People like to visualize the expanding Universe as a sort of a stretching rubber sheet. Textbooks and popular cosmology books play up this analogy in a big way. Like most analogies, it’s useful in some ways, but taken too far it can lead to misconceptions. David Hogg and I have written an article in which we try to fight back against some of these mistakes.
The article is about how we should interpret the redshifts of distant objects. Most of the time, redshifts are Doppler shifts, indicating that something is moving away from you. In the cosmological context, though, a lot of people think that you’re not allowed to interpret the redshift in this way. The idea is that galaxies are “really” at rest with respect to the stretching rubber sheet. Since they’re not “really” moving, what we see is something different from a Doppler shift. The point of our article is to rehabilitate the Doppler shift interpretation.
The real reason I care about this is not that I think it matters much what we call the redshift, but because I think that this is a good example of the muddled thinking that the rubber sheet analogy causes. In particular, the analogy provides precisely the wrong intuitions about the nature of space and time in the theory of relativity. If you want to know more specifically what we mean by this, you’ll have to read the article!
To understand the guts of the article, you really need to have studied relativity a fair bit. (Students who took my Physics 479 course should be able to handle it.) Even if you don’t know enough relativity to understand all the technical details, the beginning and end might be interesting and accessible. (Certainly, this paper should be more accessible to non-specialists than the last one I wrote about, which is pretty technical.)