Arguments have been made that violation of the CHSH and similar inequalities shows that reality at the quantum level must be non-local. The derivation of Bell inequality is re-examined and it is shown that violations of these inequalities merely demonstrates the existence of contextuality - they say nothing about the causal influences underlying such contextuality. It is argued that contextual systems do not possess enduring (propositional) properties, merely contingent properties. An example is presented of a classical situation, a two player co-operative game, whose random variables are consistently connected in the sense of Dzhafarov, and which is contextual, violating the CHSH inequality. In fact it also violates the Tsierl'son bound. The key is that this system is generated and its properties are disposed, not determined.
Arguments have been made that violation of the CHSH and similar inequalities shows that reality at the quantum level must be non-local. The derivation of Bell inequality is re-examined and it is shown that violations of these inequalities merely demonstrates the existence of contextuality - they say nothing about the causal influences underlying such contextuality. It is argued that contextual systems do not possess enduring (propositional) properties, merely contingent properties. An example is presented of a classical situation, a two player co-operative game, whose random variables are consistently connected in the sense of Dzhafarov, and which is contextual, violating the CHSH inequality. In fact it also violates the Tsierl'son bound. The key is that this system is generated and its properties are disposed, not determined.
Arguments have been made that the violation of the CHSH and similar inequalities shows that reality at the quantum level must be non-local. The derivation of Bell inequality is re-examined, and it is shown that violations of these inequalities merely demonstrate the existence of contextuality—they say nothing about the causal influences underlying such contextuality. It is argued that contextual systems do not possess enduring (propositional) properties, merely contingent properties. An example of a classical situation is presented: a two-player co-operative game, the random variables of which are consistently connected in the sense of Dzhafarov, which is contextual, and violates the CHSH inequality. In fact, it also violates the Tsirel’son bound. The key is that this system is generated, and its properties are disposed of, not determined.
The view that non-classical phenomena are witnessed when noncontextuality inequalities are violated by quantum correlations has become widespread over the last decades, and many authors describe contextuality as a counter-intuitive and non-classical feature of quantum systems. In this paper we show that a classical input/output device generating contextual data (i.e., data violating noncontextuality inequalities) can easily be found if the following conditions are satisfied: (1) We only have access to a specific collection of epistemic measurements, namely measurements which do not necessarily reveal properties possessed by the system to the agent, and (2) not all these measurements can be jointly performed. The conclusion we draw from this example is twofold. Firstly, regarding model-independent contextuality, it suggests that, unlike Bell inequalities (whose violation allegedly implies non-locality), noncontextuality inequalities have no phenomenological significance per se: we cannot treat experiments as black-boxes and draw conclusions about the phenomenological status of their underlying structure based only on contextuality analysis of the data they generate. Secondly, regarding quantum theory, it indicates that one who accepts, as many interpretations suggest, that quantum theory satisfies both these conditions should not take for granted that quantum contextuality is a signature of non-classicality.
It is shown that when properly analyzed using principles consistent with the
use of a Hilbert space to describe microscopic properties, quantum mechanics is
a local theory: one system cannot influence another system with which it does
not interact. Claims to the contrary based on quantum violations of Bell
inequalities are shown to be incorrect. A specific example traces a violation
of the CHSH Bell inequality in the case of a spin-3/2 particle to the
noncommutation of certain quantum operators in a situation where (non)locality
is not an issue. A consistent histories analysis of what quantum measurements
measure, in terms of quantum properties, is used to identify the basic problem
with derivations of Bell inequalities: the use of classical concepts (hidden
variables) rather than a probabilistic structure appropriate to the quantum
domain. A difficulty with the original Einstein-Podolsky-Rosen (EPR) argument
for the incompleteness of quantum mechanics is the use of a counterfactual
argument which is not valid if one assumes that Hilbert-space quantum mechanics
is complete; locality is not an issue. The quantum correlations that violate
Bell inequalities can be understood using local quantum common causes.
