|MadSci Network: Astronomy|
Good question - this is something that used to confuse me too! The point you make is essentially that if all of space is expanding, then the metersticks that we use for measurements are also expanding at the same rate. So if we try to measure anything with this meterstick, we won't actually be able to detect any difference! The "cosmological redshift" is due specifically to the expansion of space. Light is made of waves, or a series of crests and troughs. The wavelength is the distance between two adjacent crests. As such a wave moves through expanding space, this distance will increase. A longer wavelength means redder light, hence the name. The problem you point out is that whatever we use to examine the wavelength should also be expanding - so how could we measure its expansion?
To understand why this isn't quite what occurs, we have to understand a bit more about why the universe expands. Essentially, the Big Bang gave space an initial push, causing it to expand very quickly. But, space contains matter, and matter is subject to gravity. Gravity is an attractive force, so matter in different parts of the universe pulls at each other and slows down the expansion. General relativity tells us that gravity not only slows down the matter, but also slows down the expansion of space itself. If there were enough matter in the universe, the gravity it creates would be strong enough to eventually halt the expansion and cause space to recollapse. If there is very little matter, on the other hand, the deceleration due to gravity will be small enough that the universe will keep expanding forever. Recent measurements suggest that our universe has only a relatively small amount of matter and will expand forever. (In fact, our universe contains an exotic type of energy called the cosmological constant that actually accelerates the expansion.)
When cosmologists consider the above problem, they assume that matter is smoothly distributed around the universe (i.e., there are no clumps or voids of matter). On the largest scales (across thousands of galaxies), observations suggest that this is more or less true. This means that if we are considering the dynamics of the universe as a whole, it's okay to treat the matter as smoothly distributed. In this case, we find that general relativity predicts an expanding universe, and the redshift is one piece of observational evidence supporting this prediction.
However, the universe is clearly not smooth on the scale of a single galaxy. The Milky Way, for example, has 100 billion stars in a clump, surrounded by very nearly empty space! As you can imagine, this means that the effects of gravity are quite strong within and near the Milky Way. In particular, there is so much matter that the expansion of space within the Milky Way is completely stopped. Space around our solar system does not expand; in fact, it behaves almost exactly like our intuition suggests space should behave. That is, it doesn't do anything at all! So our metersticks do not in fact expand, and we can detect the expansion of the space between galaxies via the redshift and other effects. Because we live in a relatively dense environment, we live in a region of the universe that has "broken away" from the cosmological expansion and remains static.
For more information about redshifts and their sources, see this page or Timothy Ferris' book The Red Limit.
[Moderator's Note: On the scale of small bodies, such as metersticks, the attractive forces between atoms and molecules are large enough to overcome the expansion of spacetime, which is why our bodies (for example) don't expand as the Universe expands.]
Try the links in the MadSci Library for more information on Astronomy.