The results of Cubitt et al. on the spectral gap problem add a new chapter to the issue of undecidability in physics, as they show that it is impossible to decide whether the Hamiltonian of a quantum many-body system is gapped or gapless. This implies, amongst other things, that a reductionist viewpoint would be untenable. In this paper, we examine their proof and a few philosophical implications, in particular ones regarding models and limitative results. In more detail, we examine the way these theorems model many-body quantum systems, and we question what, if anything, is the physical counterpart of the models used by Cubitt et al. We argue that these models are non-representational and that, even if they are so artificial that it is hard to imagine a physical system arising from them, they nonetheless offer an opportunity to learn about the world and the relation between mathematics and reality. On this basis, we draw the conclusion that their results do not undermine the reductionist viewpoint in a strong sense but leave the question open in a weak sense.

Cubitt等人的结果。关于谱隙问题的研究为物理学的不确定性问题增加了新的篇章，因为它们表明不可能确定量子多体系统的哈密顿量是有间隙的还是无间隙的。除其他外，这意味着还原主义观点是站不住脚的。在本文中，我们检查了它们的证明和一些哲学含义，尤其是关于模型和限制性结果的含义。更详细地讲，我们研究了这些定理对多体量子系统进行建模的方式，并质疑Cubitt等人所使用的模型的物理对应物（如果有的话）是什么。我们认为这些模型是非代表性的，即使它们是人为的，以至于很难想象由此产生的物理系统，尽管如此，它们还是提供了一个了解世界以及数学与现实之间关系的机会。在此基础上，我们得出的结论是，它们的结果不会破坏在某种程度上的还原主义观点。意识强，但问题弱。