  I summarize a research program that aims to reconstruct quantum theory from a
fundamental physical principle that, while a quantum system has no intrinsic
hidden variables, it can be understood using a reference measurement. This
program reduces the physical question of why the quantum formalism is
empirically successful to the mathematical question of why complete sets of
equiangular lines appear to exist in complex vector spaces when they do not
exist in real ones. My primary goal is to clarify motivations, rather than to
present a closed book of numbered theorems, and consequently the discussion is
more in the manner of a colloquium than a PRL.
