The strange (hi)story of particles and waves

TL;DR

This paper offers a historical and conceptual overview of quantum theory emphasizing global unitarity, proposing a reinterpretation of wave functions as field modes and discussing the nature of quantum states.

Contribution

It introduces a novel interpretation of single-particle wave functions as field modes and emphasizes the importance of global unitarity in quantum theory.

Findings

Wave functions are best viewed as field modes occupied once.

Multiple excitations produce apparent many-particle wave functions.

Quantum states are fundamentally defined on configuration space of fields.

Abstract

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.