numbers combine according to Feynman's sum and product rules, with the modulussquared yielding the probability of a sequence of outcomes. We then discuss how complementarity  the key guiding idea in the derivation  can be understood as a consequence of the intrinsically relational nature of measurement, and discuss the implications of this for our understanding of the status of the quantum state.
Date: 01/10/2009  3:30 pm
Collection: PIAF 09' New Perspectives on the Quantum State
