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For The First Time, Researchers Have Proved That A Fundamental Physics Problem Is Actually Unsolvable

When it comes to the realm of particle and quantum physics, physicists have a whole lot of unanswered questions but one of the most essential of those is going to stay that way, with researchers proving for the first time that the problem is mathematically unsolvable. So the problem in question is related to the spectral gap, which is a term used for the energy required for an electron to transition from a low-energy state to an excited state. What that truly means is that no matter how perfectly and totally we can mathematically define a material on the microscopic level, we're never going to be able to forecast its macroscopic behavior. If you listen closely, you can almost hear the dreams of physicists everywhere being shattered.
Image SourceL Viktoriya/Shutterstock.com

Spectral gaps are important because they're a vital property of semiconductors, which are essential components of most electrical circuits, and physicists had expected that if they'd be able to work out whether a material is superconductive at room temperature (a highly desirable trait) merely by inducing from a complete-enough microscopic depiction.  But distributing their outcomes in Nature, an international group of scientists has now revealed that defining whether a material has a spectral gap is what's known as "an undecidable question".

One of the scientists, Toby Cubitt from University College London in the UK, said "Alan Turing is famous for his role in cracking the Enigma code. But amongst mathematicians and computer scientists, he is even more famous for proving that certain mathematical questions are 'undecidable' - they are neither true nor false, but are beyond the reach of mathematics,"

"What we've shown is that the spectral gap is one of these undecidable problems. This means a general method to determine whether matter described by quantum mechanics has a spectral gap, or not, cannot exist. Which limits the extent to which we can predict the behaviour of quantum materials, and potentially even fundamental particle physics."

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