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Published September 15, 2014 | Published
Journal Article Open

Photons with sub-Planckian energy cannot efficiently probe space-time foam

Abstract

Extra-galactic sources of photons have been used to constrain space-time quantum fluctuations in the Universe. In these proposals, the fundamental "fuzziness" of distance caused by space-time quantum fluctuations has been directly identified with fluctuations in optical paths. Phase-front corrugations deduced from these optical-path fluctuations are then applied to light from extra-galactic point sources, and used to constrain various models of quantum gravity. However, when a photon propagates in three spatial dimensions, it does not follow a specific ray, but rather samples a finite, three-dimensional region around that ray—thereby averaging over space-time quantum fluctuations all through that region. We use a simple, random-walk type model to demonstrate that, once the appropriate wave optics is applied, the averaging of neighboring space-time fluctuations will cause much less distortion to the phase front. In our model, the extra suppression factor due to diffraction is the wave length in units of the Planck length, which is at least 10^(29) for astronomical observations.

Additional Information

© 2014 American Physical Society. Received 23 October 2013; Published 24 September 2014. The authors would like to thank D. G. Blair, Z. Cai, X. Fan, H. Nikolai, and C. Zhao for helpful discussions. We thank Ning Jiang for this help in calculating the background of quasar PG2112 þ 059. Y. C. and L.W. were supported by the Alexander von Humboldt Foundation's Sofja Kovalevskaja Programme (funded by the German Federal Ministry of Education and Research). We also thank Dr. Ron Burman for reading the manuscript. Y. C. is currently supported by NSF Grant No. PHY-1068881 and CAREER Grant No. PHY-0956189. L.W. acknowledges funding supports from the Australian Research Council. Y. M. is currently supported by the Australian Department of Education, Science and Training.

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Published - PhysRevD.90.063011.pdf

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