Mimicking within Euclidean space a cosmological time dilation of gamma-ray burst durations

If gamma-ray burst sources are cosmological in origin, then the time dilation at large z can correlate a burst's duration with its peak flux. Detection of this effect is thought by many to be strong evidence for a cosmological burst origin. In this Letter I show that an apparent time distortion--either a dilation or contraction--is generally expected for an ensemble of bursts that is spatially limited within Euclidean space. The appearance of this effect is correlated with the falling away of the log N-log P curve from a -3/2 slope line. An example of this effect is provided by the relativistic bulk motion model, which produces a strong time dilation when spatially limited in Euclidean space. As a consequence, envidence that weak bursts have longer durations than strong bursts is not evidence of a cosmological burst origin.