10,615 research outputs found

    What Pedro could do

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    This paper discusses Bernard Williams's famous case of Jim and the Indians. It contrasts two ways of diagnosing the alleged errors of Act Utilitarianism in considering this case. One approach suggests that Act Utilitarianism fails to appreciate the importance of what Jim does; it fails to understand the significance of Jim's agency. This paper favours an alternative diagnosis, according to which Act Utilitarianism fails to appreciate the importance of what Pedro could do; it fails to understand the significance of Pedro's agency

    Linearized Weyl-Weyl Correlator in a de Sitter Breaking Gauge

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    We use a de Sitter breaking graviton propagator to compute the tree order correlator between noncoincident Weyl tensors on a locally de Sitter background. An explicit, and very simple result is obtained, for any spacetime dimension D, in terms of a de Sitter invariant length function and the tensor basis constructed from the metric and derivatives of this length function. Our answer does not agree with the one derived previously by Kouris, but that result must be incorrect because it not transverse and lacks some of the algebraic symmetries of the Weyl tensor. Taking the coincidence limit of our result (with dimensional regularization) and contracting the indices gives the expectation value of the square of the Weyl tensor at lowest order. We propose the next order computation of this as a true test of de Sitter invariance in quantum gravity.Comment: 31 pages, 2 tables, no figures, uses LaTex2

    A Lower Bound on the Mixing Time of Uniformly Ergodic Markov Chains in Terms of the Spectral Radius

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    We give a bound on the mixing time of a uniformly ergodic, reversible Markov chain in terms of the spectral radius of the transition operator. This bound has been established previously in finite state spaces, and is widely believed to hold in general state spaces, but a proof has not been provided to our knowledge

    Some Inconvenient Truths

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    A recent paper by Fr\"ob employs the linearized Weyl-Weyl correlator to construct the tensor power spectrum. Although his purpose was to argue that infrared divergences and secular growth in the graviton propagator are gauge artefacts, a closer examination of the problem leads to the opposite conclusion. The analogies with the BMS symmetries of graviton scattering on a flat background, and with the Aharonov-Bohm effect of quantum mechanics, suggest that de Sitter breaking secular growth is likely to be observable in graviton loop effects. And a recent result for the vacuum polarization does seem to show it.Comment: 14 pages, uses LaTeX2
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