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Bell’s inequalities prove quantum correlations are real and non-local — two particles, measured far apart, show correlations that no local hidden variable theory can explain. Yet no faster-than-light signal is possible. This mystery has puzzled physicists for sixty years. A machine-checked theorem gives the formal resolution: EPR correlations arise from semantic gluing — global semantic structure not determined locally. And the barrier to FTL signaling is the same diagonal barrier that underlies Gödel’s theorem. Correlation is real. Signaling is proved impossible. Both follow from the same structure.
The EPR Puzzle
Einstein, Podolsky, and Rosen identified the puzzle in 1935. Two particles that have interacted can be in an entangled quantum state — their properties are correlated in a way that seems to transcend any local description. When you measure one particle, the other particle’s state is instantaneously determined, regardless of how far away it is. Einstein called this “spooky action at a distance” and argued it must indicate an incomplete description — there must be hidden variables that predetermined the outcomes.
John Bell showed in 1964 that no local hidden variable theory can reproduce the quantum correlations. Experiment has confirmed this repeatedly. The correlations are real and they are non-local in a precise mathematical sense. And yet no faster-than-light signal has ever been transmitted using entanglement. The non-locality is real; the non-signaling is also real. Both.
The NEMS program gives a formal resolution of both halves.
Semantic Gluing Explains the Correlations (Paper 45)
Paper 45 introduces a factorization axiom at the semantic level: the global satisfaction of an observational proposition is the conjunction of local predicates applied to fragments. Global semantic truth is glued together from local semantic truths — not causally, but algebraically through the constraint structure of the semantic ledger.
The key result: world-type is determined by the global map from fragments to local views. Even if each local fragment satisfies the same local predicate, the global world-type depends on how those local views fit together into a global semantic structure. The correlations between distant measurements are not caused by some local mechanism — they arise from the global semantic glue that holds the world-type together.
This is not a physical explanation of entanglement in terms of some new force or mechanism. It is a structural explanation: the correlations arise from the algebraic structure of semantic gluing, exactly as the formal factorization axiom requires. The “nonlocality” is semantic, not causal.
Why FTL Signaling Is Impossible (Papers 46–47)
Paper 46 proves: under PSC, stable records, and diagonal capability, no total-effective local procedure can determine world-type from local views alone. Local semantic determinacy is impossible in the effective sense. This rules out the possibility of using local measurements to extract global semantic facts in a total-effective way.
Paper 47 applies this to signaling: no internal total-effective procedure can serve as a “spooky-to-signal compiler” — a device that converts EPR correlations into controllable FTL information transfer. Such a compiler would be a total-effective decider for a nontrivial extensional predicate of the globally glued semantics. The diagonal barrier (reducing to halting undecidability) rules this out.
The formal result is: EPR correlations are real and structurally necessary (semantic gluing). FTL signaling is structurally impossible (diagonal barrier). Both follow from the same formal structure. The apparent tension between “real nonlocality” and “no FTL signaling” is resolved — they are both necessary features of a PSC universe with semantic gluing and diagonal capability.
Lean anchor: NoSpookyToSignal.no_signaling_compiler.
The Papers and Proofs
- Paper 45 — Semantic Nonlocality Engine
- Paper 46 — Causal Nonlocality from Closure
- Paper 47 — No Spooky-to-Signal Compiler
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