Stretchy Space?

 See Stretchy space - useful books for a list of books related to this subject
When considering the expansion of the universe, we are often told that we shouldn't think of it in terms of the galaxies moving apart, rather we should think of the intervening space expanding. But is thinking in terms of moving galaxies so wrong? Below I make the case that not only is it OK to think that way, but also that thinking in terms of expanding space may lead to some wrong intuitions.
 You can find more on the question of space stretching v moving galaxies at the physics FAQ or in Ned Wright's cosmology FAQ In fact all of Ned Wright's cosmology tutorial is worth reading

The Fruit loaf model

One way of thinking of the expansion is that it is like a fruit loaf being cooked. The dough expands but the raisins (galaxies) don't. This suggests that the space inside the galaxies is somehow different to intergalactic space - which it isn't. A similar model is that of a balloon being blown up (with galaxies as dots on the balloon). This suggests that some physical input is required to keep the universe expanding (As does the fruit loaf model) This seems to me to be a regression to the time before the Newtonian idea that an undisturbed object will keep on moving, back to the Aristotelian idea that it will slow down and stop.

Redshift

Redshift of distant galaxies is what tells us that the universe is expanding. In the stretching space model it is explained in terms of the expansion of the space which the light is travelling through, which increases it's wavelength. Again this suggests that something physical is happening to the light which isn't really the case. Instead of light, suppose a spaceprobe had been sent, at nearly the speed of light, from a distant galaxy. When it reached us it would be travelling a lot slower, so that like the light it would have lost energy. Would we say that somehow its energy had been sucked out of it during its journey. I think its more likely that we would say it had always been travelling at the slower speed with respect to us.

Thinking Mathematically

Another reason given against moving galaxies is that it suggests a centre which they are moving away from and a space which they are moving into. But does it? Thinking mathematically involves the ability of being able to select out the important points from a model, and I don't see that there's so much of a problem in thinking of galaxies moving away from each other without having a preferred frame of reference. Indeed, the 'rubber sheet' models would naturally suggest an external space containing the sheet, which seems worse from my point of view.

Faster than light

One reason for thinking in terms of the stretching of space is that thinking in terms of recession would mean galaxies moving away from us faster than light, which would be unphysical. However, this isn't so much to do with the physics of the situation as with the choice of the coordinate system. General relativity allows a lot of freedom in choosing a coordinate system. Cosmologists choose coordinates which reflect the homogeneity of the universe. However, they could equally well choose coordinates which required a constant speed of light as in special relativity (and sometimes I think they should)

Stretchy Space?

So is there any reason to think in terms of stretching space. Well maybe there are a couple. Firstly, calculations in cosmology use general relativity, and the normal notions of distance and time don't apply. So a model will be useful if it helps you to let go of these notions. In cosmology there is a term called the scale factor which describes how much the universe has expanded at a particular time. If we consider light emitted form a distant galaxy, then the factor by which its wavelength increases is just the scale factor when it is observed divided by the scale factor when it was emitted. This is much simpler than trying to think in terms of recession velocities and then having to consider how the cosmological model you are using will affect things. However you should always remember that general relativity deals with the behaviour of spacetime, not just of space. The second reason to think in terms of stretching space is if you are dealing with positive cosmological constant. In this case the expansion of the universe is accelerating - here there really is something physical drving the acceleration. It is very hard to think of this in terms of the usual ideas of forces, so a different model is useful. Note that some explanations of the cosmological constant are in terms of the quantum vacuum, meaning that 'empty' space is considered not just as something separating things, but as having properties of its own. In that case is doesn't seem so bad to think of it as stretching.