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Severe Limits on Variations of the Speed of Light with Frequency.pdf

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Severe Limits on Variations of the Speed of Light with Frequency

a r X i v : a s t r o - p h / 9 8 1 0 4 7 9 v 1 2 9 O c t 1 9 9 8 Severe Limits on Variations of the Speed of Light with Frequency Bradley E. Schaefer Physics Department, Yale University, PO Box 208121, New Haven CT 06520-8121 schaefer@grb2.physics.yale.edu (February 1, 2008) Explosive astrophysical events at high red shift can be used to place severe limits on the fractional variation in the speed of light (?c/c), the photon mass (mγ), and the energy scale of quantum gravity (EQG). I find ?c/c 6.3× 10?21 based on the simultaneous arrival of a flare in GRB 930229 with a rise time of 220 ± 30μs for photons of 30 keV and 200 keV. The limit on mγ is 4.2 × 10 ?44g for GRB 980703 from radio to gamma ray observations. The limit on EQG is 8.3× 10 16 GeV for GRB 930131 from 30 keV to 80 MeV photons. The question of whether the speed of light varies with frequency is of fundamental and current interest: 1) Einstein’s postulate of the invariance of light is the cornerstone of much of modern physics, so tests of the correctness of this postulate should be pushed as far as possible. 2) With the recent evidence from Super-Kamiokande that the neutrino likely has a mass [1], the question of the mass of the photon should be re-examined. 3) Quantum gravity models suggest [2] [3] that the speed of light has an effective energy dependence. Classical textbooks [4] and review articles [5] report the status as of the middle 1970’s. Laboratory and accelerator experiments were not able test for fractional variations in the speed of light (?c/c) to better than roughly 10?8. The first limit that took advantage of astronomical distances compared the arrival time of radio and optical emission from flare stars to constrain ?c/c 10?6 [6]. Then B. Warner and R. Nather measured the phase difference for pulses of the Crab Pulsar between optical wavelengths of 0.35 and 0.55 microns 1 to be less than 10 microseconds [7]. At a distance of 2 kpc, this limits ?c/c to be less than 5× 10?17. Surpri