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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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