Undecidability of the Spectral Gap (full version) · HackerPapers discussions

Undecidability of the Spectral Gap (full version) — mentioned by markisus

Sat, 08 Mar 2025 13:38:01 GMT

Here is a free updated version from 2022. https://arxiv.org/pdf/1502.04573 Edit: Alright, I'm back after skimming the paper. This is a halting oracle. Here is what I understand, with my limited knowledge of QM. There are two ingredients (Theorem 3: Main Theorem, page 6). 1. For each integer n, the authors construct a spin lattice model H(n). 2. There is a specific Universal Turing Machine, that halts on n iff H(n) is gapped. Here is how to construct the oracle. For any Turing machine, find out what integer n it corresponds to for the specific Universal Turing Machine of the paper. Then…

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Undecidability of the Spectral Gap (full version) — mentioned by wardedVibe

Thu, 23 Nov 2023 23:22:56 GMT

So the most physically grounded example I know of is the undecidability of some spectral gaps[0] (is there a discrete jump between the ground state and the excited states), which as far as I can tell doesn't rely on self-reference. [0]: https://arxiv.org/pdf/1502.04573.pdf

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Undecidability of the Spectral Gap (full version) — mentioned by poelzi

Fri, 03 Jun 2016 17:32:44 GMT

Like many stuff in theoretical physics - hey, most of the physical model is rather unlikely. They not even have a proper arrow of time in the standard model nor can they predict the spectral gap with certainty along a long list of problems. https://arxiv.org/abs/1502.04573 But you know, changing paradigms is a slow process and physicists have been shown to be the slowest to accept new things, especially multidisciplinary theories/findings: http://www.pnas.org/content/112/24/7426.full Which confirms my contact experience with many of them - not all of course :)

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Undecidability of the Spectral Gap (full version) — mentioned by swehner

Thu, 10 Dec 2015 23:17:15 GMT

I can't tell how much of this is "quantum physics" and how much is "mathematical theory that also arises in quantum physics". As in, I doubt their construction allows "building something" which then allows solving a conventionally unsolvable problem. With new physics you may be able to build machines that can compute more; however I don't think they are talking about such physics here. But, they do quote: Marian B. Pour-El and Jonathan I. Richards. Computability in Analysis and Physics. Springer, 1989. M. B. Pour-El and J. Richards have earlier results…

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Undecidability of the Spectral Gap (full version) — mentioned by fspeech

Thu, 10 Dec 2015 17:02:00 GMT

Thanks! The companion comment also provides a link to the non-paywalled and full arxiv version: http://arxiv.org/abs/1502.04573

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Undecidability of the Spectral Gap (full version) — mentioned by mathgenius

Thu, 10 Dec 2015 07:27:42 GMT

Long version: http://arxiv.org/abs/1502.04573 Short version: http://arxiv.org/abs/1502.04135

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Undecidability of the Spectral Gap (full version) — HN submission

Tue, 01 Dec 2015 18:05:36 GMT

Quantum mechanics is undecidable ()

1 point; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.