  Gamma-Ray Bursts have been observed out to very high redshifts and provide
time measures that are directly related to intrinsic time scales of the burst.
Einstein's theory of relativity is quite definite that if the universe is
expanding then the observed duration of these measures will increase with
redshift. Thus gamma-ray burst measures should show a time dilation
proportional to redshift. An analysis of gamma-ray burst data shows that the
hypothesis of time dilation is rejected with a probability of
4.4$\times10^{-6}$ for redshifts out to z=6.6. Traditionally the lack of an
apparent time dilation has been explained by an inverse correlation between
luminosity and time measures together with strong luminosity selection as a
function of redshift. It is shown that the inverse correlation between
luminosity and some time measures is confirmed, but using concordance cosmology
strong luminosity selection cannot be achieved. It may be possible to explain
the apparent lack of time dilation with a combination of gamma-ray burst
selection, some luminosity evolution and some time measure evolution. But this
requires a remarkable coincidence in order to produce the apparent lack of time
dilation. However the data are consistent with a static cosmology in a
non-expanding universe.
