Computation and Spacetime Structure
Mike Stannett
We investigate the relationship between computation and spacetime structure, focussing on the role of closed timelike curves (CTCs) in promoting computational speedup. We note first that CTC traversal can be interpreted in two distinct ways, depending on ones understanding of spacetime. Focussing on one interpretation leads us to develop a toy universe in which no CTC can be traversed by a computer more than once, whence no direct computational speedup is possible. Focussing on the second (and more standard) interpretation leads to the surprising conclusion that CTCs may act as perfect information repositories: just as black holes have entropy, so do CTCs. If we also assume P = NP, we find that all observers agree that, even if unbounded time travel existed in their youth, this capability eventually vanishes as they grow older. Thus the computational assumption P = NP is also an assumption concerning cosmological structure.