I don’t understand how the Hubble expansion can be linear with respect to distance. Let L be the distance at which galaxies are moving at 1% of c. Say that there are galaxies A and B, colinear with M (the Milky Way), that are 25L and 50L, respectively, away from M. Let v(X,Y) be the velocity of X with respect to Y. v(A,M)=.25c; v(B,M)=.50c. Clearly v(M,A) is just -.25c. But what is v(B,A)? If I remember the boost formula correctly, v(B,A)=[v(B,M)-v(A,M)]/[1-v(B,M)*v(A,M)]=4c/7
But the distance between A and B is still equal to the distance between M and A. So how can |v(M,A)|!=|v(B,A)|? Doesn’t that violate the linearity of the expansion? Is this the only place that the expansion is linear? Or is the linearity merely an approximation that only works for nearby galxies?
Linearity is only an approximation, which breaks down before relativity and the speed of light become relevant. The big game of modern cosmology is to determine the exact manner in which it departs from linearity. In the simplest models, the expansion should be faster for distant galaxies, because we’re seeing them as they were a long time ago, and gravity should be slowing the expansion. This is not, however, what we see, and the Universe actually seems to be accelerating. There’s still room for plenty of PhD theses on just why it’s accelerating.
Just remember: Everything in physics is linear, if you look at it on the right scale.
Thanks for clearing that up. What got me thinking about this was the claim that since the expansion was linear, at some point galazies are moving away at c, so we can’t see anything past that (since any light coming from beyond that radius would be redshifted out of existence). Is that valid even without linearity? It seems rather hard to believe.
Well, fractals aren’t, by definition. Or do you not consider those to be part of physics?