When Causality Is Relaxed: Classical Correlations, Computation, and Time Travel

          @misc{ pirsa_PIRSA:18040106,
            doi = {10.48660/18040106},
            url = {https://pirsa.org/18040106},
            author = {Baumeler, Aemin},
            keywords = {Quantum Foundations},
            language = {en},
            title = {When Causality Is Relaxed: Classical Correlations, Computation, and Time Travel},
            publisher = {Perimeter Institute},
            year = {2018},
            month = {apr},
            note = {PIRSA:18040106 see, \url{https://pirsa.org}}
          }
          

Abstract

Following Stefan Wolf’s talk, we address the doubts expressed on fundamental space-time causality. Usually it is assumed that causal structures represent a definite partial ordering of events. By relaxing that notion one risks problems of logical nature. Yet, as we show, there exists a logically consistent world beyond the causal, even in the classical realm where quantum theory is not invoked. We explore the classical correlations within and the computational limits of that world. It turns out that relaxing causality in that fashion does not allow for efficient computation of NP-hard problems. These results are related to closed time-like curves: Contrary to previous models of time travel, which necessitate quantum theory and violate the NP-hardness assumption, we obtain a computationally tame model for classical and reversible time travel where freedom of choice is unrestricted.