Wavefunction collapse and Schr\odinger steering are calculational procedures,
not physical processes. A general Principle of Einstein Locality rules out
nonlocal influences between noninteracting quantum systems. Some suggestions
are made for changes in terminology that could clarify discussions of quantum
foundations and be less confusing to students.
Bell-CHSH inequalities are trivial algebraic properties satisfied by each line of Nx4 spreadsheets containing ±1 entries, thus it is surprising that their violation in some experiments allows to speculate about the existence of nonlocal influences in nature and casts doubt on the existence of external physical reality. Such speculations are rooted in incorrect interpretations of quantum mechanics and in a failure of local realistic hidden variable models to reproduce quantum predictions for spin polarisation correlation experiments (SPCE). In these models, one uses a counterfactual joint probability distribution of only pairwise measurable random variables (A, A’, B, B’) to prove Bell-CHSH inequalities. In SPCE Alice and Bob, using 4 incompatible pairs of experimental settings, estimate imperfect correlations between clicks registered by their detectors. Clicks announce detection of photons and are coded by ±1. Expectations of corresponding random variables: E (AB), E (AB’), E (A’B) and E (A’B’) are estimated and compared with quantum predictions. These estimates significantly violate CHSH inequalities. Since variables (A, A’) as well as (B, B’) cannot be measured jointly, neither Nx4 spreadsheets nor a joint probability distribution of (A, A’, B, B’) exist, thus Bell-CHSH inequalities may not be derived. Nevertheless, imperfect correlations between clicks in SPCE may be explained in a locally causal way, if contextual setting-dependent parameters describing measuring instruments are correctly included in the description. The violation of Bell-CHSH inequalities may not therefore justify the existence of a spooky action at the distance, super-determinism or speculations that an electron can be here and a meter away at the same time. In this paper we review and rephrase several arguments proving that such conclusions are unfounded. Entangled photon pairs cannot be described as pairs of socks nor as pairs of fair dice producing in each trial perfectly correlated outcomes. Thus the violation of inequalities confirms only that the measurement outcomes and `the fate of photons ` are not predetermined before the experiment is done. It does not allow for doubt regarding the objective existence of atoms, electrons and other invisible elementary particles which are the building blocks of the visible world around us including ourselves.
In a sequence of papers, Marian Kupczynski has argued that Bell’s theorem can be circumvented if one takes correct account of contextual setting-dependent parameters describing measuring instruments. We show that this is not true. Despite first appearances, Kupczynksi’s concept of a contextual locally causal probabilistic model is mathematically a special case of a Bell local hidden variables model. Thus, even if one takes account of contextuality in the way he suggests, the Bell–CHSH inequality can still be derived. Violation thereof by quantum mechanics cannot be easily explained away: quantum mechanics and local realism (including Kupczynski’s claimed enlargement of the concept) are not compatible with one another. Further inspection shows that Kupczynski is actually falling back on the detection loophole. Since 2015, numerous loophole-free experiments have been performed, in which the Bell–CHSH inequality is violated, so, despite any other possible imperfections of such experiments, Kupczynski’s escape route for local realism is not available.
A violation of Bell-CHSH inequalities does not justify speculations about quantum non-locality, conspiracy and retro-causation. Such speculations are rooted in a belief that setting dependence of hidden variables in a probabilistic model (called a violation of measurement independence (MI)) would mean a violation of experimenters’ freedom of choice. This belief is unfounded because it is based on a questionable use of Bayes Theorem and on incorrect causal interpretation of conditional probabilities. In Bell-local realistic model, hidden variables describe only photonic beams created by a source, thus they cannot depend on randomly chosen experimental settings. However, if hidden variables describing measuring instruments are correctly incorporated into a contextual probabilistic model a violation of inequalities and an apparent violation of no-signaling reported in Bell tests can be explained without evoking quantum non-locality. Therefore, for us, a violation of Bell-CHSH inequalities proves only that hidden variables have to depend on settings confirming contextual character of quantum observables and an active role played by measuring instruments. Bell thought that he had to choose between non-locality and the violation of experimenters’ freedom of choice. From two bad choices he chose non-locality. Today he would probably choose the violation of MI understood as contextuality.