# Expansion around gravitational clusters

1. Sep 8, 2009

### Riffraff

Hello everyone!

Ok so from what I've read in various text books & wiki is that the red-shift of observed galaxies is caused by the expansion of space through which the light travels (naively seen as galaxies moving away from us and causing a doppler shift).

This got me thinking that if 'our space' around us expands with the same rate we wouldn't notice such effect. Then I read that inside gravitionally bound systems, objects aren't subject to the general expansion of space. Now this obviously expains why we can observe the redshift, but why does this occur in the first place?

Thanks, Riffraff

Last edited: Sep 8, 2009
2. Sep 8, 2009

### marcus

Hi, welcome to the forum. I hope some of the others will respond. You can keep asking questions and gradually get the response you need. I will start with a kind of rough general reply.

As far as we can tell the geometry of space and time is governed by the 1915 Einstein equation of GR, also called the "einstein field equation". This equation is simple to write down and it says how the metric is shaped by the matter, in a local neighborhood around any given point.

The metric is a localized distance function that basically describes geometry itself (it can be used to tell distances, areas, volumes, angles...). And the metric IS the gravitational field. Gravity IS geometry, so it is the metric describing geometry which is the field describing gravity.

So the lefthand side of the equation consists of derivatives (changes) of the metric. And the righthand side tells the matter story: local density, pressure, flow.

So the two relate how the local changes in the geometry is affected by the matter.

And a FIELD can only change gradually over space. So even if your matter is clumped the field has to work out how it changes gradually in between the clumps where there isn't any matter. And the field can only change gradually in time. So if it started out expanding it can't stop abruptly, it can only gradually slow down or speed up in response to the matter. If nothing happens it will keep on.

And nothing says the expansion must be exactly uniform. Each locale only knows what has been happening in its own neighborhood and what the current local matter situation is.

So that means the uniform pattern of distance increase which is Hubble Law is only an approximation. It is a very good approximation because evidently the expansion started off nearly uniform and on large scale the distribution of matter which would have gradually slowed it is nearly uniform. It looks speckly and clustery but on large scale average it is uniform. So the expansion of distance is NOT uniform but on largescale average it is almost.

And this expansion has totally no connection with the size of pencils or long-nose pliers or the solar system, or even the milkyway galaxy. Because these things are held together by forces in equilibrium, like a crystal lattice is or a planetary system is.

So as for observing any local expansion forget it. Expansion of distance does not apply to mechanically or chemically bound and regulated structures. It applies to unbound patterns on a scale of tens or hundreds of millions of lightyears and larger. And that includes the waves of light which travel over those distances.

And furthermore expansion is actually uneven. Only approximately uniform.

OK. Now I really only started the discussion. You can read what I said, if you want, and think about it and still ask why, why this and why that. It's fair enough, since I presented a point of view but didn't finally answer your question. And if you dig enough you will probably come to the questions that nobody around here can answer, but that's how it goes.

3. Sep 9, 2009

### Riffraff

Thank you very very much Marcus!

Apart from making my problem much clearer you also helped on several issues I didn't even know I needed helping :)