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arXiv:1207.5294

Quantum Randi Challenge

Sascha Vongehr

Published Jul 23, 2012• 8 citations
arXivHTMLPDF

Abstract

Observed violations of Bell type inequalities exclude all relativistic micro causal ("local"), counterfactual definite ("real") hidden variable models of nature. This further relativization of our concept of reality triggers a growing pseudoscientific resistance against quantum mechanics (QM). I define Didactic Randi Challenges (DRC) via five characteristics. These are challenges which, according to the laws of nature, are impossible to meet. They effectively refute pseudoscientific claims according to which the challenge could easily be met. DRC work by being known to exist while never having been overcome, despite the large rewards which would follow from meeting the challenge. Pseudoscience exploits well meaning engagement in argument to create the appearance of an expert dispute (sowing doubt). DRC decline to discuss "until the challenge is met", without solidifying the perception of establishment conspiracy. This requires transparency, thus DRC are efficient didactic tools. The Quantum Randi Challenge (QRC) is a DRC designed to reject hidden variable models by simply teaching QM; there is no bet or interaction with challengers. The QRC is a computer game that anybody can modify. The present version includes a simulation of true QM behavior that violates Bell 99% of the time, hidden variables that violate the Bell and CHSH inequality with 50% probability, and ones which violate Bell 85% of the time when missing 13% anti-correlation. The DRC challenge is to modify the hidden variables so that the predicted QM behavior arises, including anti-correlation. If such were possible, the presented programs would make it trivial to meet the challenge. This fact and the whole QRC can be taught to a wide audience via the presented heuristics. Demanding anti-correlation is argued to be superior to employing CHSH.

