Quantum physics problem proved unsolvable

A mathematical problem underlying fundamental questions in particle physics and quantum physics is provably unsolvable, according to scientists at UCL, Universidad Complutense de Madrid - ICMAT and Technische Universität München. The findings show that even a perfect and complete description of the microscopic properties of a material is not enough to predict its macroscopic behaviour. The study investigated the problem of the 'spectral gap' - the energy needed for a material to transfer from its lowest-energy state to an excited state. 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 and the properties of the material can undergo dramatic changes. For example, when a material at a very low temperature transitions from insulating to superconducting, this dramatic change is the result of its spectral gap closing. 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 an 'undecidable' question.