As the universe expands, why do some things stretch but not others? 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?
 A: This is not my field but the way I understand it is that the expansion involves unbound states. It does not affect bound states. For example protons, bound by the strong interaction, once generated, during the expansion, and decoupled, i.e. the quark gluon plasma has stopped existing, remain protons with the dimensions we know them. 
Incorporating your comment question:

Is there an answer as to whether the cosmological or atomic force was larger initially?

I assume that by "cosmological force" you mean the effect of the cosmological expansion, cosmological constraints.. In the current model of the universe energy is contained within it in a progressively larger volume, where particles appear in an interacting soup and thermodynamically the available energy per particle is very large, forming a quark-gluon plasma.
As expansion progresses locally the cosmological constraint  becomes smaller than the strong force ( in the case of protons appearing) and therefore there is no longer a dissolution and recreation of protons from the energy soup of the Big Bang, in this case the quark gluon plasma which should exist before protons can appear. Atoms and molecules are equally strongly bound by the electromagnetic force.
The same is true for galaxies, which are a gravitationally  bound state and separate between each other due to the expansion but remain bound internally.
The effect of the extra effective dispersive potential of the expansion on the binding of matter is very very small.

However the only locally visible effect of the accelerating expansion is the disappearance (by runaway redshift) of distant galaxies; gravitationally bound objects like the Milky Way do not expand.

Photons (and neutrinos) are not bound states, and therefore follow the expansion of space changing their wavelength due to it. Always keep in mind that this expansion happens locally at every spacetime point of what we define as space time for usual physics studies.
This is a field which is researched still, but this model seems to fit observations up to now. 
A: When you model the expanding universe in cosmology, you do so with a particular solution to the Einstein field equations called the FRW metric.  The defining feature of this metric is, of course, metric expansion.  This means that distances will increase over time.  One assumption that goes into the FRW metric is homogeneity.  Since the universe is homogeneous on large scales, this works excellently for very large portions of the universe.  However, galaxies are certainly not homogeneous.  So, you need to use a different metric inside of galaxies - and because of this, space inside of galaxies is totally unaffected by metric expansion.  It's not even that the effect is too small to be noticed, galaxies are totally unaffected by expansion.  So, we can generalize this to say that expansion occurs in between bound systems.  There is a good entry on this at the Usenet FAQ:
http://math.ucr.edu/home/baez/physics/Relativity/GR/expanding_universe.html
Dark energy, however, is a bit trickier.  Since it is a negative pressure vacuum energy, it exerts an extremely small force everywhere.  So, it has a small effect inside of bound systems.  This is because dark energy is a cosmological constant - which is also a term in the Einstein field equations.  Since these still govern gravitational interactions inside of galaxies, dark energy has an effect there.  The easiest way to see by is by looking at attractive gravitational force between two objects with a cosmological constant in the Newtonian limit: $$F = {GMm \over r^2} - {\Lambda m c^2 \over 3} r$$  However, this effect is utterly negligible. 
A: 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.
A: I do not think anyone at this time can answer this question with certainty because there could be a number of explanations of what others are observing. I think we need to learn from nature for some of these more difficult questions. My theory could be; that the whole universe is expanding, including you, me and everything that consists of the universe. For example instead of the big bang or the big stretch, we could have the big revolve. This option would follow the course of nature maybe a little more closely. Most things that we know of in the universe revolve and or orbit. Everything in space that we see is moving and orbiting something or another. It appears that by measuring light we can see a shift of some moving away and others moving closer. Now you read that they say that the space in between is stretching. Maybe it is expanding as we are expanding and then the observation could be similar. If it were true and we are all expanding then it can explain some parts of the laws of gravity as well but not all of them. Maybe they can be explained under a different law. In nature the earth itself is revolving and it is renewing itself by the movement if its plates. Over time all of our records of existence will be wiped off the face of the earth. Maybe our sun and our stars known as the white light is part of a dimension that we can see, and all of the particles from this source are travelling and expanding through space and then will eventually collect into the black holes to be spit out the other side ( another dimension ) to again be returned to our dimension through the sun and stars. Thus we have the big revolve. We have a related view point, it will take billions of years for this to happen. Maybe from another view it will take a split second by their time. Maybe our universe is inside and is a part of another universe, maybe someone in the other universe is cold and will throw another log on the fire, and thus our universe goes up in a puff of smoke. All I know for sure is we have a long way to go to get closer to the truth, the guys at NASA are on the right track, one step at a time and by using only proven science to build upon the next mission.
