On Friday, November 22, 2024 at 7:19:10 AM UTC-7 PGC wrote:
These discussions around Bell's theorem, the Many-Worlds Interpretation (MWI), and the challenges of deriving the Born rule continue invoking the interplay between epistemic frameworks and ontological commitments. A significant point of contention is whether MWI can account for the correlations observed in entangled systems without additional postulates, such as collapse, and how these correlations map onto the observer accounts and global description perspectives. There are interpretational gaps that persist. John’s description of branching in the Many-Worlds Interpretation (MWI) assumes that decoherence ensures each branch corresponds to a distinct outcome of a quantum measurement. This can be expressed using the density matrix ρ in a composite system-environment state: ρ=∣ψ⟩⟨ψ∣,where ∣ψ⟩=i∑ci∣si⟩∣ei⟩. Decoherence suppresses off-diagonal terms in ρ, effectively yielding a mixed state: ρ′=i∑∣ci∣2∣si⟩⟨si∣. Consider the correlations in entangled systems that violate Bell's inequality. These correlations are quantitatively expressed as deviations from the CHSH inequality: S=∣E(a,b)+E(a′,b)+E(a,b′)−E(a′,b′)∣≤2, where E(a,b) represents the expectation value of measurements along directions a and b. Experimental results consistently show that S>2, as predicted by quantum mechanics but inconsistent with local hidden variable theories (Bell, 1964, p.195). In MWI, these results follow from the unitary evolution of the wavefunction. The wavefunction for an entangled pair, ∣ψ⟩=21(∣↑⟩A∣↓⟩B−∣↓⟩A∣↑⟩B), evolves unitarily under the Schrödinger equation. Decoherence ensures that interference terms vanish in the density matrix describing macroscopic observers, giving the appearance of distinct "branches." However, Bruce keeps raising the critical challenge: how do these branches remain correlated across spacelike separations? In MWI, the correlations are not post-measurement artifacts but inherent to the global wavefunction. The key is the consistency enforced by the universal wf's structure, which ensures that for any measurement basis, the resulting "branches" respect the original entanglement. The reduced density matrix formalism explicitly demonstrates this: ρA=TrB(∣ψ⟩⟨ψ∣), yielding probabilities consistent with the Born rule. Yet, the Born rule itself remains elusive within MWI's framework and demands further clarification, as acknowledged by Carroll (2014, p.18). Critics like Brent and Bruce argue that without an explicit derivation of the Born rule, MWI fails to fully account for observed probabilities. This is valid but reflects a broader epistemological gap. Probabilities, as noted, have different interpretations: frequentist, Bayesian, and, uniquely in computational contexts, "objective" probabilities derived from "subjective probabilities" (Everett used "subjective probabilities" iirc, and Bruno's refinement was terming them "objective" in this sense). In this framework, probabilities emerge not as axioms but as limits of frequency operators over the ensemble of computations or histories: Something akin to: n→∞limn1i=1∑nPi≈PBorn, where PBorn=∣⟨ψ∣ϕ⟩∣2. This connects subjective perspectives (what the observer experiences) to 3p descriptions (what the formalism predicts), which is insufficiently addressed/incomplete in MWI or collapse approaches and open with Bruno's approach iirc (correct me, if otherwise). The merit of this kind of approach is that observer experience is no longer outside the scope of the clearest ontology. Now, consider the Gödelian critique. All frameworks—whether MWI, collapse postulates, or alternatives like Invariant Set Theory (Palmer, 2009)—assume arithmetical or stronger foundations. Gödel's incompleteness theorems (Gödel, 1931) demonstrate that within any sufficiently rich formal system F, there exist true statements T that are unprovable within F. Explicitly: ∃T(T∈True∧T∈/Provable in F). Applied to quantum mechanics and ontology, this indicates that any framework aiming for ontological finality will inevitably encounter unprovable truths if it includes arithmetic or its use in its formulations. For example, the observer's role versus the formalism's predictions remains a gap that cannot be fully bridged within any single system. Collapse postulates introduce "magic" by assuming the wavefunction's reality only to dismiss it post-measurement, while MWI faces the unresolved challenge of deriving probabilities without external axioms. The whack-a-mole nature of these discussions therefore may find an explanation in this incompleteness. Every attempt to resolve one gap (e.g., deriving Born within MWI) introduces others (e.g., defining the observer). As Saibal notes, local hidden variables fail due to Bell's theorem, but Bruce counters that this implies non-locality within standard QM. Both points reflect the limits of purely formal reasoning without acknowledging the epistemic/ontological split. In conclusion, these discussions risk circularity if participants prioritize defending their preferred interpretations over collaborative inquiry. Recognizing the limitations imposed by Gödelian constraints and the potential irreducibility of observer perspectives relative to global descriptions is essential. While frameworks like MWI or collapse postulates have epistemic value, they are better seen as tools for exploring the boundaries of what can be explained or inspiration for developing new problems and possible application, rather than as definitive ontological inquiry. The quest for consensus may remain elusive, but acknowledging these limits instead of giving in to the whack-a-mole discourse may mitigate circularity risk. Work has to be done from all sides. Have a great weekend, whether collapse or in some world, or while riding computations. *Let's go beyond the sophisticated rhetoric. Remember; I'm just a simple country lawyer. Admit it. At the end of the day, what do you have, or aspire to have? Even if you resolve Born's Rule for the MWI, what do you have, or aspire to have? Answer; nothing! Your presumed branches are non-interacting, so there's no way to confirm the MWI. It's all speculation, or to be more precise, philosophy, and there's no way to go beyond this. It all a disservice to real science. Physics has taken a turn to the foolish. AG* -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/1defc081-a0a8-4856-9cc4-4254c2827b56n%40googlegroups.com.