DOI
10.48550/arxiv.1207.5294

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Observed violations of Bell type inequalities exclude all relativistic micro causal ("local"), counterfactual definite ("real") hidden variable models of nature. This further relativization of our concept of reality triggers a growing pseudoscientific resistance against quantum mechanics (QM). I define Didactic Randi Challenges (DRC) via five characteristics. These are challenges which, according to the laws of nature, are impossible to meet. They effectively refute pseudoscientific claims according to which the challenge could easily be met. DRC work by being known to exist while never having been overcome, despite the large rewards which would follow from meeting the challenge. Pseudoscience exploits well meaning engagement in argument to create the appearance of an expert dispute (sowing doubt). DRC decline to discuss "until the challenge is met", without solidifying the perception of establishment conspiracy. This requires transparency, thus DRC are efficient didactic tools. The Quantum Randi Challenge (QRC) is a DRC designed to reject hidden variable models by simply teaching QM; there is no bet or interaction with challengers. The QRC is a computer game that anybody can modify. The present version includes a simulation of true QM behavior that violates Bell 99% of the time, hidden variables that violate the Bell and CHSH inequality with 50% probability, and ones which violate Bell 85% of the time when missing 13% anti-correlation. The DRC challenge is to modify the hidden variables so that the predicted QM behavior arises, including anti-correlation. If such were possible, the presented programs would make it trivial to meet the challenge. This fact and the whole QRC can be taught to a wide audience via the presented heuristics. Demanding anti-correlation is argued to be superior to employing CHSH.
Eighty years ago Einstein, Podolsky and Rosen demonstrated that instantaneous reduction of wave function, believed to describe completely a pair of entangled physical systems, led to EPR paradox. The paradox disappears in statistical interpretation of quantum mechanics (QM) according to which a wave function describes only an ensemble of identically prepared physical systems. QM predicts strong correlations between outcomes of measurements performed on different members of EPR pairs in far-away locations. Searching for an intuitive explanation of these correlations John Bell analysed so called local realistic hidden variable models and proved that correlations consistent with these models satisfy Bell inequalities which are violated by some predictions of QM and by experimental data. Several different local models were constructed and inequalities proven. Some eminent physicists concluded that Nature is definitely nonlocal and that it is acting according to a law of nonlocal randomness. According to these law perfectly random, but strongly correlated events, can be produced at the same time in far away locations and a local and causal explanation of their occurrence cannot be given. We strongly disagree with this conclusion and we prove the contrary by analysing in detail some influential finite sample proofs of Bell and CHSH inequalities and so called Quantum Randi Challenges. We also show how one can win so called Bell's game without violating locality of Nature. Nonlocal randomness is inconsistent with local quantum field theory, with standard model in elementary particle physics and with causal laws and adaptive dynamics prevailing in the surrounding us world. The experimental violation of Bell-type inequalities does not prove the nonlocality of Nature but it only confirms a contextual character of quantum observables and gives a strong argument against counterfactual definiteness and against a point of view according to which experimental outcomes are produced in irreducible random way.
Bell’s [Physics 1 (1964) 195–200] theorem is popularly supposed to establish the nonlocality of quantum physics. Violation of Bell’s inequality in experiments such as that of Aspect, Dalibard and Roger [Phys. Rev. Lett. 49 (1982) 1804–1807] provides empirical proof of nonlocality in the real world. This paper reviews recent work on Bell’s theorem, linking it to issues in causality as understood by statisticians. The paper starts with a proof of a strong, finite sample, version of Bell’s inequality and thereby also of Bell’s theorem, which states that quantum theory is incompatible with the conjunction of three formerly uncontroversial physical principles, here referred to as locality, realism and freedom. Locality is the principle that the direction of causality matches the direction of time, and that causal influences need time to propagate spatially. Realism and freedom are directly connected to statistical thinking on causality: they relate to counterfactual reasoning, and to randomisation, respectively. Experimental loopholes in state-of-the-art Bell type experiments are related to statistical issues of post-selection in observational studies, and the missing at random assumption. They can be avoided by properly matching the statistical analysis to the actual experimental design, instead of by making untestable assumptions of independence between observed and unobserved variables. Methodological and statistical issues in the design of quantum Randi challenges (QRC) are discussed. The paper argues that Bell’s theorem (and its experimental confirmation) should lead us to relinquish not locality, but realism.
Abstract The experimentally verified violation of Bell’s inequalities apparently implies that at least one of two beliefs, which are accepted as true in almost all scientific practice, must be false. These beliefs are: that effects propagating at infinite velocity do not exist, and that natural phenomena occur independently of being observed. Giving up any one of these two beliefs (usually known together as Local Realism) is controversial. For many years, many theories have been proposed to reconcile the violation of Bell’s inequalities with Local Realism, but none has been fully successful. In this paper, it is recalled that Bell’s inequalities are equivalent to the conditions to decide the completeness of a theory according to Boolean logic. Therefore, any theory aimed to violate Bell’s inequalities must start by giving up Boolean logic. Two problems are therefore defined: the “soft” one is to explain the violation of Bell’s inequalities without violating (non-Boolean) Local Realism; the “hard” one is to predict the time values when single particles are detected, in such a way that the resulting number of coincidences violates Bell’s inequalities. A simple hidden variables model is introduced, which solves the “soft” problem even in an ideal setup. This is possible thanks to the use of vectors in real space as the hidden variables and the corresponding operation (projection), which do not hold to Boolean logic. This model reconciles the violation of Bell’s inequalities with Local Realism and should end a controversy that has lasted for decades. Regarding the “hard” problem, the introduced model is as incomplete as Quantum Mechanics is. It is claimed that solving the “hard” problem requires devising a new kind of quantum computer, which should be able to accept (non-Boolean) hidden variable values as input data and to replace the statistical Born’s rule of Quantum Mechanics with a deterministic threshold condition.
In 1935 Einstein, Podolsky, and Rosen (EPR) published an important paper in which they claimed that the whole formalism of quantum mechanics together with what they called "Reality Criterion" imply that quantum mechanics cannot be complete. That is, there must exist some elements of reality that are not described by quantum mechanics. There must be, they concluded, a more complete description of physical reality behind quantum mechanics. There must be a state, a hidden variable, characterizing the state of affairs in the world in more details than the quantum mechanical state, something that also reflects the missing elements of reality. Under some further but quite plausible assumptions, this conclusion implies that in some spin-correlation experiments the measured quantum mechanical probabilities should satisfy particular inequalities (Bell-type inequalities). The paradox consists in the fact that quantum probabilities do not satisfy these inequalities. And this paradoxical fact has been confirmed by several laboratory experiments in the last three decades. The problem is still open and hotly debated among both physicists and philosophers. It has motivated a wide range of research from the most fundamental quantum mechanical experiments through foundations of probability theory to the theory of stochastic causality as well as the metaphysics of free will.
Einstein, Podolsky, and Rosen (EPR) have designed a gedanken experiment that suggested a theory that was more complete than quantum mechanics. The EPR design was later realized in various forms, with experimental results close to the quantum mechanical prediction. The experimental results by themselves have no bearing on the EPR claim that quantum mechanics must be incomplete nor on the existence of hidden parameters. However, the well known inequalities of Bell are based on the assumption that local hidden parameters exist and, when combined with conflicting experimental results, do appear to prove that local hidden parameters cannot exist. This fact leaves only instantaneous actions at a distance (called "spooky" by Einstein) to explain the experiments. The Bell inequalities are based on a mathematical model of the EPR experiments. They have no experimental confirmation, because they contradict the results of all EPR experiments. In addition to the assumption that hidden parameters exist, Bell tacitly makes a variety of other assumptions; for instance, he assumes that the hidden parameters are governed by a single probability measure independent of the analyzer settings. We argue that the mathematical model of Bell excludes a large set of local hidden variables and a large variety of probability densities. Our set of local hidden variables includes time-like correlated parameters and a generalized probability density. We prove that our extended space of local hidden variables does permit derivation of the quantum result and is consistent with all known experiments.