| _version_ | 1866902016690749440 |
|---|---|
| author | Fathi, Kevin |
| author_facet | Fathi, Kevin |
| contents | <p>We propose that quantum measurement is structurally equivalent to a Bateson Function operating over a probabilistic grammar. Extending the theory of symbolic entropy and derivational complexity to non-ideal systems, we define stochastic rewrite systems where grammars are non-confluent. We formally integrate the concepts of Ambiguity Entropy ($\tilde{H}_{G}$) and Soft Degeneracy ($\overline{\Delta}_{G}$) to model the probabilistic nature of quantum collapse. In this model, quantum systems evolve deterministically under unitary rules but collapse irreversibly under probabilistic selection (the Born rule) at measurement, which we identify as a probabilistic canonicalization. The resulting framework reinterprets quantum indeterminacy as derivational ambiguity. We rigorously prove that measurement satisfies the criteria of an Ambiguity-Based (compressing) Bateson function, demonstrating information loss via frame (basis) suppression using a formal information-theoretic argument. We establish that the Quantum Semantic Inference Problem (QSIP) is QMA-complete, anchoring irreversibility in computational complexity. Furthermore, we ground the framework in decoherence theory, showing that Soft Degeneracy quantifies the redundancy in Quantum Darwinism, and provide a concrete realization using Tensor Networks.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_16787132 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Quantum Measurement as a Bateson Function: Probabilistic Grammar and Irreversibility Fathi, Kevin Quantum Measurement One-Way Functions Symbolic Entropy Probabilistic Grammars Bateson Function Collapse Rule Quantum Irreversibility Decoherence Kolmogorov Complexity Computational Physics Information Loss Canonical Normal Form Semantic Ambiguity Quantum Computation Symbolic Logic <p>We propose that quantum measurement is structurally equivalent to a Bateson Function operating over a probabilistic grammar. Extending the theory of symbolic entropy and derivational complexity to non-ideal systems, we define stochastic rewrite systems where grammars are non-confluent. We formally integrate the concepts of Ambiguity Entropy ($\tilde{H}_{G}$) and Soft Degeneracy ($\overline{\Delta}_{G}$) to model the probabilistic nature of quantum collapse. In this model, quantum systems evolve deterministically under unitary rules but collapse irreversibly under probabilistic selection (the Born rule) at measurement, which we identify as a probabilistic canonicalization. The resulting framework reinterprets quantum indeterminacy as derivational ambiguity. We rigorously prove that measurement satisfies the criteria of an Ambiguity-Based (compressing) Bateson function, demonstrating information loss via frame (basis) suppression using a formal information-theoretic argument. We establish that the Quantum Semantic Inference Problem (QSIP) is QMA-complete, anchoring irreversibility in computational complexity. Furthermore, we ground the framework in decoherence theory, showing that Soft Degeneracy quantifies the redundancy in Quantum Darwinism, and provide a concrete realization using Tensor Networks.</p> |
| title | Quantum Measurement as a Bateson Function: Probabilistic Grammar and Irreversibility |
| topic | Quantum Measurement One-Way Functions Symbolic Entropy Probabilistic Grammars Bateson Function Collapse Rule Quantum Irreversibility Decoherence Kolmogorov Complexity Computational Physics Information Loss Canonical Normal Form Semantic Ambiguity Quantum Computation Symbolic Logic |
| url | https://doi.org/10.5281/zenodo.16787132 |