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Speed of light in non-trivial vacua
Affiliation:1. Institute of Theoretical and Experimental Physics, B. Cheremushkinskaya 25, 117259 Moscow, Russia;2. Bogoliubov Laboratory for Theoretical Physics, JINR, 141980 Dubna, Russia;3. North Carolina Central University, 1801 Fayetteville Street, Durham, NC 27707, USA;4. Institute for Computer Aided Design of RAS, 123056, Moscow, Russia;5. National Research Nuclear University (NRNU MEPHI), 115409, Moscow, Russia;6. Atomic Physics Laboratory (040), Vinča Institute of Nuclear Sciences, University of Belgrade, P.O. Box 522, 11001 Belgrade, Serbia;7. Astronomical Observatory, Volgina 7, 11060 Belgrade, Serbia;1. Department of Biostatistics and Bioinformatics, Duke University School of Medicine, Durham, NC 27705, United States;2. Department of Biostatistics, University of Michigan, Ann Arbor, MI 48109, United States;1. Physics Division, National Center for Theoretical Science, Hsinchu 30010, Taiwan;2. Institute of Physics, National Chiao Tung University Hsinchu 30010, Taiwan;3. Department of Physics, National Tsing Hua University Hsinchu 30010, Taiwan
Abstract:We unify all existing results on the change of the speed of low-energy photons due to modifications of the vacuum, finding that it is given by a universal constant times the quotient of the difference of energy densities between the usual and modified vacua over the mass of the electron to the fourth power. Whether photons move faster or slower than c depends only on the lower or higher energy density of the modified vacuum, respectively. Physically, a higher energy density is characterized by the presence of additional particles (real or virtual) in the vacuum whereas a lower one stems from the absence of some virtual modes. We then carry out a systematic study of the speed of propagation of massless particles for several field theories up to two loops on a thermal vacuum. Only low-energy massless particles corresponding to a massive theory show genuine modifications of their speed while remaining massless. All other modifications are mass related, or running mass-related. We also develop a formalism for the Casimir vacuum which parallels the thermal one and check that photons travel faster than c between plates.
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