Skip to main content

Quantum physics problem proved unsolvable

Quantum physics problem proved unsolvable

(Nanowerk News) A mathematical problem underlying fundamental questions in particle and quantum physics is provably unsolvable, according to scientists at UCL, Universidad Complutense de Madrid – ICMAT and Technical University of Munich (Nature, "Undecidability of the spectral gap"). It is the first major problem in physics for which such a fundamental limitation could be proven. 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.
A small spectral gap – the energy needed to transfer an electron from a low-energy state to an excited state – is the central property of semiconductors. In a similar way, the spectral gap plays an important role for many other materials. When this energy becomes very small – i.e. the spectral gap closes – it becomes possible for the material to transition to a completely different state. An example of this is when a material becomes superconducting.
High-temperature superconductor cooled with liquid nitrogen. The prediction if and when a material becomes superconducting depends decisively on whether excitations require energy or not. However, a prediction of that property is more difficult than imagined, as an underlying mathematical problem has proven to be unsolvable in principle. (Image: Ulli Benz / TUM)
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.
“Alan Turing is famous for his role in cracking the Enigma code,” says Co-author, Dr. Toby Cubitt from UCL Computer Science. “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.”
One million dollars to win!
The most famous problem concerning spectral gaps is whether the theory governing the fundamental particles of matter itself – the standard model of particle physics – has a spectral gap (the `Yang-Mills mass gap' conjecture). Particle physics experiments such as CERN and numerical calculations on supercomputers suggest that there is a spectral gap. Although there is a $1m prize at stake from the Clay Mathematics Institute for whoever can, no one has yet succeeded in proving this mathematically from the equations of the standard model.
Dr. Cubitt added, “It's possible for particular cases of a problem to be solvable even when the general problem is undecidable, so someone may yet win the coveted $1m prize. But our results do raise the prospect that some of these big open problems in theoretical physics could be provably unsolvable.”
"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 behavior that essentially defeats any attempt to analyze them. But this bizarre behavior 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 realized in the laboratory.
Source: Technical University of Munich

Read more: Quantum physics problem proved unsolvable

Popular posts from this blog

Hidden Wiki

Welcome to The Hidden WikiNew hidden wiki url 2015 http://zqktlwi4fecvo6ri.onion Add it to bookmarks and spread it!!!
Editor's picks Bored? Pick a random page from the article index and replace one of these slots with it.
The Matrix - Very nice to read. How to Exit the Matrix - Learn how to Protect yourself and your rights, online and off. Verifying PGP signatures - A short and simple how-to guide. In Praise Of Hawala - Anonymous informal value transfer system. Volunteer Here are five different things that you can help us out with.
Plunder other hidden service lists for links and place them here! File the SnapBBSIndex links wherever they go. Set external links to HTTPS where available, good certificate, and same content. Care to start recording onionland's history? Check out Onionland's Museum Perform Dead Services Duties. Introduction - Clearnet search engine for Tor Hidden Services (allows you to add new sites to its database). DuckDuckGo - A Hidden S…


Good News [May 08, 2015]: IDM developers got smarter, but the crackers are always a step ahead. Follow this article and send an email to if you are desperate. I can NOT post any crack here for legal reasons. Happy Downloading with IDM. ;) *********** first tip is to use latest crack for idm from idm universal web crack and make sure u are using all latest vers I am sure many of us are too much dependent on Internet Download Manager a.k.a. IDM. The main reason didn’t permanently switch to linux was IDM. I mainly use it for batch downloading and download streaming videos. Till yesterday, IDM was working fine with me (of course with fake serial numbers, keygen, crack, patch etc. which could be found with little effort). But few days ago, with the latest update version 6.18 build 7 (released on Nov 09, 2013) Internet Download Manager was literally had a breakthrough and crushed all the serial numbers, …

DoubleAgent Attack Turns Your Antivirus Into Malware And Hijacks Your PC

Short Bytes: Cybellum security researchers have uncovered a new attack mechanism that can be used to take control of your antivirus and turn it into a malware. Called DoubleAgent, this attack exploits an old and undocumented vulnerability in Windows operating system. This Zero Day code injection technique affects all major antivirus vendors and has the power to hijack permissions. The security researchers from Cybellum have found a new technique that can be used by the cybercriminals to hijack your computer by injecting malicious code. This new Zero-Day attack can be used to take full control over all the major antivirus software. Instead of hiding from the antivirus, this attack takes control of the antivirus itself. Called DoubleAgent, this attack makes use of a 15-year-old legitimate feature of Windows (read vulnerability)–that’s why it can’t be patched. It affects all versions of Microsoft Windows. Cybellum blog mentions that this flaw is still unpatched by most antivirus v…