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The universal path integral

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Abstract

Path integrals calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration. This paper defines a universal path integral, which sums over all computable structures. This path integral contains as sub-integrals all possible computable path integrals, including those of field theory, the standard model of elementary particles, discrete models of quantum gravity, string theory, etc. The universal path integral possesses a well-defined measure that guarantees its finiteness. The probabilities for events corresponding to sub-integrals can be calculated using the method of decoherent histories. The universal path integral supports a quantum theory of the universe in which the world that we see around us arises out of the interference between all computable structures.

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Acknowledgments

This work was supported by the W.M. Keck Center for Extreme Quantum Information Theory (xQIT), DARPA, ARO under a MURI program, NSF, ENI via the MIT Energy Initiative, Lockheed Martin, Intel, Jeffrey Epstein, and by FQXi. The authors would like to thank Janna Levin and Max Tegmark for helpful discussions.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Seth Lloyd

  2. Kimbernstieg 26, 22455, Hamburg, Germany

    Olaf Dreyer

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  1. Seth Lloyd
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  2. Olaf Dreyer
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Correspondence to Seth Lloyd.

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Lloyd, S., Dreyer, O. The universal path integral. Quantum Inf Process 15, 959–967 (2016). https://doi.org/10.1007/s11128-015-1178-7

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  • DOI: https://doi.org/10.1007/s11128-015-1178-7

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