cask1 said:
Is our 3-dimensional space expanding because it is the "skin" of a higher dimensional space which is expanding? Is that why there seems to be no point of origin for the big bang?
That is a good way to think about it for a little while, to build up some intuition. But I don't think it is something to continue to *believe in*.
Because we don't have any physical evidence that there is such a 4d region of which our world is the surface.
In science there is kind of a code of behavior that says things like
"assume as little as possible"
"admit that some questions you can't answer"
"don't make up stuff"
"don't claim more than you know"
"live with uncertainty about some basic questions"
"wait for real evidence"
And there are professionals, some highly visible, who break these rules and are very noisy about it.
Like the "multiverse" people. But they aren't a majority. The center of gravity is still, I think, with
the scientists who are quietly cautious and skeptical.
It's a very good picture though. It's the basis of the expanding balloon analogy. In the clean way of imagining that, all existence is concentrated on the surface. There is no inside of the balloon nor outside, nor is there even any rubber. The balloon picture is meant to show how the geometry changes, how distances between things increase while they stay in the same latitudelongitude place, and how photons of light travel across the surface always at the same speed. for an animation google "wright balloon model"
and get http://www.astro.ucla.edu/~wright/Balloon2.html
So the balloon picture is a purely 2D world that just happens to curve around, so that it is spatially finite.
the challenge (which you are attempting and asking about) is to jack the dimension up from 2d to 3d and imagine an expanding 3-sphere (which MIGHT be the surface of a 4-ball, but we don't know that)
What would it be like to be 3d creatures, as we are, living in an expanding 3-sphere? as perhaps we are. Could a photon of light ever circumnavigate? What do the angles of a triangle add up to and does it depend on the size?
How does the circumference of a circle depend on the radius, if the radius gets really big? And so on Mental exercises to try to understand the experience of living in a world with a very slight, almost unmeasurably slight, positive curvature.
But not to believe in an inside or outside of the balloon. In math, a 3d manifold does not have to be embedded in some larger dimension space. It can be all there is.