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arXiv:1506.02179 · American Journal of Physics

Ghostly action at a distance: A non-technical explanation of the Bell inequality

Mark Alford

Published May 23, 2016• 9 citations
arXivHTMLPDF

Abstract

We present a non-mathematical explanation of Bell's inequality. Using the inequality, we show how the results of Einstein-Podolsky-Rosen (EPR) experiments violate the principle of strong locality. This indicates, given some reasonable-sounding assumptions, that some sort of faster-than-light influence is present in nature. We discuss the implications, emphasizing the relationship between EPR and the Principle of Relativity, the distinction between causal influences and signals, and the tension between EPR and determinism.

DOI
10.1119/1.4945408

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We present a non-mathematical explanation of Bell's inequality. Using the inequality, we show how the results of Einstein-Podolsky-Rosen (EPR) experiments violate the principle of strong locality. This indicates, given some reasonable-sounding assumptions, that some sort of faster-than-light influence is present in nature. We discuss the implications, emphasizing the relationship between EPR and the Principle of Relativity, the distinction between causal influences and signals, and the tension between EPR and determinism.
It is argued that the lesson we should learn from Bell's inequalities is not that quantum mechanics requires some kind of action at a distance, but that it leads us to believe in parallel worlds. Introduction Bell's work [1] led to a revolution in our understanding of nature. I remember attending my first physics conference, on “Microphysical Reality and Quantum Formalism,” in Urbino, 1985. Most of the talks were about Aspect's experiment [2] confirming the nonlocality of quantum mechanics based on experimental violations of Bell's inequalities. Although I did not share the skepticism of many speakers regarding the results of Aspect, I was not ready to accept that a local action in one place can instantaneously change anything at another place. So, while for the majority the lesson from Bell was that quantum mechanics requires some “spooky action at a distance”, I was led by Bell's result to an alternative revolutionary change in our view of nature. I saw no other way than accepting the manyworlds interpretation (MWI) of quantum mechanics [3, 4]. I shall start by presenting the Einstein–Podolsky–Rosen (EPR) [5] argument. Then I will present Bell's presented using the Greenberger–Horne–Zeilinger setup [6] in the form proposed by Mermin [7, 8]. The discussion of nonlocality will suggest that Bell's inequalities are the only manifestation of action at a distance in nature. The demonstration of the necessity of action at a distance will be done through a detailed analysis of the GHZ experiment. Then I shall show how multiple worlds resolve the problem of action at a distance. After discussing the issue of nonlocality in the MWI, I shall conclude by citing Bell's views on the MWI. EPR–Bell–GHZ The story of Bell cannot be told without first describing the EPR argument. Instead of following the historical route, I shall use the GHZ setup, which, in my view, is the clearest way to explain the EPR and Bell's discovery.
An explicit model-example is presented to simulate Einstein-Podolsky-Rosen (EPR) experiments without invoking instantaneous influences at a distance. The model-example, together with the interpretation of past experiments by Kwiat and coworkers, uncovers logical inconsistencies in the application of Bell’s theorem to actual EPR experiments. The inconsistencies originate from topological-combinatorial assumptions that are both necessary and sufficient to derive all Bell-type inequalities including those of Wigner-d’Espagnat and Clauser-Horne-Shimony-Holt. The model-example circumvents these inconsistencies.
The EPR paradox dates back to 1935 when Einstein et al., through the use of non commuting operators, proposed that quantum mechanics was not complete[1] in that it suggested a "spooky action at a distance." Later in 1964 John Bell was able to express the dilemma in a simple inequality[2] involving spin singlet states. If the inequality were satisfied then Einstein was correct and if it were violated then it favored the quantum mechanics point of view. In what follows, we present two approaches to Bell's inequality, and then offer an interpretation from the viewpoint of quantum mechanics based on the principle that the whole is more than the sum of its parts. This is then combined with the properties of the SU (2) group to give a more intuitive understanding of non-locality and spin entanglement from the perspective of the relativistic characteristics of rotations.
Maudlin has claimed that no local theory can reproduce the predictions of standard quantum mechanics that violate Bell’s inequality for Bohm’s version (two spin-half particles in a singlet state) of the Einstein-Podolsky-Rosen problem. It is argued that, on the contrary, standard quantum mechanics itself is a counterexample to Maudlin’s claim, because it is local in the appropriate sense (measurements at one place do not influence what occurs elsewhere there) when formulated using consistent principles in place of the inconsistent appeals to “measurement” found in current textbooks. This argument sheds light on the claim of Blaylock that counterfactual definiteness is an essential ingredient in derivations of Bell’s inequality.
We begin with a review of the famous thought experiment that was proposed by Einstein, Podolsky and Rosen (EPR) and mathematically formulated by Bell; the outcomes of which challenge the completeness of quantum mechanics and the locality of Nature. We then suggest a reinterpretation of the EPR experiment that utilizes observer complementarity; a concept from quantum gravity which allows spatially separated observers to have their own, independent reference frames. The resulting picture provides a self-consistent resolution of the situation that does not jeopardize causality nor unitarity, nor does it resort to ''spooky'' (non-local) interactions. Our conclusion is that EPR and Bell rely on an overly strong definition of locality that is in conflict with fundamental physics.
An overview of the history of Bell’s inequality is given, beginning with the so-called EPR paradox originally put forward by Einstein, Podolsky and Rosen and the impossibility proof of von Neumann. Bell’s inequality, which ultimately shifted the discussion from arguments based on philosophically introduced postulates to the domain of experimental physics, is presented together with experimental attempts from the early 1970s to 2010s to violate this inequality. We introduce three historical loopholes in the experimental schemes which have prevented experimentalists from being able to fully disprove the possibility of a hidden-variables description of nature. Recent experimental data indicate that all the main loopholes are now closed for photons (albeit not simultaneously in one experiment). Besides the class of stochastic local realism that have been tested experimentally, some other possible classical interpretations are mentioned.