Neat, suggesting that we look at it as if everything were shrinking. It's fun thinking: "Yeah, that probably is mathematically the same, but is it physically the same?" At the sub-atomic level I suspect not, but that's a side-issue.
However, for explanatory purposes (in my truly humble opinion) I'd prefer to stick with expansion, so as not to cause conceptual distractions. I haven't taught this subject, so I may be wrong, but at least to me it's easier to focus on the question of whether the expanding universe is expanding "into" something. That's where the hangup exists.
At each moment of the expansion, there's no "out there, beyond" the universe. It always occupies all the space there is. But distances keep growing. Anyway, that works for me.
I don't understand. Are you saying that there's something about the physical universe that is not describable mathematically?
I'd prefer to stick with expansion, so as not to cause conceptual distractions. I haven't taught this subject, so I may be wrong, but at least to me it's easier to focus on the question of whether the expanding universe is expanding "into" something.
But that in itself is a conceptual distraction. Again: the universe is not an object that exists in space, and which needs to take up more space as it grows. The universe is the space itself. It requires no medium in which it can float.
[Geek alert: there are several popular models that postulate the existence of additional physical dimensions, but these don't solve your conceptual problem. In some models these additional dimensions are themselves expanding, and in others, they are radically contracting! These models are denoted "AdS5" models, which means that the 5th dimension is "anti-deSitter". In such models, the universe as we see it is a 4-dimensional slice of a 5-dimensional space. The 5th dimension extends outwards from our slice, but it's constantly contracting back towards the slice. Any particle that makes an excursion into the 5th dimension is inexorably drawn by geometry back to this orbifold plane. So you see that although in such a model, our universe does exist in an external medium, there is no sense in which our universe "expands into" that medium. But expand it nevertheless does.]
.... which is mathematically indistinguishable from from rulers getting shorter.
:-)
It does for me, too. Do you struggle at all with "without confusion, without separation"?
(I'm not trying to argue. I'm sincerely fascinated by your comment.)