Why Quantum Theory is Complex
Philip Goyal ( Perimeter Institute for Theoretical Physics )
- 15:00 2nd February 2010 ( week 3rd week, Hilary Term 2010 )Lecture Theatre A Comlab
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 that it is possible to derive the complex nature of the quantum formalism directly from the assumption that a pair of real numbers is associated to each sequence of measurement outcomes, and that the probability of this sequence is a real-valued 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 modulus-squared yielding the probability of a sequence of outcomes.
Reference: arXiv:0907.0909 (http://arxiv.org/abs/0907.0909)
We also discuss the implications of this reconstruction of quantum for our understanding of the nature of quantum reality, and for the program of quantum gravity.
Reference: arXiv:0907.0909 (http://arxiv.org/abs/0907.0909)
Starts 3:00pm
Lecture Theatre A, in Comlab (basement, keyless entry towards the left of the main entrace)