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 behavior of quantum materials, and potentially even fundamental particle physics."

Learn more
here.

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