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丛林里的犹太人游击队《反抗军》(Defiance)
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作者 曾喆 《数码先锋》 2009年第2期120-120,共1页
一句话影评《数码先锋》:与以往影视作品不同的是,本片展示了犹太人倔强的一面《纽约客》:一个激动人心的故事,展现了最多的细节同时仅用了最少的修饰凤凰网:虽然克雷格灰头土脸的形象和007大相径庭。
关键词 克雷格 游击队 犹太人 defiance
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Quantum Violation of Bell’s Inequality: A Misunderstanding Based on a Mathematical Error of Neglect
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作者 Frank Lad 《Journal of Modern Physics》 2021年第8期1109-1144,共36页
This paper intends to show how the fabled violation of Bell’s inequality by the probabilistic specifications of quantum mechanics derives from a mathematical error, an error of neglect. I have no objection to the pro... This paper intends to show how the fabled violation of Bell’s inequality by the probabilistic specifications of quantum mechanics derives from a mathematical error, an error of neglect. I have no objection to the probabilities specified by quantum theory, nor to the inequality itself as characterized in the formulation of Clauser, Horne, Shimony, and Holt. Designed to assess consequences of Einstein’s principle of local realism, the inequality pertains to a linear combination of four polarization products <em>on the same pair of photons</em> arising in a gedankenexperiment. My assessment displays that in this context, the summands of the relevant CHSH quantity<em> s</em>(<span style="white-space:nowrap;"><em>λ</em></span>) inhere four symmetric functional relations which have long been neglected in analytic considerations. Its expectation E[<em style="white-space:normal;">s</em><span style="white-space:normal;">(</span><em>λ</em><span style="white-space:normal;">)</span>] is not the sum of four “marginal” expectations from a joint distribution, as quantum theory explicitly avoids such a specification. Rather, I show that <span style="white-space:normal;">E[</span><em style="white-space:normal;">s</em><span style="white-space:normal;">(</span><em style="white-space:normal;">λ</em><span style="white-space:normal;">)</span><span style="white-space:normal;">]</span> has four distinct representations as the sum of <em>three</em> expectations of polarization products plus the expectation of a fourth which is restricted to equal a function value determined by the other three. Analysis using Bruno de Finetti’s fundamental theorem of prevision (FTP) yields only a bound for <em>E</em>(<em>s</em>) within <span style="white-space:nowrap;">(1.1213,2]</span> , surely not <img src="Edit_91a32f90-4b68-4415-98bc-3819733feca8.png" alt="" />at all as is commonly understood. I exhibit slices of the 4-dimensional polytope of joint<em> P</em><sub>++</sub> probabilities actually motivated by quantum theory at the four stipulated angle settings, as it passes through 3-dimensional space. Bell’s inequality is satisfied everywhere within the convex hull of extreme distributions cohering with quantum theoretic specifications, even while in keeping with local realism. Aspect’s proposed “estimation” of <em>E</em>(<em>s</em>) near to <img src="Edit_91a32f90-4b68-4415-98bc-3819733feca8.png" alt="" style="white-space:normal;" />is based on polarization products from different photon pairs that do not have embedded within them the functional relations inhering in the relevant gedankenexperiment. When one actively embeds the restrictions into Aspect’s estimation procedure, it yields an estimate of 1.7667, although this is not and cannot be definitive. While my analysis supports the subjectivist construction of probability as clarifying issues relevant to the interpretation of quantum theory, the error resolved herein is purely mathematical. It pertains to the reconsideration of Bell violation irrespective of one’s attitude toward the meaning of probability. 展开更多
关键词 Bell Inequality defiance CHSH Formulation Fundamental Theorem of Probability Probability Bounds 4-Dimensional Cuts
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