The Einstein-Jordan conundrum and its relation to ongoing foundational research in local quantum physics

Abstract

We demonstrate the extraordinary modernity of the 1924/25 "Einstein-Jordan fluctuation conundrum", a Gedankenexperiment which led Jordan to his quantization of waves published as a separate section in the famous Born-Heisenberg-Jordan 1926 "Dreim\"annerarbeit". The thermal nature of energy fluctuations caused by the restriction of the QFT vacuum to a subvolume remained unnoticed mainly because it is not present in QM. In order to understand the analogy with Einstein's fluctuation calculation in a thermal black body system, it is important to expose the mechanism which causes a global vacuum state to become impure on a localized subalgebra of QFT. The present work presents the fascinating history behind this problem which culminated in the more recent perception that "causal localization" leads to thermal manifestations. The most appropriate concept which places this property of QFT into the forefront is "modular localization". These new developments in QFT led to a new access to the existence problem for interacting quantum fields whose solution has remained outside the range of renormalized perturbation theory. It also clarifies open problems about the relation of particles and fields in particular about the incompletely understood crossing property. Last not least it leads to a constructive understanding of integrable versus non-integrable QFTs..