Do we understand quantum mechanics – finally?

  • Jürg M. Fröhlich

    ETH Zürich, Switzerland
  • Baptiste Schubnel

    ETH Zürich, Switzerland
Do we understand quantum mechanics  –  finally? cover

A subscription is required to access this book chapter.


This paper reviews some of our understanding of general quantum mechanics. It starts with the exposition of an abstract algebraic formalism useful to formulate classical and quantum-mechanical models of physical systems. It then highlights the essential differences between classical models (commutative algebra) and quantum-mechanical models (non-commutative algebra) of physical systems. It is explained in which sense classical models are “realistic” and deterministic, while quantum-mechanical models are intrinsically probabilistic – in spite of the fact that the Heisenberg time-evolution of operators representing physical quantities is “deterministic”.

The quantum theory of time-ordered sequences of measurements is developed in some detail, and the crucial role of “decoherence” in the emergence of facts – or “(almost) consistent histories” – is explained.

Some technical matters (Bell inequalities, quantum marginal problem) are discussed in appendices.