Some galaxies are very luminous in the radio part of the spectrum. These ＇radio galaxies＇ have extensive (hundreds of kiloparsecs) lobes of emission powered by plasma jets originating at a central black hole(1). Some radio galaxies can be seen at very high redshifts(2), where in principle they can serve as probes of the early evolution of the Universe. Here we show that, for any model of radio-galaxy evolution in which the luminosity decreases with time after an initial rapid increase (that is, essentially all reasonable models(3)), all observable high-redshift radio galaxies must be seen when the lobes are less than 10(7) years old. This means that high-redshift radio galaxies can be used as a high-time-resolution probe of evolution in the early Universe. Moreover, this result explains many observed trends of radio-galaxy properties with redshift(4-9), without needing to invoke explanations based on cosmology(10) or strong evolution of the surrounding intergalactic medium with cosmic time(6), thereby avoiding conflict with current theories of structure formation(11).