Judaism and Science

A mathematical problem underlying fundamental questions in particle and quantum physics is provably unsolvable, according to an online report on phys.org December 9, 2015. 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 make a phase 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 (12/9/15) 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. read more