The Computational Power of Minkowski Spacetime

The Lorentzian length of a timelike curve connecting both endpoints of a classical computation is a function of the path taken through Minkowski spacetime. The associated runtime difference is due to time-dilation: the phenomenon whereby an observer finds that another’s physically identical ideal clock has ticked at a different rate than their own clock. Using ideas appearing in the framework of computational complexity theory, time-dilation is quantified as an algorithmic resource by relating relativistic energy to an nth order polynomial time reduction at the completion of an observer’s journey. These results enable a comparison between the optimal quadratic Grover speedup from quantum computing and an n = 2 speedup using classical computers and relativistic effects. The goal is not to propose a practical model of computation, but to probe the ultimate limits physics places on computation.