Operational Quantum Mechanics, Quantum Axiomatics and Quantum Structures

  • Diederik Aerts

Operational quantum mechanics and quantum axiomatics have their roots in a work of John von Neumann in collaboration with Garett Birkhoff, that is almost as old as quantum mechanics itself [1]. Indeed already during the beginning years of quantum mechanics, the formalism that is now referred to as standard quantum mechanics [5], was thought to be too specific by the founding fathers themselves. One of the questions that obviously was at the origin of this early dissatisfaction is: ‘Why would a complex ► Hilbert space deliver the unique mathematical structure for a complete description of the microworld? Would that not be amazing? What is so special about a complex Hilbert space that its mathematical structure would play such a fundamental role?’


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© Springer-Verlag Berlin Heidelberg 2009

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  • Diederik Aerts

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