Is the Spectral Gap Problem in Quantum Mechanics Undecidable?

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The spectral gap problem in quantum mechanics (QM) is identified as an undecidable issue, meaning that mathematical frameworks may not always predict the behavior of quantum systems. Researchers emphasize that while mathematical models are incomplete, nature inherently resolves these uncertainties. This conclusion aligns with Gödel's incompleteness theorems, which state that within any logical system, there exist propositions that cannot be definitively proven true or false. The implications of this finding challenge the predictability of quantum mechanics.

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andresB
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There is a group of researchers that say that there is a problem in QM (the spectral gap problem) that is undecidable in generalhttp://www.nature.com/news/paradox-...-unanswerable-1.18983?WT.mc_id=TWT_NatureNews
http://www.nature.com/nature/journal/v528/n7581/full/nature16059.htmlI'm finding it very interesting, but my grasp of condensed matter physics and Gödel theory is limited so I'm unsude. it would be great if anyone can explain to me what the result actually is.
 
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There is aleady a thread on this paper here:

https://www.physicsforums.com/threads/spectral-gap-or-gapless-undecidable.847554/

The simple answer is that our math won't always able to predict what happens to a QM given system of particles. However, nature will know what to do and so our math is incomplete.

Godel's proof showed that in any given system of logic there will always be some statements which cannot be proven true or false and so are undecidable statements.

http://www.scientificamerican.com/article/what-is-godels-theorem/

Closing thread...
 

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