We analyze measurement-setting sequences from the 2015 loophole-free Bell tests: Hensen et al. (Delft, two runs, 8,664 trials) and Shalm et al. (NIST, main blind and classical-RNG XOR, 535 million settings). We search for signatures predicted by the minimum-MI class of superdeterministic models. Under a Markov persistence model, the bound I(X_i;X_{i+1})<3×10^{-11} bits constrains λ persistence to q<2×10^{-4}, excluding any persistent-λ model at >1000σ. The NIST blind dataset provides the most stringent limits: |P(X_i=X_{i-1})−0.5|<4×10^{-5} at 95% CL and consecutive-setting MI below 3×10^{-11} bits. Cross-source comparison of quantum and classical RNGs reveals no structure. Delft 2 pre-upgrade data shows mild non-uniformity (χ²=10.84, p=0.013) traceable to a known phase-diffusion artifact; all other Delft 2 tests are null. These results constrain any superdeterministic model with memory across the full complexity hierarchy.
We analyze measurement-setting sequences from the 2015 loophole-free Bell tests: Hensen et al. (Delft, two runs, 8,664 trials) and Shalm et al. (NIST, main blind and classical-RNG XOR, 535 million settings). We search for signatures predicted by the minimum-MI class of superdeterministic models. Under a Markov persistence model, the bound I(X_i;X_{i+1})<3×10^{-11} bits constrains λ persistence to q<2×10^{-4}, excluding any persistent-λ model at >1000σ. The NIST blind dataset provides the most stringent limits: |P(X_i=X_{i-1})−0.5|<4×10^{-5} at 95% CL and consecutive-setting MI below 3×10^{-11} bits. Cross-source comparison of quantum and classical RNGs reveals no structure. Delft 2 pre-upgrade data shows mild non-uniformity (χ²=10.84, p=0.013) traceable to a known phase-diffusion artifact; all other Delft 2 tests are null. These results constrain any superdeterministic model with memory across the full complexity hierarchy.
We present an eliminative analysis of no-signaling equalities in the NIST loophole-free Bell test (Shalm et al., 2015).Standard analyses examine outcome correlations to compute CHSH S values. We instead examine whether one party'sdetection rate depends on the other party's setting choice. Under quantum mechanics, these marginal probabilities must beindependent of the remote setting. Using a six-gate streaming pipeline on 356 million event-level trials, we apply theexperiment's own timing calibration (phase filter: pk=90, radius=4) to select genuine entangled photon detections inPockels cell slots 5-7. In the phase-filtered data, Alice's marginal detection rate for setting a=2 shows a stationary deviation:z = 2.41, permutation p = 0.017, 95% bootstrap CI [1.44e-6, 1.31e-5] excluding zero. The combined chi-squared is 9.40 (4df), one tick below the p < 0.05 threshold of 9.49. The deviation is temporally stationary across 100 time windows spanningthe full experimental run, with near-zero autocorrelation and near-zero linear trend. Without phase filtering, all trialsproduce a null result (p = 0.40), consistent with noise dilution from background detector clicks. A second NIST run using adifferent random number generator (ClassicalRNG XOR) lacks detection-level data and cannot be phase-filtered,precluding direct replication with matching detection definitions.
We demonstrate extraction of randomness from spontaneous-emission events less than 36 ns in the past, giving output bits with excess predictability below 10^{-5} and strong metrological randomness assurances. This randomness generation strategy satisfies the stringent requirements for unpredictable basis choices in current "loophole-free Bell tests" of local realism [Hensen et al., Nature (London) 526, 682 (2015); Giustina et al., this issue, Phys. Rev. Lett. 115, 250401 (2015); Shalm et al., preceding Letter, Phys. Rev. Lett. 115, 250402 (2015)].
Relying on some auxiliary assumptions, usually considered mild, Bell’s theorem proves that no local theory can reproduce all the predictions of quantum mechanics. In this work, we introduce a fully local, superdeterministic model that by explicitly violating ‘settings independence’—one of these auxiliary assumptions, requiring statistical independence between measurement settings and systems to be measured—is able to reproduce all the predictions of quantum mechanics. Moreover, we show that contrary to widespread expectations, our model can break settings independence without an initial state that is too complex to handle, without visibly losing all explanatory power, and without outright nullifying all of experimental science. Still, we argue that our model is unnecessarily complicated and does not offer true advantages over its non-local competitors. We conclude that while our model does not appear to be a viable contender to its non-local counterparts, it provides the ideal framework to advance the debate over violations of statistical independence via the superdeterministic route.
