From Physical Information to Meaning: A Relational Tensor Formalization of Quantum Correlation and Local Record Establishment

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Original abstract

Abstract Einstein, Podolsky and Rosen argued in 1935 that quantum mechanics must be incomplete: if measuring one member of a correlated pair lets you predict the result of measuring the other, the second particle must already possess that property. Bohr’s reply, published the same year, rejected the premise — a physical property, he argued, is not well defined independently of the experimental arrangement used to determine it. That reply has stood for ninety years primarily as a philosophical stance rather than a mathematical one. This paper makes Bohr’s relational reply mathematically precise, and then extends it into a separate, falsifiable physical hypothesis. The entangled pair is represented not by two separate local properties but by a single non-separable relational object — the correlation tensor of the joint state — and we show explicitly, via the vanishing local Bloch vectors of the singlet state, that no information whatsoever exists at either particle in isolation. “Meaning,” in the sense of a definite, locally accessible outcome, is then generated only through the local interaction between this joint resource and a physical interpreter; we prove that this construction reproduces the maximal quantum (Tsirelson-bound) violation of the CHSH inequality while remaining fully consistent with the no-communication theorem, and we prove a general lemma showing that no purely local extension of a hidden-variable model — regardless of how many additional local arguments, including an explicit interpreter variable, are added to it — can do the same. We further show that a natural strengthening of the interpreter concept — treating interpretation as a discrete, threshold-gated event rather than a continuous quantity — reproduces the classical detection (fair-sampling) loophole first identified by Pearle unless interpreter efficiency exceeds the Clauser–Horne bound, and we state that condition explicitly as part of the hypothesis rather than leaving it implicit. This is the weak hypothesis: an interpretive, quantitatively grounded formalization of relational quantum mechanics, introducing no new physics. The paper then asks a separate, genuinely new question: once a local record of an interaction is established, does its persistence, accessibility, and redundancy have any further physical consequence beyond ordinary decoherence? We propose a specific, minimal dynamical ansatz — a local dephasing term proportional to a measurable record-establishment index — construct explicit toy Hamiltonians proving both that a naive downstream test of this idea is logically invalid (by the no-communication theorem) and that a concurrent-protocol replacement is logically coherent, and derive a quantitative experimental target for a superconducting-qubit implementation. The strong hypothesis is further organized into three nested claims — that the record-state vector has residual dynamical relevance at all, that this dependence factors through the scalar record-establishment index, and that the residual is linear in that index —with paired equal-index, different-vector experimental conditions testing the scalar compression independently of the linear coupling term. This strong hypothesis is falsifiable and, unlike the weak hypothesis, is not already implied by orthodox quantum mechanics. AI assistance. This manuscript was developed through extensive collaborative dialogue with multiple AI systems — Claude (Anthropic), ChatGPT (OpenAI), and Gemini (Google DeepMind) — each used in a substantive capacity: deriving and stress-testing the mathematical arguments of Sections 2–4 and 8–9 — including the CHSH local-extensibility lemma of Section 2.3, the correlation-tensor formalization of Section 3, the no-signaling proof of Appendix A, and the toy-Hamiltonian existence proofs of Section 9 — identifying and correcting several formulations that arose during development and were later shown to be untenable (including local hidden-variable constructions excluded by Bell’s theorem, and a threshold- based interpreter model shown to reproduce the classical detection loophole of Pearle and Clauser–Horne), and manuscript drafting throughout. Citation verification — confirming that cited sources exist and are represented accurately — and the mathematical derivations themselves were performed primarily by these AI systems, including AI-executed literature searches; the author directed the inquiry, exercised judgment over which lines of reasoning to pursue and what to include, and takes responsibility for the final content, but did not independently re-derive the mathematics or re-verify the primary sources. This manuscript has not undergone external peer review. Full context: https://www.linkedin.com/pulse/im-physicist-heres-what-happened-when-i-tried-turn-ai-ruiz-izaguirre-6012c/

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