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.

Undecidability of the spectral gap: an epistemological look / Ippoliti, Emiliano; Caprara, Sergio. - In: JOURNAL FOR GENERAL PHILOSOPHY OF SCIENCE. - ISSN 0925-4560. - 52:1(2021), pp. 157-170. [10.1007/s10838-020-09549-9]

Undecidability of the spectral gap: an epistemological look

Emiliano Ippoliti
Primo
;
Sergio Caprara
Secondo
2021

Abstract

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.
2021
undecidability; physics; philosophy; logic; methods
01 Pubblicazione su rivista::01a Articolo in rivista
Undecidability of the spectral gap: an epistemological look / Ippoliti, Emiliano; Caprara, Sergio. - In: JOURNAL FOR GENERAL PHILOSOPHY OF SCIENCE. - ISSN 0925-4560. - 52:1(2021), pp. 157-170. [10.1007/s10838-020-09549-9]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1508732
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