In his groundbreaking paper of 1927, Heisenberg presented his famous principle in a largely informal and intuitive way. While it is clear that he distinguishes two versions, only one of these was made rigorous and was proven as a quantum mechanical theorem very soon afterwards and has since become the well-known textbook uncertainty relation. We refer to this as an expression of preparation uncertainty as it concerns a limitation of the possibilities of simultaneously defining sharp values of noncommuting quantum observables. Heisenberg's second idea was that of a tradeoff in the necessary errors in any attempted joint measurement of such quantities; this should be expressed as a measurement uncertainty relation. It has taken many decades before measurement uncertainty was properly formulated and proven. Here I review the history of this problem and the scientific controversy that surrounded the question of measurement uncertainty relations. I will explain the conceptual and mathematical steps that needed to be achieved before these relations could be rigorously established.
Paul Busch，英国约克大学数学与统计系教授。主要研究方向为：量子信息论及统计物理的数学基础。他担任期刊 “Foundations of Physics”的编委，也担任施普林格专著系列《物理学基础理论》的编委。2016-2018年， 担任国际量子结构协会主席。2017-2018，Paul Busch获得皇家学会Leverhulme高级研究奖金（Royal Society Leverhulme Trust Senior Research Fellowship）资助。他已在物理知名期刊《Physical Review Letters》，《New Journal of Physics》，《Reviews of Modern Physics》等发表论文多篇。