# Limits on Spacetime Foam - Astrophysics > Cosmology and Nongalactic Astrophysics

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Abstract: Plausibly spacetime is -foamy- on small distance scales, due to quantumfluctuations. We elaborate on the proposal to detect spacetime foam by lookingfor seeing disks in the images of distant quasars and AGNs. This is a null testin the sense that the continued presence of unresolved -point- sources at themilli-arc second level in samples of distant compact sources puts severeconstraints on theories of quantized spacetime foam at the Planckian level. Wediscuss the geometry of foamy spacetime, and the appropriate distance measurefor calculating the expected angular broadening. We then deal with recent dataand the constraints they put on spacetime foam models. While time lags fromdistant pulsed sources such as GRBs have been posited as a possible test ofspacetime foam models, we demonstrate that the time-lag effect is rathersmaller than has been calculated, due to the equal probability of positive andnegative fluctuations in the speed of light inherent in such models. Thus far,images of high-redshift quasars from the Hubble Ultra-Deep Field UDF providethe 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 spacetimefoam 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 forthis study. Using existing data in the {\it Hubble Space Telescope HST}archive we find it is impossible to rule out the $\alpha=2-3$ model, butexclude all models with $\alpha<0.65$. By comparison, current GRB time lagobservations only exclude models with $\alpha<0.3$.

Author: ** Wayne A. Christiansen, David J. E. Floyd, Y. Jack Ng, Eric S. Perlman**

Source: https://arxiv.org/