The Bell theorem [103] can be seen in several different ways, as the EPR argument. Initially, Bell invented it as a direct logical continuation of the EPR theorem: the idea is to take the existence of the EPR elements of reality seriously, and to push it further by introducing them explicitly into the mathematics with the notation λ; one then proceeds to study all possible kinds of correlations that can be obtained from the fluctuations of one or several variables λ, making the condition of locality explicit in the mathematics (locality was already useful in the EPR theorem, but not used in equations). The reasoning develops within determinism (considered as proved by the EPR reasoning) and classical probabilities; it studies in a completely general way all kinds of correlations that can be predicted from the fluctuations of some classical common cause in the past – if one prefers, from some random choice concerning the initial state of the system. This leads to the famous inequalities. But subsequent studies have shown that the scope of the Bell theorem is not limited to determinism; for instance, the λ variables may determine the probabilities of the results of future experiments, instead of the results themselves (see Appendix B), without canceling the theorem. We postpone the discussion of the various possible generalizations to §4.2.3. For the moment, we just emphasize that the essential condition for the validity of the Bell theorem is locality: all kinds of fluctuations can be assumed, but their effect must affect physics only locally.
The Bell theorem [103] can be seen in several different ways, as the EPR argument. Initially, Bell invented it as a direct logical continuation of the EPR theorem: the idea is to take the existence of the EPR elements of reality seriously, and to push it further by introducing them explicitly into the mathematics with the notation λ; one then proceeds to study all possible kinds of correlations that can be obtained from the fluctuations of one or several variables λ, making the condition of locality explicit in the mathematics (locality was already useful in the EPR theorem, but not used in equations). The reasoning develops within determinism (considered as proved by the EPR reasoning) and classical probabilities; it studies in a completely general way all kinds of correlations that can be predicted from the fluctuations of some classical common cause in the past – if one prefers, from some random choice concerning the initial state of the system. This leads to the famous inequalities. But subsequent studies have shown that the scope of the Bell theorem is not limited to determinism; for instance, the λ variables may determine the probabilities of the results of future experiments, instead of the results themselves (see Appendix B), without canceling the theorem. We postpone the discussion of the various possible generalizations to §4.2.3. For the moment, we just emphasize that the essential condition for the validity of the Bell theorem is locality: all kinds of fluctuations can be assumed, but their effect must affect physics only locally.
2014.06.03 – the 25th anniversary of my phone-call re Mermin (1988) – 1989.06.03 Abstract: Generalizing Bell 1964:(15) to realizable experiments, CHSH (1969) coined the term “Bell’s theorem”. Since the results of such experiments (eg, see Aspect 2002) contradict Bell’s theorem: at least one step in his supposedly com-monsense analysis must be false. Using undergraduate maths and logic, we find a mathematical error, a false equality, in Bell (1964). Uncorrected, and therefore continuing, this error undermines all of Bell’s EPR-based analysis and many later variants, rendering them false. We can therefore predict with certainty that all loophole-free EPRB-style experiments will also give the lie to Bell’s theorem. “It is a matter of indifference... whether λ denotes a single variable or a set, or even a set of functions, and whether the variables are discrete or continuous. However, [Bell writes] as if λ were a single continuous parameter, ” Bell (1964:195). λ may denote “any number of hypothetical additional complementary variables needed to complete quantum mechanics in the way envisaged by EPR, ” Bell (2004:242); from his final essay. #1. Re Bell (1964) (which, like other key essays here, is available online; see References): Let the unnumbered equations between Bell’s (14)-(15) be (14a)-(14c). Let a,b, c replace his ~a,~b,~c. Given Bell’s (2004:242) λ specification above (from his final essay), let A(a, λi) and B(b, λ′i) denote the respective outcomes (±1) when Alice and Bob test the i-th particle-pair. #2. NB: Primes (′) distinguish λs in Bob’s domain from those in others. With i = 1, 2,.., N (and j similarly), there is no requirement here that any two particle-pairs should be the same. #3. Let expectation 〈A(a)B(b) 〉 replace Bell’s equivalent term P (~a,~b); etc. Let P (. | Z) denote a probability conditioned on Z: where Z is shorthand for EPRB, the experiment based
EPR (1935) famously argue that additional variables will bring locality and causality to QM's completion; we show that they are right. More famously, Bell (1964) cried 'impossible' against such variables; we give the shortest possible refutation of his theorem. With EPR-based variables -- and no QM -- a thought-experiment delivers common-sense locally-causal accounts of EPRB and GHZ in 3-space. We then find the flaw in Bell's theorem: Bell's 1964:(14a) does not equal Bell's 1964:(14b). Thus, at odds with EPR (and us), Bell's unrealistic theorem and its many variants (eg, Mermin, Peres) miss their mark. In short, mixing common-sense with undergrad math and physics in the classical way so favored by Einstein, we interpret QM locally and realistically. Long may EPR rule OK we say.
