Abstract
This review consists of two parts. The first part establishes certain astrophysical bounds on the smoothness of classical spacetime.Some of the best bounds to date are based on the absence of vacuum Cherenkov radiation in ultrahigh‐energy cosmic rays. The second part discusses possible implications of these bounds for the quantum structure of spacetime. One conjecture is that the fundamental length scale of quantum spacetime may be different from the Planck length.
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