Methods of selecting samples from larger populations may produce bias, in either direction: inducing correlations between variables independent in the full population, or masking correlations between variables dependent in the full population. Here we propose a surprising application of these familiar ideas. We argue that they are relevant to puzzling correlations uncovered in quantum theory by John Stewart Bell (Bell 1964). In the light of Bell's work and subsequent experiments it is widely believed that the quantum world is 'nonlocal', in apparent tension with relativity. Many hold that the only alternative is to abandon 'realism', the view that there is an objective world independent of measurement. We propose instead that Bell's correlations are selection artefacts, in tension neither with relativity nor realism. In standard two-particle Bell experiments the relevant selection is a preselection, achieved by the preparation of the initial state. Again, selection bias via preselection is familiar elsewhere in science, but it doesn't seem to have been noticed that it is applicable in this case.
Comments
28 pages, 14 figures; this version revises and clarifies the argument in several places, incorporating material that was previously an appendix. arXiv admin note: original version had substantial text overlap with arXiv:2602.16985
Methods of selecting samples from larger populations may produce bias, in either direction: inducing correlations between variables independent in the full population, or masking correlations between variables dependent in the full population. Here we propose a surprising application of these familiar ideas. We argue that they are relevant to puzzling correlations uncovered in quantum theory by John Stewart Bell (Bell 1964). In the light of Bell's work and subsequent experiments it is widely believed that the quantum world is 'nonlocal', in apparent tension with relativity. Many hold that the only alternative is to abandon 'realism', the view that there is an objective world independent of measurement. We propose instead that Bell's correlations are selection artefacts, in tension neither with relativity nor realism. In standard two-particle Bell experiments the relevant selection is a preselection, achieved by the preparation of the initial state. Again, selection bias via preselection is familiar elsewhere in science, but it doesn't seem to have been noticed that it is applicable in this case.
In statistics and causal modeling it is common for a selection process to induce correlations in a subset of an uncorrelated ensemble. We propose that EPR and Bell correlations are selection artefacts of this kind. The selection process is preparation of the initial state of the relevant experiments. Choice of initial state amounts to preselection of a subensemble of a larger, uncorrelated, virtual ensemble of possible histories. Because it is preselection rather than postselection, the resulting correlations support the intuitive counterfactuals of the EPR argument and Bell nonlocality. In this respect, and in its temporal orientation, the case differs from familiar forms of selection bias. Given the ubiquity of quantum entanglement, the result may thus be of independent interest to students of causal modeling. The paper concludes with a discussion of its novel implications in that field.
We show that Bell correlations may arise as a special sort of selection artefact, produced by ordinary control of the initial state of the experiments concerned. This accounts for nonlocality, without recourse to any direct spacelike causality or influence. The argument improves an earlier proposal in (arXiv:2101.05370v4 [quant-ph], arXiv:2212.06986 [quant-ph]) in two main respects: (i) in demonstrating its application in a real Bell experiment; and (ii) in avoiding the need for a postulate of retrocausality. This version includes an Appendix, discussing the relation of the proposal to the conclusions of Wood and Spekkens (arXiv:1208.4119 [quant-ph]).
In his late piece 'La nouvelle cuisine' (Bell 1990), John Bell describes the steps from an intuitive, informal principle of locality to a mathematical rule called Factorizability. This rule stipulates that when possible past causes are held fixed, the joint probabilities of outcomes of spacelike separated measurements, conditional on measurement settings, be the product of the local conditional probabilities individually. Bell shows that Factorizability conflicts with predictions of QM, predictions since confirmed in many experiments. However, Bell warns his readers that the steps leading to Factorizability should 'be viewed with the utmost suspicion'. He says that 'it is precisely in cleaning up intuitive ideas for mathematics that one is likely to throw the baby out with the bathwater' (1990, 239). Bell's suspicions were well-founded, for he himself misses an important baby. Here we retrieve and identify it: it is selection bias. We explain how failure of Factorizability may be regarded as a selection artefact, requiring no violation of locality in the intuitive, conceptual sense with which Bell begins his analysis. The argument begins with a central principle of causal discovery, Reichenbach's Principle of Common Cause (PCC). It is well known that correlations due to selection bias are not subject to PCC. Several writers have proposed that EPR-Bell correlations are also an exception to PCC, but it has not been noticed that they fall under this well-known exclusion. The point is relevant not only to the status of Bell nonlocality, but also for statistics and causal modeling. For these fields, the news is that selection effects play a ubiquitous role in quantum phenomena, in a form akin to collider bias.
Explaining observations in terms of cause-and-effect (causal) relations is central to empirical science. However, in his seminal 1964 work [1], John Bell showed that the correlations between entangled quantum systems cannot be explained in terms of, possibly hidden, cause and effect relations. After four decades of experimental effort, Bell's prediction has recently been confirmed in an unambiguous way by a series of loophole-free Bell-test experiments [2-4]. These experiments, however, cannot reveal where exactly quantum mechanics breaks with our classical notion of cause and effect. Specifically, Bell's theorem is based on the central assumptions of realism and local causality. Realism posits that physical systems have real, objective properties, independent of whether we observe them or not, and local causality assumes that causal influences cannot propagate faster than the speed of light.
Spooky Action at a Distance In the context of correlation experiments involving pairs of experiments performed at very nearly the same time in very far-apart experimental regions, Einstein famously said [1], But on one supposition we should in my opinion hold absolutely fast: “The real factual situation of the system S2 is independent of what is done with system S1 which is spatially separated from the former.” This demand is incompatible with the basic ideas of standard (Copenhagen/orthodox) quantum mechanics, which makes two relevant claims: (1) Experimenters in the two labs make “local free choices” that determine which experiments will be performed in their respective labs. These choices are free in the sense of not being predetermined by the prior history of the physically described aspects of the universe, and they are localized in the sense that the physical effects of these free choices are inserted into the physically described aspects of the universe only within the laboratory in which the associated experiment is being performed. (2) These choices of what is done with the system being measured in one lab can (because of a measurement-induced global collapse of the quantum state) influence the outcome of the experiment performed at very close to the same time in the very faraway lab. This influence of what is done with the system being measured in one region upon the outcome appearing at very nearly the same time in a very faraway lab was called “spooky action at a distance” by Einstein, and was rejected by him as a possible feature of “reality.” John Bell's Quasi-classical Statistical Theory Responding to the seeming existence in the quantum world of “spooky actions,” John Bell [2] proposed a possible alternative to the standard approach that might conceivably be able to reconcile quantum spookiness with “reality.” This alternative approach rests on the fact that quantum mechanics is a statistical theory.We already have in physics a statistical theory called “classical statistical mechanics.”
One of the most notable aspects of quantum systems is that their components can exhibit correlations much stronger than those allowed by classical physics. Two examples of quantum correlations are quantum entanglement and Bell nonlocality, but generally there is a hierarchy of many types of quantum correlations. Among these correlations, Bell nonlocality holds a special place because it plays a dual role in distinguishing theories where local realism is a valid description. A Bell test, which is a test of local realism, typically needs to be augmented with assumptions to address possible loopholes in the experimental setup. In this work, we study Bell tests in experiments in which the detector reports the correct outcome with a specified probability. This mirrors the situation at high-energy colliders, where particle spins are not measured directly but inferred from the angular distributions of their decay products. We show that, in this setup, a test of local realism is not possible. Quantum correlations, however, are still present, measurable, and informative in high-energy colliders. These correlations are the building blocks of the interesting, developing quantum information science program at high-energy colliders. The measurements of entanglement by the ATLAS and CMS experiments are the first steps in this initiative.