It was sort of hard to follow what exactly some of the concepts are, but I generally understood these things:
"We knew about the possibility of problems that are undecidable in principle since the works of Turing and Gödel in the 1930s," added Co-author Professor Michael Wolf from Technical University of Munich. "So far, however, this only concerned the very abstract corners of theoretical computer science and mathematical logic. No one had seriously contemplated this as a possibility right in the heart of theoretical physics before. But our results change this picture. From a more philosophical perspective, they also challenge the reductionists' point of view, as the insurmountable difficulty lies precisely in the derivation of macroscopic properties from a microscopic description."
Not all bad news
Co-author, Professor David Pérez-García from Universidad Complutense de Madrid and ICMAT, said: "It's not all bad news, though. The reason this problem is impossible to solve in general is because models at this level exhibit extremely bizarre behaviour that essentially defeats any attempt to analyse them. But this bizarre behaviour also predicts some new and very weird physics that hasn't been seen before. For example, our results show that adding even a single particle to a lump of matter, however large, could in principle dramatically change its properties. New physics like this is often later exploited in technology."
The researchers are now seeing whether their findings extend beyond the artificial mathematical models produced by their calculations to more realistic quantum materials that could be realised in the laboratory."
It's unfortunate that my own attempt to describe this in any of my own words, but I'm wondering if the problem, the spectral gap as they call it, is inherently attached to the standard model, or if the issue might be able to be addressed with another model, though it does not maintain consistency with the standard model.
Anyway, pretty weird that everything humanity has figured out so far about all of math and physic and chemistry, has led to this brilliant moment of discovering or a proof that we can't ever know.
Would also be nice to know what "quantum material" is exactly.
"Mathematically extrapolating from a microscopic description of a material to the bulk solid is considered one of the key tools in the search for materials exhibiting superconductivity at ambient temperatures or other desirable properties. A study, published today in Nature, however, shows crucial limits to this approach. Using sophisticated mathematics, the authors proved that, even with a complete microscopic description of a quantum material, determining whether it has a spectral gap is, in fact, an undecidable question."
Given that normal matter has some element of being able to describe it with macroscopic language, I wish I knew what this special superconductive quantum material is, and what it means for it to have "spectral gap."
