Entropy and Surface Area

An important part of science, a fun part, is following up interesting observations in the hope that something will come of it. One great paper I enjoyed reading was full of observations like this. It was by A. Unzicker (arxiv:gr-qc/0702009v6) and he gives a theory-independent overview of observations regarding gravity.

One observation he mentioned is either a meaningless coincidence, which it could be, or means something interesting. The idea is that if you approximate the area of galaxies by 2*pi*r^2, where r is the galactic radius, take r as 10,000 pc and assume, realistically, that there are 1.25*10^11 galaxies in the Hubble volume (Hubble Space Telescope, 1999). You then get a total area of 7*10^52 m^2 (with a big error bar). This is close to the surface area of the Hubble volume, which is 4*pi*R^2 = 2.3*10^53 m^2 (another big error bar) where R is the Hubble radius. He says this is an astonishing coincidence of the present epoch, since galaxies are not thought to change in size (p15). It sounds somewhat similar to the holographic principle too, in that the entropy or disorder in the universe (which I take to be proportional to the surface area between matter and empty space) is determined by the surface area of the bounding surface.

MiHsC agrees with this sort of picture, though I haven't modelled it in this context yet. In MiHsC the inertial mass increases as the Hubble volume expands. This means that stars at the edge of galaxies should progressively, as cosmic time goes on, have more inertial mass and be less willing to be bent into orbit by gravity, so galaxies should expand with time to follow the expansion of the Hubble volume (I don't know yet what the exact dependence would be). If it is linear, then no matter what epoch you're in, the equivalence between galactic surface areas and the Hubble surface area would be true: it is then no coincidence.