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 AGNs .
This is a null test in the sense that the continued presence of unresolved “ point ” sources at the milli-arc second 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 GRBs 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 ( UDF ) 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 \sim 1 parametrizes the different spacetime foam models according to which the fluctuation of a distance l is given by \sim l ^ { 1 - \alpha } l _ { P } ^ { \alpha } with l _ { P } being the Planck length .
Indeed , we see a slight wavelength-dependent blurring in the UDF 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 GRB time lag observations only exclude models with \alpha < 0.3 .