The Computational Power of Minkowski Spacetime

Jacob D. Biamonte

doi:10.1088/1742-6596/229/1/012020

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arXiv · 0907.1579

The Computational Power of Minkowski Spacetime

Jacob D. Biamonte

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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.

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BibTeX RIS

Jacob D. Biamonte. 2009-07-09. The Computational Power of Minkowski Spacetime. https://doi.org/10.1088/1742-6596%2F229%2F1%2F012020

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