BELL ASSUMPTION MAP

Bell did not abolish reality. He made the price list explicit.

Bell is routinely wielded like a priestly prohibition: “realism is dead, stop asking.” The theorem deserves better than that abuse. It kills a precise conjunction of assumptions, not the idea that reality exists.

Singlet correlation curve with Hall measurement-dependent model checks — Hall’s adapter reproduces the singlet curve while paying an explicit measurement-dependence cost. Mathematics: green. Physical origin: still red.

For two separated measurement stations with settings x,y, outcomes a,b, and a putative underlying state λ, Bell-local models take the factorized form:

P(a,b | x,y) = ∫ dλ ρ(λ) P(a | x,λ) P(b | y,λ)

with measurement independence: ρ(λ | x,y) = ρ(λ).

Observed Bell-inequality violations exclude the conjunction represented by this architecture. Loophole-free experiments have made detector inefficiency and ordinary subluminal communication between the stations increasingly implausible rescue routes. That is a major empirical fact.

But a theorem forbids a conjunction of assumptions. It does not select one metaphysics from all imaginable ones.

Route A: abandon local causality.

de Broglie–Bohm theory does exactly this: it retains an objective ontology and deterministic dynamics but is explicitly nonlocal. Bell himself discussed this route. A classical-reconstruction program could likewise entertain global fields or nonlocal beables, but it must then explain compatibility with observed no-signalling and relativity rather than pretending locality was preserved.

Route B: relax measurement independence.

Bell derivations normally assume the hidden state is statistically independent of the later measurement settings. Michael Hall constructed an explicit local deterministic, no-signalling model reproducing singlet correlations by relaxing this assumption. We now execute Hall’s published response functions and setting-dependent hidden-state density directly: the adapter reproduces the singlet joint probabilities and 1/2 marginals to floating-point precision. Hall’s 2016 erratum corrects the singlet measurement-dependence value to M ≈ 0.276434; the public receipt recovers 0.276433706. None of that supplies the missing microscopic mechanism for why λ and the settings have that correlation. Hossenfelder and Palmer have argued that superdeterministic model building deserves direct physical scrutiny rather than dismissal by vocabulary. Cosmic Bell tests push ordinary common-cause correlations deeper into the past; they do not logically prove exact statistical independence.

Donadi–Hossenfelder: an important non-equivalence

The 2022 Donadi–Hossenfelder toy collapse model is useful because it makes future-input dependence concrete: detector-basis information enters an effective deterministic collapse dynamics and Born statistics emerge after averaging hidden variables. But our executable audit refuses to call that Hall’s mechanism. A generated-equivalent sampler reproduces the singlet CHSH value and 1/2 marginals, yet the deterministic joint outcome map depends on both settings. With the primitive hidden variable alone the source density is setting-independent; repackaging the setting-dependent effective dynamics into a larger λ merely moves the dependence into λ without deriving Hall’s unique conditional density or its measurement-dependence cost.

More importantly for this project, the published toy model uses Hilbert-space amplitudes, Lindblad-form dynamics and the detector eigenbasis as input. It therefore does not satisfy our classical ontology contract. Its status is REPRESENTATION_NOT_HALL_MECHANISM, not a classical Bell reconstruction.

Open the executable Donadi/Hall comparison receipt.

Relaxing the same Bell premise does not make two models physically equivalent.

Route C: retrocausal or all-at-once boundary conditions.

Retrocausal models also relax the ordinary measurement-independence structure, but do so by allowing future measurement settings to participate in the boundary conditions of the earlier hidden state. This preserves a form of spacetime locality at the cost of ordinary forward-only causal structure. Whether that is a bargain or a disaster is a physical question, not a semantic one.

Route D: reject the hidden-variable factorization itself.

One may deny that λ can be separated from the measurement context in the way Bell factorization assumes. But contextuality by itself is not enough: a contextual model that still satisfies Bell local causality and measurement independence remains constrained by Bell inequalities. The model must state exactly which conditional independence fails and why.

What Bell therefore means here

Local + measurement-independent hidden variablesExperimentally excluded for the tested Bell scenarios.

Nonlocal realist dynamicsNot excluded by Bell; must pay the relativity/no-signalling bill.

Measurement-dependent local dynamicsNot logically excluded by Bell; must physically explain setting-state correlations without ad hoc tuning.

Retrocausal/global boundary dynamicsNot excluded by Bell; must produce a coherent causal account and new tests.

The reconstruction demand

Do not say “Bell proves classical physics impossible.” Say what the data actually demand: any successful objective reconstruction must leave the Bell-local, measurement-independent factorization class. Then make the candidate theory expose exactly how it leaves.

Brunner et al. (2014), Bell nonlocality
Hensen et al. (2015), loophole-free Bell test
Hall (2010), local deterministic singlet model with relaxed measurement independence
Hall (2016), erratum correcting M_singlet
Executable Hall adapter receipt
Hall & Branciard (2020), measurement-dependence cost
Hossenfelder & Palmer (2020), Rethinking Superdeterminism
Handsteiner et al. (2017), Cosmic Bell test

Bell is not the end of reconstruction. Bell is where reconstruction stops being cheap.