Is the Spectral Gap Problem in Quantum Mechanics Undecidable?

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In summary, there is a group of researchers who have found a paradox at the heart of mathematics that makes it impossible to answer a fundamental physics problem known as the spectral gap problem in general. This problem arises from Godel's proof, which states that there will always be undecidable statements in any system of logic, rendering our mathematical predictions incomplete. This has implications for condensed matter physics and raises questions about the limitations of our understanding of quantum mechanics.
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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...
 

1. What is an undecidable problem in quantum mechanics?

An undecidable problem in quantum mechanics is a problem that cannot be solved or proven to be true or false using the laws and principles of quantum mechanics. This means that the answer to the problem cannot be determined with certainty.

2. How is an undecidable problem different from a regular problem in quantum mechanics?

An undecidable problem is different from a regular problem in quantum mechanics because a regular problem can be solved using the principles and equations of quantum mechanics, while an undecidable problem cannot be solved in the same way.

3. Can we ever find a solution to an undecidable problem in quantum mechanics?

No, we cannot find a solution to an undecidable problem in quantum mechanics because it is fundamentally impossible to do so using the principles and laws of quantum mechanics. It is a limitation of our current understanding of the quantum world.

4. Why are undecidable problems important in quantum mechanics?

Undecidable problems are important in quantum mechanics because they highlight the limitations of our current understanding of the quantum world. They also push scientists to continue exploring and expanding our knowledge of quantum mechanics.

5. Can undecidable problems be solved using other methods or principles?

Undecidable problems in quantum mechanics cannot be solved using the principles and laws of quantum mechanics, but they may be solvable using other methods or principles from fields such as computer science or mathematics. However, this has not yet been proven to be possible.

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