Many quantum gravity theories imply that the vacuum is filled with virtual black holes. This paper explores the process in which high energy photons interact with virtual black holes and decay into gravitons and photons of lower energy. The effect requires violation (or modification) of Lorentz invariance and implies that high energy photons cannot propagate over arbitrarily large distances. For the standard Planck mass and the likely form for the interaction cross section, this quantum foam limit becomes $\dist < 450$ Mpc $(\egam/10^7 {\rm GeV})^{-5}$. (Refer to PDF file for exact formula.) For quantum gravity theories that posit a lower Planck scale, the interaction rate is larger and the limit is stronger. This paper uses extant observations of gamma rays from cosmological sources to constrain this process for varying values of the Planck mass and a range of forms for the interaction cross sections.

Publication Date



This is the pre-print of an article published by Elsevier. The final, published version is located here: https://doi.org/10.1016/j.physletb.2004.01.075

© 2004 Elsevier B.V.

Also archived at: arXiv:astro-ph/0402570 v2 25 Feb 2004

This work was supported by the University of Michigan, in part through the Michigan Center for Theoretical Physics.

Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works in February 2014.

Document Type


Department, Program, or Center

School of Physics and Astronomy (COS)


RIT – Main Campus