2013/03/27 by Anton Kapustin, Kapustin, Anton
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.1303.6917
23 pages, latex. v3: commentaries on the axioms expanded, a non-technical summary added, references added, typos fixed. v4: version accepted for publication in Journal of Mathematical Physic (under a different title). Axiomatics is simplified and the number of axioms reduced, some proofs clarified, typos fixed
arxiv created 2013/06/03 · arxiv updated 2013/06/04
We formulate physically-motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to Quantum Mechanics as the only nontrivial consistent theory. Complex numbers and the existence of the Planck constant common to all systems arise naturally in this approach. The axioms are divided into two groups covering kinematics and basic measurement theory respectively. We show that even if the second group of axioms is dropped, there are no deformations of Quantum Mechanics which preserve the kinematic axioms. Thus any theory going beyond Quantum Mechanics must represent a radical departure from the usual a priori assumptions about the laws of Nature.