Specker’s principle, the condition that pairwise orthogonal propositions must be jointly orthogonal (or rather, the ‘exclusivity principle’ that follows from it), has been much investigated recently within the programme of finding physical principles to characterize quantum mechanics. Specker’s principle, however, largely appears to lack a physical justification. In this paper, I present a proof of Specker’s principle from three assumptions (made suitably precise): the existence of ‘maximal entanglement’, the existence of ‘non-maximal measurements’ and no-signalling. I discuss these three assumptions and describe canonical examples of non-Specker sets of propositions satisfying any two of them. These examples display analogies with various approaches to the interpretation of quantum mechanics, including retrocausation. I also discuss connections with the work of Popescu & Rohrlich. The core of the proof (and the main example violating no-signalling) is illustrated by a variant of Specker’s tale of the seer of Nineveh, with which I open the paper. This article is part of the theme issue ‘Quantum contextuality, causality and freedom of choice’.

中文翻译：

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斯派克原理的证明

斯佩克原理，即成对正交命题必须共同正交的条件（或者更确切地说，由此得出的“排他性原理”），最近在寻找表征量子力学的物理原理的计划中得到了广泛的研究。然而，斯佩克的原理在很大程度上似乎缺乏物理依据。在本文中，我从三个假设（适当精确）证明了斯派克原理：“最大纠缠”的存在、“非最大测量”的存在和无信号。我讨论了这三个假设，并描述了满足其中任何两个假设的非斯佩克命题集的典型例子。这些例子展示了与量子力学解释的各种方法的类比，包括逆因果关系。我还讨论了与 Popescu 和 Rohrlich 的作品的联系。证明的核心（以及违反无信号的主要例子）是通过斯派克关于尼尼微先知的故事的一个变体来说明的，我用它来打开这篇论文。本文是“量子背景、因果关系和选择自由”主题的一部分。