Abstract

Decision problems in physics have been an active field of research for quite a few decades resulting in some interesting findings in recent years. However, such research investigations are based on a priori knowledge of theoretical computer science and the technical jargon of set theory. Here, I discuss a particular, but a significant, instance of how decision problems in physics can be realised without such specific prerequisites. I expose a hitherto unnoticed contradiction, that can be posed as as decision problem, concerning the oil drop experiment, thereby resolve it by refining the notion of ‘existence’ in physics. This consequently leads to the undecidability of the charge spectral gap through the notion of ‘undecidable charges’ which is in tandem with the completeness condition of a theory as was stated by Einstein, Podolsky and Rosen in their seminal work. Decision problems can now be realised in connection with basic physics, in general, rather than quantum physics, in particular, as per some recent claims.

中文翻译：

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不可判定电荷间隙与油滴实验

摘要

物理学中的决策问题几十年来一直是一个活跃的研究领域，近年来产生了一些有趣的发现。然而，此类研究调查是基于理论计算机科学的先验知识和集合论的技术术语。在这里，我讨论一个特定但重要的例子，说明如何在没有这些特定先决条件的情况下实现物理学中的决策问题。我揭露了一个迄今为止未被注意到的矛盾，它可以作为决策问题，与油滴实验有关，从而通过改进物理学中“存在”的概念来解决它。因此，通过“不可判定电荷”的概念，这导致电荷谱间隙的不可判定性，这与爱因斯坦、波多尔斯基和罗森在其开创性工作中所述的理论的完整性条件相一致。一般来说，决策问题现在可以与基础物理学联系起来实现，而不是根据最近的一些说法特别是与量子物理学联系起来。