  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
$n$th order polynomial time reduction at the completion of an observer's
journey. These results enable a comparison between the optimal quadratic
\emph{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.
