The Origin of Complex Quantum Amplitudes
Philip Goyal, Kevin H. Knuth, John Skilling, Paul M. Goggans, Chun-Yong Chan · AIP conference proceedings · 2009
Abstract. Physics is real. Measurement produces real numbers. Yet quantum mechanics uses com-plex arithmetic, in which √−1 is necessary but mysteriously relates to nothing else. By applying the same sort of symmetry arguments that Cox [1, 2] used to justify probability calculus, we are now able to explain this puzzle. The dual device/object nature of observation requires us to describe the world in terms of pairs of real numbers about which we never have full knowledge. These pairs combine according to complex arithmetic, using Feynman’s rules.