The strange (hi)story of particles and waves

This is a non-technical presentation (in historical context) of the quantum theory that is strictly based on global unitarity. While the first part was written for a general readership, Sect. 5 may appear a bit provocative. I argue that the single-particle wave functions of quantum mechanics have to be correctly interpreted as field modes that are "occupied once" (that is, first excited states of the corresponding quantum oscillators in the case of a boson field). Multiple excitations lead non-relativistically to apparent many-particle wave functions, while the quantum states proper are defined by wave function(al)s on the configuration space of fundamental fields, or on another, as yet elusive, fundamental basis.