BooksesiCollected Volumepp. 37–84

Do we understand quantum mechanics – finally?

  • Jürg M. Fröhlich

    ETH Zürich, Switzerland
  • Baptiste Schubnel

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

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.