A derivation of quantum theory from physical requirements

Details A derivation of quantum theory from physical requirements A derivation of quantum theory from physical requirements

2010-04-09

arxiv.org/abs/1004.1483v4

New J.Phys.13:063001,2011

Physics

Quantum Physics

16 pages, 2 figures. V3: added alternative formulation of Requirement 5, extended abstract, some minor modifications

Scientific paper

10.1088/1367-2630/13/6/063001

Quantum theory is usually formulated in terms of abstract mathematical postulates, involving Hilbert spaces, state vectors, and unitary operators. In this work, we show that the full formalism of quantum theory can instead be derived from five simple physical requirements, based on elementary assumptions about preparation, transformations and measurements. This is more similar to the usual formulation of special relativity, where two simple physical requirements -- the principles of relativity and light speed invariance -- are used to derive the mathematical structure of Minkowski space-time. Our derivation provides insights into the physical origin of the structure of quantum state spaces (including a group-theoretic explanation of the Bloch ball and its three-dimensionality), and it suggests several natural possibilities to construct consistent modifications of quantum theory.

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