What is the distance between two galaxies?
In the old picture, this is an easy question to answer theoretically (though not necessarily in practice!). Just get yourself a giant tape measure and clip it to a faraway galaxy, then come back to our galaxy and hold on tight. As the galaxy moves away, it will pull on the tape measure, and you will easily be able to read off the distance as the tape measure unwinds… one billion light-years, one and half billion light-years, two billion light-years, etc. In our new picture of the universe, however, with the raisins and the dough, the tape measure will not unwind at all as the universe expands, because the galaxies are not actually moving with respect to each other! Instead, it will read one billion light-years the whole time. You could be perfectly justified in saying that the distance between the galaxies has not changed as time goes on. When you bring the tape measure back in, however, you will notice something unusual; due to the stretching of space, your tape measure will have st