Undecidability as a Structural Invariant Across Computation and Quantum Physics — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Undecidability is not a computational quirk but a structural invariant of formal systems, extending into quantum many-body physics — the halting problem's diagonalization argument mirrors a fundamental incompleteness in any axiomatic description of physical reality. | MATH: Gödel's incompleteness (∃G: ¬⊢G ∧ ¬⊢¬G); Halting problem (∄H: ∀(P,I), H(P,I) terminates ⟺ P(I) halts); Rice's theorem (any non-trivial semantic property of programs is undecidable); Quantum reduction: spectral gap problem shown undecidable for translation-invariant 1D Hamiltonians (Cubitt, Perez-Garcia, Wolf, 2015) — implies no finite algorithm can decide if a physical system has a gap, even with full Hamiltonian specification. | CONNECTION: The diagonalization argument (Cantor's 2^ℵ₀ > ℵ₀) is a combinatorial shadow of the golden ratio's self-similarity — both encode non-well-founded recursion. The undecidability of the spectral gap for translation-invariant systems ties to lattice structures: the proof con
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Related
- Quantum Entanglement Proves Undecidability: MIP*=RE Deepens Computation's Limits — E8 Intelligence Research
- Undecidability as Structural Physics: From Halting to Spectral Gaps — E8 Intelligence Research
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- Undecidability as Structural Truth: Gödel and Turing's Shared Limit — E8 Intelligence Research
- The Golden Ratio as a Universal Structural Constant in Physics, Audio, and Computation — E8 Intelligence Research
BibTeX
@misc{caldin2026undecidability,
title = {{Undecidability as a Structural Invariant Across Computation and Quantum Physics — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23465410},
url = {https://zenodo.org/records/23465410},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Undecidability as a Structural Invariant Across Computation and Quantum Physics — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/19
PB - Zenodo
DO - 10.5281/zenodo.23465410
UR - https://zenodo.org/records/23465410
AB - FINDING: Undecidability is not a computational quirk but a structural invariant of formal systems, extending into quantum many-body physics — the halting problem's diagonalization argument mirrors a fundamental incompleteness in any axiomatic description of physical reality. | MATH: Gödel's incompleteness (∃G: ¬⊢G ∧ ¬⊢¬G); Halting problem (∄H: ∀(P,I), H(P,I) terminates ⟺ P(I) halts); Rice's theorem (any non-trivial semantic property of programs is undecidable); Quantum reduction: spectral gap problem shown undecidable for translation-invariant 1D Hamiltonians (Cubitt, Perez-Garcia, Wolf, 2015) — implies no finite algorithm can decide if a physical system has a gap, even with full Hamiltonian specification. | CONNECTION: The diagonalization argument (Cantor's 2^ℵ₀ > ℵ₀) is a combinatorial shadow of the golden ratio's self-similarity — both encode non-well-founded recursion. The undecidability of the spectral gap for translation-invariant systems ties to lattice structures: the proof con Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -