Undecidability as a Structural Feature of Quantum Field Theory — E8 Intelligence Research

FINDING: Undecidability is not a quirk of formal logic but a structural feature of physical theory — quantum field theory contains undecidable spectral-gap and correlation-function problems, and the halting problem is formally equivalent to the spectral gap problem for certain Hamiltonians. | MATH: (1) Turing 1936: no total computable function h(P,x) decides whether program P halts on x; proof by diagonalization — define D(P) = if h(P,P) then loop else halt, contradiction at D(D). (2) Gödel 1931: any consistent, effectively axiomatized theory T extending Robinson arithmetic is incomplete — ∃ sentence G with T ⊬ G and T ⊬ ¬G; G encodes "this sentence is unprovable" via Gödel numbering. (3) Rice's theorem: every non-trivial semantic property of programs is undecidable. (4) Cubitt–Perez-Garcia–Wolf 2015 (Nature): the spectral gap problem is undecidable — no algorithm decides whether a given translation-invariant 2D Hamiltonian has a gap; reduction from halting. (5) Tachikawa 2022: undecid Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com