The reported violations of Bell inequalities are routinely read as an experimental refutation of local realism. This preprint asks how firmly the record supports that reading. We catalogue the classical routes by which a strictly local apparatus can report |S| > 2 - from outcome-dependent loss and coincidence-window selection (demonstrated in hardware) to synchronisation, electronics-level click shifts and analysis-parameter selection - and show that below the Eberhard efficiency the exact quantum correlation curve certifies nothing, being reproduced exactly by a known local detection model. We then define the first family-level synchronisation audit (plateau membership, bias index, sub-bound fraction), validate it on synthetic data with known ground truth, and execute it under preregistered protocols on three public archives. The raw Innsbruck record passes: across the full longdist series, every standard-configuration violation is a property of the raw data, not of the calibration. On the Delft event-ready data, a 50,000-member heralding-acceptance family answers the standing postselection critique: the violation is generic, not an acceptance choice. On the NIST 2015 record, an outsider reconstruction of the certified pipeline recovers the Bell geometry and gate optima but stalls at undisclosed cleaning parameters - a documented limit of third-party reproducibility. The programme distils into seven cleanliness criteria (C1–C7) for any dataset and eight provenance requirements (M1–M8) for future experiments. All figures and numbers are reproducible from the supplementary scripts (deterministic, fixed seeds, minutes on a laptop); raw data are fetched from the official public archives.
Superdeterminism—where the Measurement Independence assumption in Bell’s Theorem is violated—is frequently assumed to imply implausibly conspiratorial correlations between properties λ of particles being measured and measurement settings x and y. But it does not have to be so: a superdeterministic but non-conspiratorial locally causal model is developed where each pair of entangled particles has unique λ. The model is based on a specific but arbitrarily fine discretisation of complex Hilbert space, where λ defines the information, over and above the freely chosen nominal settings x and y, which fixes the exact measurement settings X and Y of a run of a Bell experiment. Pearlean interventions, needed to assess whether x and y are Bell-type free variables, are shown to be inconsistent with rational-number constraints on the discretised Hilbert states. These constraints limit the post-hoc freedom to vary x keeping λ and y fixed but disappear with any coarse-graining of λ, X, and Y, rendering so-called drug-trial conspiracies irrelevant. Points in the discretised space can be realised as ensembles of symbolically labelled deterministic trajectories on an ‘all-at-once’ fractal attractor. It is shown how quantum mechanics might be ‘gloriously explained and derived’ as the singular continuum limit of the discretisation of Hilbert space. It is argued that the real message behind Bell’s Theorem has less to do with locality, realism, or freedom to choose, and more to do with the need to develop more explicitly holistic theories when attempting to synthesise quantum and gravitational physics.
Our article described an experiment that adjudicates between different causal accounts of Bell inequality violations by a comparison of their predictive power, finding that certain types of models that are structurally radical but parametrically conservative---of which a class of superdeterministic models are an example---overfit the data relative to models that are structurally conservative but parametrically radical in the sense of endorsing an intrinsically quantum generalization of the framework of causal modeling. In their comment [Phys. Rev. A 109, 026201 (2024)], Hance and Hossenfelder argue that we have misrepresented the purpose of superdeterministic models. We here dispute this claim by recalling the different classes of superdeterministic models we defined in our article and our conclusions regarding which of these are disfavored by our experimental results. Their confusion on this point seems to have arisen in part from the fact that we characterized superdeterministic models within a causal modeling framework and from the fact that we referred to this framework as ``classical'' in order to contrast it with an intrinsically quantum alternative. In this Reply, therefore, we take the opportunity to clarify these points. They also claim that if one is adjudicating between a pair of models, where one model can account for strictly more operational statistics than the other, the first model will tend to overfit the data relative to the second. Because this model inclusion relation can arise for pairs of models in a reductionist hierarchy, they conclude that overfitting should not be taken as evidence against the first model. We point out here that, contrary to this claim, one does not expect overfitting to arise generically in cases of model inclusion, so that it is indeed sometimes appropriate to consider overfitting as a criterion for adjudicating between such models.