We discuss the role of counter-factual meaningfulness (a weaker cousin of "counter-factual definiteness") as a premise in the derivation of the Bell and CHSH inequalities. The basic question motivating the discussion is this: can the CHSH inequality, unlike the original Bell inequality, be derived without making a hidden-variables (or equivalent counter-factual definiteness) assumption? We answer, somewhat tentatively, in the negative, and suggest that an appropriately-modified version of the EPR argument is needed to rigorously establish that the empirical violation of Bell-type inequalities can only be blamed on the failure, in nature, of local causality.
We discuss the role of counter-factual meaningfulness (a weaker cousin of "counter-factual definiteness") as a premise in the derivation of the Bell and CHSH inequalities. The basic question motivating the discussion is this: can the CHSH inequality, unlike the original Bell inequality, be derived without making a hidden-variables (or equivalent counter-factual definiteness) assumption? We answer, somewhat tentatively, in the negative, and suggest that an appropriately-modified version of the EPR argument is needed to rigorously establish that the empirical violation of Bell-type inequalities can only be blamed on the failure, in nature, of local causality.
Bell's theorem is 50 years old. Still there is a controversy about its implications. Much of it has its roots in confusion regarding the premises from which the theorem can be derived. Some claim that a derivation of Bell's inequalities requires just locality assumption, and nothing more. Violations of the inequalities are then interpreted as ``nonlocality'' or ``quantum nonlocality''. We show that such claims are unfounded and that every derivation of Bell's inequalities requires a premise -- in addition to locality and freedom of choice -- which is either assumed tacitly, or unconsciously, or is embedded in a single compound condition (like Bell's ``local causality''). The premise is equivalent to the assumption of existence of additional variables which do not appear in the quantum formalism (in form of determinism, or joint probability for outcomes of all conceivable measurements, or ``additional causes`'', or ``hidden variables'', ``complete description of the state'' or counterfactual definiteness, etc.). A certain irony is that perhaps the main message of violation of Bell's inequalities is that our notion of locality should be based on an operationally well-defined no-signalling condition, rather than on local causality.
The empirical evidence tends to confirm the quantum - mechanically (QM) predicted violation of Bell's - type inequalities. The latter are widely accepted to be correct representation of the objective reality (OR) underlying EPR's gedankenexperiment. Contrariwise, we argue here that the starting premises leading to Bell's and CHSH's inequalities are not appropriate formulations of OR in the EPR context. Indeed, the essence of EPR argument is the correlation between pair of particles travelling with some well defined orientations. To measure such correlation, one requires detectors with high resolution, and some appropriately defined relative orientations. On the contrary, experimental tests of Bell's inequalities typically involve counting the number of particles with some value of spin (or polarisation) using low-resolution detectors and completely arbitrary orientations. Depending upon the relative orientation of good-resolution detectors, we obtain two families of CHSH-type inequalities. One of these families is the most often used version of CHSH inequality, that was derived by Clauser and Horne with the supplementary no - enhancement assumption: here, it is obtained without special provisions. The other family is completely new and refers to coincidence counts from multiple events. Experimental test to distinguish between the QM and OR descriptions of nature should take into account these new constraints.
The empirical evidence tends to confirm the quantum - mechanically (QM) predicted violation of Bell's - type inequalities. The latter are widely accepted to be correct representation of the objective reality (OR) underlying EPR's gedankenexperiment. Contrariwise, we argue here that the starting premises leading to Bell's and CHSH's inequalities are not appropriate formulations of OR in the EPR context. Indeed, the essence of EPR argument is the correlation between pair of particles travelling with some well defined orientations. To measure such correlation, one requires detectors with high resolution, and some appropriately defined relative orientations. On the contrary, experimental tests of Bell's inequalities typically involve counting the number of particles with some value of spin (or polarisation) using low-resolution detectors and completely arbitrary orientations. Depending upon the relative orientation of good-resolution detectors, we obtain two families of CHSH-type inequalities. One of these families is the most often used version of CHSH inequality, that was derived by Clauser and Horne with the supplementary no - enhancement assumption: here, it is obtained without special provisions. The other family is completely new and refers to coincidence counts from multiple events. Experimental test to distinguish between the QM and OR descriptions of nature should take into account these new constraints.
