We show that there is no non-constant assignment of zeros and ones to points of a unit sphere in \(\mathbb{R}^3\) such that for every three pairwisely orthogonal vectors, an odd number of them is assigned 1. This is a new strengthening of the Bell–Kochen–Specker theorem, which proves the non-existence of hidden variables in quantum theories.

中文翻译：

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三维广义 Kochen-Specker 定理

我们表明，在\(\mathbb{R}^3\) 中，单位球体的点没有非常量的零和一赋值，因此对于每三个成对正交的向量，奇数个向量被赋值为 1。这是 Bell-Kochen-Specker 定理的新强化，证明了量子理论中不存在隐藏变量。