论文标题
不确定性和不可证明性
Indeterminism and Undecidability
论文作者
论文摘要
本文的目的是争辩说，自出生以来哥本哈根解释的信徒所主张的（所谓的）不确定的量子力学不确定主义，可以从Chaitin的后续行动来证明Goedel（第一个）不完整的定理。 In comparison, Bell's (1964) theorem as well as the so-called free will theorem-originally due to Heywood and Redhead (1983)-left two loopholes for deterministic hidden variable theories, namely giving up either locality (more precisely: local contextuality, as in Bohmian mechanics) or free choice (i.e. uncorrelated measurement settings, as in 't Hooft's cellular automaton interpretation量子力学）。要点是，贝尔和其他人没有利用量子力学的完整经验内容，其中由一系列重复测量的结果组成（理想地为无限二进制序列）：他们的论点仅使用了从该系列的长期相对频率得出的相对频率，因此仅要求从某些可变性的概率定义某些定义的bip，因此仅要求可变性的概率。如果我们将公平量子硬币翻转的二元结果串视为无限序列，则量子力学预测，这些量子通常（即几乎肯定）具有逻辑中称为1随机性的特性，这比不可兼容强得多。这是我主张的关键，这是基于确定论的强（但令人信服）的概念，而不是隐藏变量理论的文献中的常见。
The aim of this paper is to argue that the (alleged) indeterminism of quantum mechanics, claimed by adherents of the Copenhagen interpretation since Born (1926), can be proved from Chaitin's follow-up to Goedel's (first) incompleteness theorem. In comparison, Bell's (1964) theorem as well as the so-called free will theorem-originally due to Heywood and Redhead (1983)-left two loopholes for deterministic hidden variable theories, namely giving up either locality (more precisely: local contextuality, as in Bohmian mechanics) or free choice (i.e. uncorrelated measurement settings, as in 't Hooft's cellular automaton interpretation of quantum mechanics). The main point is that Bell and others did not exploit the full empirical content of quantum mechanics, which consists of long series of outcomes of repeated measurements (idealized as infinite binary sequences): their arguments only used the long-run relative frequencies derived from such series, and hence merely asked hidden variable theories to reproduce single-case Born probabilities defined by certain entangled bipartite states. If we idealize binary outcome strings of a fair quantum coin flip as infinite sequences, quantum mechanics predicts that these typically (i.e.\ almost surely) have a property called 1-randomness in logic, which is much stronger than uncomputability. This is the key to my claim, which is admittedly based on a stronger (yet compelling) notion of determinism than what is common in the literature on hidden variable theories.
