Intrinsic red-shift is an idea proposed by the astronomer Halton Arp in order to explain the red-shift associated with quasars.
Quasars are young galaxies that appear to be physically linked to older galaxies. In some cases, a visible connection can be seen, like an umbilical cord, connecting the quasar to its parent galaxy.
However, the tremendous red-shift associated with quasars pose a great problem for those trying to interpret the visual data.
Using red-shift as a measure of distance, we end up with quasars being extremely distant.
This conflicts with their visible connection to galaxies that are estimated to be much closer to us.
Another problem with quasars is that they are relatively bright. If they are as distant as they appear to be based on red-shift estimates, they must be mindbogglingly energetic.
To get around this problem, Halton Arp proposed that quasars are made up of matter that is less massive than matter found in our solar system.
Hydrogen in quasars are lighter than hydrogen on Earth. The light spectrum of hydrogen in quasars is therefore red-shifted relative to the light spectrum of hydrogen found on our planet.
The red-shifts seen in quasars are not indicative of distance, but of age.
Matter starts out with little mass. As time progresses, mass condenses onto matter, making it gradually more heavy. Light from young matter is red compared to its older, heavier counterpart.
To see that this is a valid proposition, we can compare the light spectrum of hydrogen to that of its heavier isotope, deuterium.