Published February 8, 2026
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The Heisenberg Uncertainty Principle as a Physical Projection of Gödel's Incompleteness Theorem
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We establish a structural isomorphism between Gödel's incompleteness theorem and the Heisenberg uncertainty principle within a hierarchical ontology of nested computational realities {Rn}. Each level consists of a formal language, observers with finite capacity, and an Oracle with access to the probabilistic code. Main results include:
1. Non-commuting observables correspond to syntactically incompatible propositions.
2. The uncertainty relation quantifies the Gödelian barrier.
3. The Planck constant is the minimal action quantum required to cross level boundaries.
4. Measurement randomness emerges from deterministic projection. Conclusion: Quantum mechanics is an operational theory of observation at the Gödelian boundary.
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- Is cited by
- Preprint: 10.5281/zenodo.17794107 (DOI)
- Is supplemented by
- Preprint: https://orcid.org/0009-0009-6438-8730 (URL)
References
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