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Einstein could explain this one... T_T (too bad I didn't listen to my physics teacher when we tackled this) sorry... my bad :(
Space is not a thing by itself would be the starting point, but space becomes "something" when its three dimensions are coupled with a time dimension, and this is actually what is being measured when we say space is expanding. There are not physical properties like matter has (which I think may be the understanding you are trying to connect to a "thing with physical properties expanding.") There is matter in the fabric of space-time that IS actually moving apart from other matter, all at a uniform rate. Yet, the matter itself is NOT moving "through" space, it is moving "with" space. We know this because light itself changes its color (or energy level) as it tries to traverse more and more expanded space, before we see it here on Earth. If you were to attribute a physical property that explains this, you COULD say that it is the fabric created by space not being independent of time, but it is not a physical fabric as you might attribute to matter.
Space-time has a fabric "unlike" that of matter? Then what is it LIKE? Is it metaphysical-spiritual? I can't wrap my mind around the idea of an expanding universe. At the so called point of singularity there was no space, just energy. Then Ka booom and there is space AND energy. So space was suddenly created out of nothing and is to this day still expanding. What is on the other side of the outer limit of expansion? What is the nature of the outside of the outside? The red shift and microwave background discoveries aren't convincing enough to me. They may be misinterpretations. Nature is modelable. There is no credible model, just a lot of abstruse equations. Experiment shows that for all expansion there is contraction. A balloon expands and gets thinner or contracts in its thickness. Where is the universe contracting?
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It's curious that you are asking questions on a similar track to the one I have been on about the same subject. It would take a while to answer every question you posed, or maybe we could just answer the arrival point of the track you seem to be on. You are very right to say there is no credible model, even the best science says that. Models only describe what happens on a repeatable basis. And the space-time model is repeatable, and is responsible for example, for how your GPS device works (without calculations based on relativity, GPS would be inaccurate.) I also believe that this model is incomplete, as the final work of Einstein admittedly suggests (he could not model relativity on molecular scales). On the track you are taking, what you are suggesting is that the space-time model is false, or at least incomplete. Well, the incomplete part is this idea of your excluding the property of expansion from anything that is not "physical." That is simply not the case. The part of relativity that is "repeatable" in experimentation, that deals with your question, is that when light moves through space, it has to obey the laws of time even though it has to move at a constant speed. Space doesn't have to be physical for light to have to obey the laws of physics. Trying to impose physical laws of matter on something that is not matter is confusing your question. I will say this, though, that it's fairly clear that there is a giant gap in the understanding of the way the universe is expanding versus the present model (as stated above), and a very drastic re-thinking is necessary.