I got into watching a video on Olbers' Paradox a few days ago, and from there read about the origins of the universe, its expansion, and so on… it's always fascinated me, but now something about it bothers me. I've heard many analogies about it (the dot-balloon, the raisin bread loaf, and others), but none really seem to explain this question. (This comes close, but dances around the answer more than explain it.)
At the beginning of the universe as we know it, the universe itself was very small, so all the stars giving off light would have made it very bright (16:29 in this video). Since that time, the wavelength of that light has been stretched (17:01, same video). I found a few explanations saying that space itself stretched (here; described as "ether" in the article), which would stretch out the wavelengths.
But here's what bothers me: If space is stretching out, redshifting all the light soaring around our universe, why are we not stretching? Theoretically, the universe is expanding an incredible amount faster than the speed of light, and the edge of the universe is an unimaginably large number of megaparsecs away from us. But should we not notice some of the stretch here, too?
That is to say, if the light in space (the "ether", though I'm not fond of that term) is stretching out, why is everything on Earth still the same size as it was a hundred years ago? Is it stretching uniformly, but we are just unable to notice such a small stretch? Or does mass have some property that space and light do not, that prevents it from stretching out? I've also heard about time stretching, too; does this have an impact on it?
Best Answer
The expansion of the universe is due to the expansion of spacetime. There's a good article on this here.
Suppose you take two non-interacting particles, put them some distance apart and make them stationary with respect to each other. If you now watch them for a few billion years you'll see the particles start to accelerate away from each other. This happens because the spacetime between the two particles is stretching i.e. there is more "space" between them.
One way of interpreting the acceleration is to say there is a force between the two particles repelling them. This is a slightly dodgy description because there isn't really a force; it's just expansion of space. Nevertheless, if you tied the two particles together with a rope and watch for a few billion years there would be a tension in the rope so the force is real in this sense.
Anyhow, now we have everything we need to understand why the Earth isn't stretching. The expansion of spacetime creates a stretching force, but this will only have an effect if there is no other force to oppose it. For example you are indeed being stretched by the expansion, but the interatomic forces between the atoms in your body are vastly stronger than the stretching due to expansion, so you remain the same size. Likewise the gravitational force between the Sun and Earth is vastly greater than the stretching force so the Earth's orbit doesn't change.
The stretching force is vanishingly small at small distances, but it gets greater and greater with increasing distance so at some point it wins. Galaxies and indeed galaxy clusters are still too small to be stretched, but at greater sizes than this the stretching wins. That's why galaxy clusters are the largest objects observed in the universe. At greater sizes spacetime expansion wins.
A footnote: if anyone's still interested in this subject, there's a paper Local cosmological effects of order H in the orbital motion of a binary system just out claiming that the effect of the expansion on the Solar System might be measurable.