The empirical evidence tends to confirm the quantum - mechanically (QM) predicted violation of Bell's - type inequalities. The latter are widely accepted to be correct representation of the objective reality (OR) underlying EPR's gedankenexperiment. Contrariwise, we argue here that the starting premises leading to Bell's and CHSH's inequalities are not appropriate formulations of OR in the EPR context. Indeed, the essence of EPR argument is the correlation between pair of particles travelling with some well defined orientations. To measure such correlation, one requires detectors with high resolution, and some appropriately defined relative orientations. On the contrary, experimental tests of Bell's inequalities typically involve counting the number of particles with some value of spin (or polarisation) using low-resolution detectors and completely arbitrary orientations. Depending upon the relative orientation of good-resolution detectors, we obtain two families of CHSH-type inequalities. One of these families is the most often used version of CHSH inequality, that was derived by Clauser and Horne with the supplementary no - enhancement assumption: here, it is obtained without special provisions. The other family is completely new and refers to coincidence counts from multiple events. Experimental test to distinguish between the QM and OR descriptions of nature should take into account these new constraints.
Bell's theorem states that no description of a Bell experiment can be simultaneously local, realistic in the sense of counterfactual definiteness, and free of conspiracy between settings and hidden state. The recent generation of experiments has confirmed the predicted violation of the CHSH inequality, so one of the assumptions must be abandoned. Which one, and how one reconstructs a coherent worldview after doing so, is a question on which many authors disagree. This paper is written by three such authors. All three reject both counterfactual definiteness and conspiratorial violation of statistical independence of setting choices and state. After a joint exposition of the classical half of Bell's theorem in the language of Pearl-style causal graphs, a joint summary of the loophole-free experiments, and a joint survey of the recent literature, each author states where they have presently arrived. Gill accepts irreducible and non-local quantum randomness and finds the choice between locality and realism a false dichotomy. In his later works, Bell derives counterfactual definiteness from classical local causality, and that is what has to go. The metaphysical concepts "realism", "locality", "causality" need to be reconsidered. Helland reconstructs the Hilbert-space formalism from a theory of accessible variables, and from this theory he concludes that every observer must be limited in a specific sense. Jongejan proposes a geometric hidden-variable construction in which the degree of violation of the CHSH inequality depends on the number of dimensions of space, Tsirelson's bound corresponding to three dimensions. The authors conclude with a discussion.
Abstract: The principle of causality occupies an important place in the history of the philosophical interpretation of quantum mechanics from the beginning. In last consequence, today’s Copenhagen dominated acausal interpretation of quantum mechanics casts doubt upon traditional views in the philosophy of nature and demands the revision of the principle of causality at a fundamental level of theoretical description in physics. Testing the mathematical and logical consistency of the quantum mechanical description of nature i. e. especially such as non-locality has become a subject of an ongoing dispute and research. Today, quantum-mechanical concepts i. e. such as non-locality refer to some mathematical foundations, especially to Bell's inequality and the CHSH inequality. Experimental data, analyzed by the help of Bell’s inequality or the CHSH inequality favor a quantum mechanical description of nature, over local hidden variable theories (often referred to as local realism). In general, the use of mathematically inconsistent methods can imply a waste of money, time and effort on this account. Under some certain conditions (the assumption of independence) Bell's theorem and the CHSH inequality are already refuted. The purpose of this publication is explore the terra incognita, the interior logic that may lie beyond Bell's original theorem and the CHSH-inequality and to refute both, Bell's original theorem and the CHSH-inequality under any circumstances by the proof that we can derive a logical contradiction out of Bell's inequalities. Thus far, accept Bell's theorem or the CHSH-inequality as correct,