John Stewart Bell’s famous theorem is widely regarded as one of the most important developments in the foundations of physics. Yet even as we approach the 50th anniversary of Bell’s discovery, its meaning and implications remain controversial. Many workers assert that Bell’s theorem refutes the possibility suggested by Einstein, Podolsky, and Rosen (EPR) of supplementing ordinary quantum theory with “hidden” variables that might restore determinism and/or some notion of an observer-independent reality. But Bell himself interpreted the theorem very differently—as establishing an “essential conflict” between the well-tested empirical predictions of quantum theory and relativistic local causality. Our goal is to make Bell’s own views more widely known and to explain Bell’s little-known formulation of the concept of relativistic local causality on which his theorem rests. We also show precisely how Bell’s formulation of local causality can be used to derive an empirically testable Bell-type inequality and to recapitulate the EPR argument.
This open letter challenges Annals of Physics' Editors and Bell's supporters on this front: in the context of Bell's theorem -- after AoP (2016:67) -- ‘it's a proven scientific fact that a violation of local realism has been demonstrated theoretically and experimentally.' We show that such claims under the Bellian canon are curtailed by its foundation on a naive realism that is known to be false; ie, under Bohr's old insight (in our terms), a test may disturb the tested system. Further: (i) We define a general all-embracing local realism -- CLR, commonsense local realism -- the union of local-causality (no causal influence propagates superluminally) and physical-realism (some physical properties change interactively). (ii) Under CLR, with EPR-based variables (and without QM), a thought-experiment delivers a local-realistic account of EPRB and GHZ in 3-space. (iii) Under EPR, mixing common-sense with undergrad math/physics in the classical way so favored by Einstein, we interpret QM locally and realistically. (iv) We find the flaw in Bell's theorem: Bell's 1964:(14a) ≠ Bell's 1964:(14b) under EPRB. (v) EPR (1935) famously argue that additional variables will bring locality and causality to QM's completion; we show that they are right. (vi) Even more famously, Bell (1964) cried ‘impossible' against such variables; we give the shortest possible refutation of his claim. (vii) Using Bell's (1988:88) moot gloss on a fragment of von Neumann's work, we conclude: ‘There's nothing to Bell's theorem -- nor Bellian variants like CHSH (1969), Mermin (1990), Peres (1995); nor Bellian endorsements like those by Bricmont, du Sautoy, Goldstein et al., Maudlin, Norsen, Shimony -- it's not just flawed, it's silly; its assumptions nonsense; it's not merely false but foolish' and misleading. (viii) Our results accord with common-sense, QM, Einstein's principles, EPR's belief and Bell's hopes and expectations.
Bell's theorem contains the proposition that the Einstein-Podolsky-Rosen (EPR) theory (hypothesis) of the existence of elements of reality together with Einstein locality permits a mathematical description of EPR experiments by functions that are all defined on one common probability space. This proposition leads in turn to restrictions for possible experimental outcomes that Bell expressed in terms of his well known inequalities and that Vorob'ev and others had investigated before Bell. Summarizing several previous publications and adding new material, the above proposition is refuted by Einstein-local counterexamples from classical physics and shown to involve additional assumptions that can not be justified for mutually exclusive (incompatible) measurements and experiments. Moreover, criticism of our work by Mermin who invoked "standard sampling arguments" is shown to be false.
In papers published in the 25 years following his famous 1964 proof, John Bell refined and reformulated his views on locality and causality. Although his formulations of local causality were in terms of probability, he had little to say about that notion. But assumptions about probability are implicit in his arguments and conclusions. Probability does not conform to these assumptions when quantum mechanics is applied to account for the particular correlations Bell argues are locally inexplicable. This account involves no superluminal action and there is even a sense in which it is local, but it is in tension with the requirement that the direct causes and effects of events be nearby. Introduction I never met John Bell, but his writings have supplied me with a continual source of new insights as I read and reread them over 40 years. As I worked toward a rather different understanding of quantum mechanics he was foremost in my mind as a severe but honest critic of such attempts. We all would love to know what Einstein would have made of Bell's theorem. I confess that the deep regret I feel that Bell cannot respond to this paper is sometimes assuaged by a sense of relief. Locality and Local Causality In his seminal 1964 paper [1], John Bell expressed locality as the requirement that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past. [2, p. 14] This seems to require that the result of a measurement would have been the same, no matter what operations had been performed on such a distant system. But suppose the result of a measurement were the outcome of an indeterministic process. Then the result of the measurement might have been different even if exactly the same operations (if any) had been performed on that distant system. So can no indeterministic theory satisfy the locality requirement? Bell felt no need to address that awkward question in his 1964 paper [1], since he took the EPR argument to establish that any additional variables needed to restore locality and causalitywould have to determine a unique result of ameasurement.