We have seen galaxies around 13 billion years old. Since these galaxies formed so early in the history of the known universe, are there observables about these galaxies that are apparently different from much younger galaxies. I suppose all current physics laws had condensed out by then but was just curious about the formation and 'aging' of such old galaxies.
Nearby galaxies are seen in their old age. Distant galaxies are, on average, the same age as the local ones. But due to the finite speed of light, the farther you look, the younger you observe them. That means that the most distant galaxies are observed in their infancy, and they look much different from the old ones.Galaxy evolution
This is one reason to observe galaxies at all distances: We get a statistical picture of the galaxies through different epochs, and hence probe their evolution. From such observations, we see e.g. how they grow with time, how their star formation increase in the early Universe until the Universe was roughly four billion years (Gyr) old and the decreased (Madau et al. 1996), and how the metals and dust built up over time.Galaxy formation
Observing the most distant ones is not just a matter of breaking a previous record in distance, or time. When we look at the most distant (spectroscopically confirmed) galaxy to date, GN-z11, we see 13.4 Gyr back in time. What's the big deal if we find another one that is 13.5 Gyr back in time? Well, since the Universe at that time was only a few hundred million years (Myr) old, that would give us quite good constraints on the minimum timescale of galaxy formation. Can a galaxy form in only 300 Myr or 200 Myr, or does it need 400 Myr?Physical properties
As I said above, the most distant galaxies look vastly different from the local ones. For instance, disks hadn't formed yet, both because it takes some time to settle into a disk, and because galactic mergers were more common at that time, which disturbed the galactic dynamics. The physical properties of the interstellar medium were also different, e.g. because it was more metal-poor, since metals are formed by stars over time. Dust, which is made from metals, was also sparse. But how long time does it take for stars to form metals, and dust? Previously it was thought that most dust was produced in AGB stars which die peacefully and hence have good conditions for making dust (high density and cool gas). But these stars typically live for billions of years, and observations of the most distant galaxies showed us that they contained dust as well. So people started wondering if supernovae, which are the violent deaths of massive and hence short-lived stars, could do it, even though it was thought that the gas was much too hot too form dust right after the explosion, and much too dilute after it had cooled down. But indeed it seems they can (e.g. Kozasa et al. 2009).