Limits on spacetime foam

Plausibly spacetime is foamy on small distance scales, due to quantum fluctuations. We elaborate on the proposal to detect spacetime foam by looking for seeing disks in the images of distant quasars and active galactic nuclei. This is a null test in the sense that the continued presence of unresolved point sources at the milliarcsecond level in samples of distant compact sources puts severe constraints on theories of quantized spacetime foam at the Planckian level. We discuss the geometry of foamy spacetime, and the appropriate distance measure for calculating the expected angular broadening. We then deal with recent data and the constraints they put on spacetime foam models. While time lags from distant pulsed sources such as gamma ray bursts have been posited as a possible test of spacetime foam models, we demonstrate that the time-lag effect is rather smaller than has been calculated, due to the equal probability of positive and negative fluctuations in the speed of light inherent in such models. Thus far, images of high-redshift quasars from the Hubble ultra-deep field provide the most stringent test of spacetime foam theories. While random-walk models (alpha = 1/2) have already been ruled out, the holographic (alpha = 2/3) model remains viable. Here alpha similar to 1 parametrizes the different spacetime foam models according to which the fluctuation of a distance l is given by similar to l(1-alpha)l(P)(alpha) with l(P) being the Planck length. Indeed, we see a slight wavelength-dependent blurring in the ultra-deep field images selected for this study. Using existing data in the Hubble Space Telescope (HST) archive we find it is impossible to rule out the alpha = 2/3 model, but exclude all models with alpha < 0.65. By comparison, current gamma ray burst time-lag observations only exclude models with alpha < 0.3.