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Quantum Gravity, Information Theory and the CMB

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Abstract

We review connections between the metric of spacetime and the quantum fluctuations of fields. We start with the finding that the spacetime metric can be expressed entirely in terms of the 2-point correlator of the fluctuations of quantum fields. We then discuss the open question whether the knowledge of only the spectra of the quantum fluctuations of fields also suffices to determine the spacetime metric. This question is of interest because spectra are geometric invariants and their quantization would, therefore, have the benefit of not requiring the modding out of diffeomorphisms. Further, we discuss the fact that spacetime at the Planck scale need not necessarily be either discrete or continuous. Instead, results from information theory show that spacetime may be simultaneously discrete and continuous in the same way that information can. Finally, we review the recent finding that a covariant natural ultraviolet cutoff at the Planck scale implies a signature in the cosmic microwave background (CMB) that may become observable.

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Notes

  1. Technically, in Shannon’s theorem, a bandlimited signal is assumed to obey Dirichlet boundary conditions in the Fourier domain. A conventional lattice theory implements periodic boundary conditions in the Fourier domain.

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Correspondence to Achim Kempf.

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This work has been supported by the Discovery Program of the National Science and Engineering Research Council of Canada (NSERC).

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Kempf, A. Quantum Gravity, Information Theory and the CMB. Found Phys 48, 1191–1203 (2018). https://doi.org/10.1007/s10701-018-0163-2

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