Foundations of Physics

, Volume 49, Issue 6, pp 460–491 | Cite as

Uncertainty from Heisenberg to Today

  • Reinhard F. WernerEmail author
  • Terry Farrelly
Part of the following topical collections:
  1. Paul Busch: At the Heart of Quantum Mechanics


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 developed 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.


Uncertainty Heisenberg Measurement uncertainty relations Preparation uncertainty relations 



R.F.W. is grateful for the feedback from several audiences, beginning with the Heisenberg Society. Several errors in an earlier arXiv version were spotted by Blake Stacey.


Funding was provided by Deutsche Forschungsgemeinschaft (Grant No. SFB DQ-mat/A06).


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Authors and Affiliations

  1. 1.Quantum Information GroupLeibniz Universität HannoverHannoverGermany

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