# Has anyone studied a statistical scaling law for the universe? [closed]

How do named objects in the universe scale? Is there a predictable curve for an ordered list, say {atom, animal, planet, solar system, galaxy, etc}? Can you then use the analysis to predict when the next larger structure will be seen?

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## closed as not a real question by Manishearth♦Apr 16 '13 at 6:14

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

Hi Enjoys Math. Welcome to Physics.SE. Here's an interesting link to check out on the scale of universe. But, I don't think there's a law to predict the future observables ;-) – Waffle's Crazy Peanut Apr 15 '13 at 17:35
Yeah, I saw that. – Enjoys Math Apr 15 '13 at 17:36
Could you explain your question a bit further? Currently it's a bit unclear, I'll temporarily close it till it gets improved (flag for reopening once you finish) – Manishearth Apr 16 '13 at 6:14
The general issue of physics at different scales can be adressed by renormalization. – Dilaton Apr 17 '13 at 10:32

Let's assume for a moment that your choice of objects is somehow "natural," and universal, and not just based on words we happen to have in English.

Even then, the range of things you are covering is too large to expect a single law to cover it. The "sizes" of atoms are dictated by the strength of the electromagnetic force and the mass of the electron (and the sizes of nuclei depend on the strong force). The sizes of living cells are set by the ratio of metabolic rate to the rate of diffusion of nutrients across the surface of the cell. These rates depend on electrons' interactions, but in a very complicated way.

Planets cover well over an order of magnitude in sizes all by themselves, depending on the conditions in their particular location in the disk of material around a newly formed star. The sizes are governed by the strength of gravity (which has no effect on smaller things like atoms) and the material properties of rocks. Stars too have an enormous range of sizes, spanning quite a few orders of magnitude depending on what stage of evolution they are in. These sizes are again set by gravity, and also by nuclear reaction rates (governed by the strong and also the weak nuclear forces).

Galaxies are governed primarily by gravity, but they also have very complicated feedback mechanisms involving giant black holes, starlight, and supernova explosions. Moreover, there is evidence that their sizes have changed over the course of evolution of the universe. At this scale and larger, the scale of things depends very much on how many years have passed since the Big Bang.

Regarding predicting the next larger structure: This was an interesting question for early cosmologists. You see, the general relativity that governs the evolution of the universe would be intractably complicated if not for the assumptions we make of nearly perfect homogeneity (every point in space is basically the same) and isotropy (no direction is special). If you imagine the ladder of structure extending infinitely toward larger things, you have a fractal universe, and it is a very different beast. Eventually (much later than we proclaimed to have the basic theory of a homogeneous/isotropic universe pinned down), deep galaxy surveys did in fact reveal that there is an upper limit to structure, justifying non-fractal models. On the largest of scales (many millions of light years), everything is distributed evenly and there is no structure.

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Logarithmic Map of the Universe

This presents a very interesting illustration, although I don't see how you would assign any physical meaning to the particular numerical value.

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