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 lowenergy 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

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."
Learn more here.