The Computational Power of Minkowski Spacetime

TL;DR

This paper explores how relativistic effects like time-dilation in Minkowski spacetime can be viewed as computational resources, comparing classical, quantum, and relativistic computational limits.

Contribution

It introduces a framework relating relativistic energy and time-dilation to computational complexity, revealing fundamental physics limits on computation.

Findings

Time-dilation quantified as an algorithmic resource.

Relativistic effects can enable classical speedups comparable to quantum algorithms.

Provides a theoretical comparison between quantum and relativistic classical computation speeds.

Abstract

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.