Uncertainty from Heisenberg to Today. (arXiv:1904.06139v1 [physics.hist-ph])

We explore the different meanings of "quantum uncertainty" contained in
Heisenberg's seminal paper from 1927, and also some of the precise definitions
that were explored later. We recount the controversy about "Anschaulichkeit",
visualizability of the theory, which Heisenberg claims to resolve. Moreover, we
consider Heisenberg's programme of operational analysis of concepts, in which
he sees himself as following Einstein. Heisenberg's work is marked by the
tensions between semiclassical arguments and the emerging modern quantum
theory, between intuition and rigour, and between shaky arguments and
overarching claims. Nevertheless, the main message can be taken into the new
quantum theory, and can be brought into the form of general theorems. They come
in two kinds, not distinguished by Heisenberg. These are, on one hand,
constraints on preparations, like the usual textbook uncertainty relation, and,
on the other, constraints on joint measurability, including trade-offs between
accuracy and disturbance.

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