Bell’s Theorem Refuted: Based on Harry’s Analysis at Sciphysicsforums.com

Gordon Watson

Published May 1, 2014• 0 citations

Abstract

Generalizing Bell 1964:(15) to realizable experiments, CHSH (1969) coined the term ‘Bell’s theorem’. Using undergraduate maths and logic, we show that Bell’s theorem and its CHSH-style variants are false (as discussed with David Mermin 1989.06.03).

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Bell’s theorem refuted: Bell’s 1964:(15) is false

Gordon Watson

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

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Local Realism Generalized, EPR Refined, Bell's Theorem Refuted

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Adjusting EPR (to accord with Bohr's insight), and accepting Bell's principles (but not his false inferences), we:— (i) complete the QM account of EPR correlations in a classical way; (ii) deliver Bell's hope for a simple constructive model of EPRB; (iii) justify EPR's belief that additional variables would bring locality and causality to QM's completion; (iv) refute key claims that such variables are impossible — including CHSH, Mermin's three-particle always-vs-never variant of GHZ, and this: in the context of Bell's theorem ‘it's a proven scientific fact that a violation of local realism has been demonstrated theoretically and experimentally,' (Annals of Physics Editors, 2016). In short: we refute Bell's theorem and endorse Einstein's locally-causal Lorentz-invariant worldview.

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