Why Some Physicists Are Excited About the Undecidability of the Spectral Gap Problem and Why Should We

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

6-2017

Comments

Technical Report: UTEP-CS-17-69

Published in Bulletin of the European Association for Theoretical Computer Science, 2017, Vol. 122, pp. 100-113.

Abstract

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.