von Neumann's Theorem Revisited
von Neumann's Theorem Revisited
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DOI：
10.1007/s10701-021-00474-5
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发表时间：
2021-06-01
影响因子：
1.5
通讯作者：
Acuna, Pablo
中科院分区：
文献类型：
--
作者：
Acuna, Pablo
根据一种流行的说法，冯·诺伊曼在1932年提出了一个定理，旨在证明量子力学中隐藏变量的不可能性。然而，据叙述，贝尔后来发现了一个据称显示其无关紧要的缺陷。贝尔被广泛接受的批评受到了Bub和Dieks的挑战：他们声称证明表明可行的隐变量理论不可能是希尔伯特空间中的理论。巴布和迪克斯的重新评估反过来又受到了默明和沙克的挑战。在此，我批判性地评价他们的回答，目的是进一步澄清冯·诺伊曼定理的意义、范围和相关性。我认为，尽管Mermin和Schack做出了回应，但Bub和Dieks的重新评估是非常正确的，当我们仔细考虑冯·诺伊曼的证明和格里森定理之间的联系时，这种解读得到了强烈的加强。
According to a popular narrative, in 1932 von Neumann introduced a theorem that intended to be a proof of the impossibility of hidden variables in quantum mechanics. However, the narrative goes, Bell later spotted a flaw that allegedly shows its irrelevance. Bell's widely accepted criticism has been challenged by Bub and Dieks: they claim that the proof shows that viable hidden variables theories cannot be theories in Hilbert space. Bub's and Dieks' reassessment has been in turn challenged by Mermin and Schack. Hereby I critically assess their reply, with the aim of bringing further clarification concerning the meaning, scope and relevance of von Neumann's theorem. I show that despite Mermin and Schack's response, Bub's and Dieks' reassessment is quite correct, and that this reading gets strongly reinforced when we carefully consider the connection between von Neumann's proof and Gleason's theorem.