Why Some Physicists Are Excited About the Undecidability of the Spectral Gap Problem and Why Should We
Владик Крейнович · scholarworks - UTEP (The University of Texas at El Paso) · 2017
Since Turing's time, many problems have been proven undecidable. It is interesting though that, arguably, none of the working physicist problems had been ever proven undecidable -- until T. Cubitt, D. Perez-Garcia and M. M. Wolf proved recently that, for a physically reasonable class of systems, no algorithm can decide whether a given system has a spectral gap. We explain the spectral gap problem, its importance for physics and possible consequences of this exciting new result.