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Gamma-ray burst time histories often consist of many peaks. These peaks tendto be narrower at higher energy. If gamma-ray bursts are cosmological, theenergy dependence of gamma-ray burst time scales must be understood in order tocorrect the time scale dependence due to the expansion of the universe. Byusing the average autocorrelation function and the average pulse width, we showthat the narrowing with energy follows, quite well, a power law. The power lawindex is about -0.4. This is the first quantitative relationship betweentemporal and spectral structure in gamma-ray bursts. It is unclear what physicscauses this relationship. The average autocorrelation has a universal shapesuch that one energy range scales linearly with time into all other energyranges. This shape is approximately the sum of two exponential.Comment: 19 pages plus figures, uuencoded tar compressed Postscript. Submitted  for publication. Also available in Postscript format at  ftp://sstcx1.lanl.gov/pub/grb/energy_stretch.p

Gamma-Ray Burst Peak Duration as a Function of Energy