Quantum theory as a critical regime of language dynamics

TL;DR

This paper proposes a new mathematical framework for quantum theory based on language dynamics and complexity limits, predicting a correlation bound different from the traditional Tsirelson bound, and showing how Hilbert space emerges from discrete models.

Contribution

It introduces a novel approach linking language complexity limits to quantum correlations, deriving a new bound and explaining the emergence of Hilbert space formalism.

Findings

Derived a bipartite correlation upper bound of 2.82537, different from Tsirelson's bound.

Showed that Hilbert space formalism emerges as an effective description in the critical regime.

Provided a testable prediction connecting language complexity and quantum correlations.

Abstract

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.