An Incompleteness Theorem for Calculating the Future
David H. Wolpert · 1996
: This paper proves that one can not build a computer which can, for any physical system, take the specification of that system's state as input and then correctly predict its future state before that future state actually occurs. Loosely speaking, this means that one can not build a physical computer which can be assured of "processing information faster than the universe". This result holds even if one restricts one's attention to predicting the states of systems which are finite, purely classical, and obey dynamics which is not chaotic, and even if one uses an infinitely fast, infinitely dense computer. 2 INTRODUCTION Recently there has been heightened interest in the relationship between physics and computation ([1-22]). On the one hand, physics has been used to investigate the limits on computation imposed by operating computers in the real physical universe. Conversely, there has been speculation concerning the limits imposed on the physical universe (or at least imposed on our...