“The Spectral Gap—the energy difference between the ground state and first excited state of a system—is central to quantum many-body physics,” write Toby S. Cubitt, David Perez-Garcia & Michael M. Wolf in the abstract of the paper, Undecidability of the spectral gap, published in the journal Nature (December 10, 2015).
Photo Credit: Viktoriya; Shutterstock.comSource: Science Alert
The world of quantum physics has declared one problem as mathematically unsolvable: determining whether a material has a spectral gap, which is important for material scientists looking to exploit the properties of semi-conductors. This is not saying that it is not solvable today, but that it will likely remain unsolvable or unpredictable at the microscopic level. What is predicted at the microscopic level in regards to quantum materials (like semiconductors) does not neatly translate in a predictable way to what occurs at the macroscopic level.
Or as Technische Universität München (TUM) succinctly writes about this important finding in particle and quantum physics: “The findings are important because they show that even a perfect and complete description of the microscopic properties of a material is not enough to predict its macroscopic behavior.”
The reasons focus on the very nature of quantum physics, or at least the way theoretical physicists currently understand its laws and inner workings, which is itself based on how they have historically understood it for the last century or so. In “For the first time, researchers have proved that a fundamental physics problem is actually unsolvable” (December 10, 2015), Fiona Macdonald writes in Science Alert:
Researchers have a whole lot of unanswered questions when it comes to the worlds of particle and quantum physics, but one of the most fundamental of those is going to stay that way, with scientists proving for the first time that the problem is mathematically unsolvable.
The problem in question concerns the spectral gap, which is a term for the energy required for an electron to transition from a low-energy state to an excited state. What that really means is that no matter how perfectly and completely we can mathematically describe a material on the microscopic level, we’re never going to be able to predict its macroscopic behaviour. If you listen closely, you can almost hear the dreams of physicists everywhere being shattered.
Why are spectral gaps so important? They’re a central property of semiconductors, which are crucial components of most electrical circuits, and physicists had hoped that if they'd be able to work out whether a material is superconductive at room temperature (a highly desirable trait) simply by extrapolating from a complete-enough microscopic description.
But publishing their results in Nature, an international team of scientists has now shown that determining whether a material has a spectral gap is what’s known as “an undecidable question”.This might be one of the cases where theoretical physicists “know” that a theory is true but can’t prove it, or in this case predict the future behaviour of a quantum material. It would seem that when one is working in the world of quantum theory, it has an otherworldly aspect to it. It would appear that there is much to Einstein’s claim of “spooky action at a distance.”
Yet, such inexplicable behaviour ought not spell defeat, but rather might eventually lead to a new or a more fuller understanding of the universe. This is what happened 50 years ago with Arno Penzias and Robert Wilson, whose discovery of Cosmic Microwave Background, or CMB, supported the Big Bang theory of the origin of the universe.
For more, go to [ScienceAlert]