I don't understand what it means for points to move apart faster than the speed of light. I understand speed of a thing to be change with respect to space, so what does speed of space mean? Naively, I'd define it to be zero. If I stretch a ruler out, the 1ft mark hasn't moved with respect to the 1ft mark. I can say otherwise by comparing the ruler to what's around it. If the ruler is literally everything, we can only measure the ruler with respect to itself. I'd define measurement as with respect to the ruler (the ruler is spacetime). I know I'm wrong, but can't figure out why. Any help?
With that analogy, the balloon would be the ruler in my analogy, which leads me back to the original questions. Using the balloon analogy, if you have a normal balloon in 3D euclidean space, you can measure/define the expansion easily. Without that, what can you do?
You could define some physical process on the balloon as distance and time, like light moving and atoms vibrating, and call that our ruler. Then measure intrinsic properties like curvature? If hypothetically the speed of light instantly dropped by 5% (with respect to existing objects' distances, I guess), do you just define those objects as instantly 5% further apart now, or do you you say something like the speed of light changed? Then there'd be similar questions about changes in how we define time. This is fun to think about.
