Foundations of Physics

, Volume 45, Issue 10, pp 1341–1350 | Cite as

Quantum Theory as a Critical Regime of Language Dynamics

  • Alexei GrinbaumEmail author


Some mathematical theories in physics justify their explanatory superiority over earlier formalisms by the clarity of their postulates. In particular, axiomatic reconstructions drive home the importance of the composition rule and the continuity assumption as two pillars of quantum theory. Our approach sits on these pillars and combines new mathematics with a testable prediction. If the observer is defined by a limit on string complexity, information dynamics leads to an emergent continuous model in the critical regime. Restricting it to a family of binary codes describing ‘bipartite systems,’ we find strong evidence of an upper bound on bipartite correlations equal to 2.82537. This is measurably different from the Tsirelson bound. The Hilbert space formalism emerges from this mathematical investigation as an effective description of a fundamental discrete theory in the critical regime.


Reconstruction of quantum theory Algebraic coding theory Critical phenomena Continuity Tsirelson bound  Bipartite correlations 


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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.CEA-Saclay/IRFU/LARSIMGif-sur-YvetteFrance

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