Quantum physics problem proved unsolvable: Godel and Turing enter quantum physics

[davidm]

This is interesting.

Quantum physics problem proved unsolvable: Godel and Turing enter quantum...

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 behaviour.

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.

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,” said 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 behaviour of quantum materials, and potentially even fundamental particle physics.”

I don’t know a lot about quantum physics but I do know a little about undecidability from my computer science courses. As far as I know it’s always been a subject of interest in mathematics and computer science but up till now hasn’t manifested itself in the natural sciences. Note that this isn’t chaos theory, which does make many natural phenomena unpredictable in practice but at least predictable in theory.

I’m pretty sure it’s also not quantum uncertainty, where there simply is no answer until the process has played itself out. Undecidable problems do have an answer, just one that cannot be arrived at mathematically.

Now someone more knowledgeable than me will come along and point out that I’m completely wrong.

[Morgenstern]

@davidm

…
Now someone more knowledgeable than me will come along and point out that I’m completely wrong.

It appears you are wrong about that.

[WordMan]

@davidm

This is interesting.
Quantum physics problem proved unsolvable: Godel and Turing enter quantum physics
I don’t know a lot about quantum physics but I do know a little about undecidability from my computer science courses. As far as I know it’s always been a subject of interest in mathematics and computer science but up till now hasn’t manifested itself in the natural sciences. Note that this isn’t chaos theory, which does make many natural phenomena unpredictable in practice but at least predictable in theory.

I’m pretty sure it’s also not quantum uncertainty, where there simply is no answer until the process has played itself out. Undecidable problems do have an answer, just one that cannot be arrived at mathematically.

Now someone more knowledgeable than me will come along and point out that I’m completely wrong.

This was just discussed on BBC America and an English physicist did cite Schrodinger’s Cat as an example of unknowability.

I can’t comment because I don’t know this stuff, but am an interested layman. I assume it relates to Godel’s Set Theory, in that there is something ambiguous at the root of something we assumed would be concrete.

Physics seems to be an inexorable process of kicking our assumptions out from under us. Time doesn’t function as an objective substrate to our reality; it is relative and part of space-time. Who knew? And with Dark Matter, the Higgs Boson, Quantum Entanglement and such, it seems there is a lot of to be done to update our theories. But at the core of whatever we figure out there will always be ambiguities that can’t be resolved or truly known.

Whoa.