Dear Dr B: What Does The Universe Expand Into?

“When the universe expands, into what is it expanding? In what medium is it expanding? Is the universe similar a bubble inward a higher dimension something?
[Anonymous], Indiana, USA”

[image: luftballon-profi.at]

This is a really skillful enquiry too one, I should add, I popular off frequently. It is, I believe, to no modest business office caused yesteryear the mutual illustrations of a curved universe: it’s a rubber-sheet amongst a bowling-ball on it, it’s an inflating balloon, or – inward the rarer instance that soul tries to illustrate negative curvature, it’s a Irish Gaelic patato fighting (because genuinely I bring no sentiment what a saddle looks like).

But inward each of these cases what the illustration genuinely shows is a two-dimensional surface embedded inward a non-curved (“flat”) three-dimensional space. That’s skillful because you lot tin delineate it, but it’s bad because it raises the impression that to beak of curved sort you lot need to pose the surface into a larger space. That, however, isn’t so: Curvature is a holding of the surface itself.

To popular off an sentiment of how this works, regard the simplest illustration of a curved surface, a ball. On the ball’s surface the angles of triangles volition non add together upwards to 180 degrees. You tin calculate the curved sort from measuring all the angles inward all triangles that you lot could delineate onto the ball. This is a criterion which tin move done only on the surface itself. Or yesteryear ants crawling on the surface, if you lot wish, to occupation some other mutual analogy.

Curvature, hence, is an intrinsic holding of the surface – you lot create non need the embedding infinite to define it too to mensurate it. Also banking concern complaint that the curved sort is a local property; it tin modify from 1 house to the next, exactly that a ball has constant curvature.

General relativity uses the same notion of local, intrinsic curvature, exactly that inward this instance nosotros aren’t dealing amongst ii dimensions of infinite too ants crawling on it, but amongst 3 dimensions of space, 1 dimension of time, too humans crawling closed to inward it. So the math is to a greater extent than complicated too all the properties of space-time are collected inward something called the curvature-tensor, but that is silent an only internal construct. We tin mensurate it yesteryear tracking the motion of particles, too it’s this curved sort that creates the upshot nosotros usually cite to every bit gravity.

Now, what cosmologists hateful when they beak of the expansion of the universe is a tendency of for certain criterion results that, using Einstein’s equations, tin move interpreted every bit existence due to an increasing distance betwixt galaxies. Again, this expansion is an only internal notion. It is defined too measured inward our universe. You create non bring to embed this 4 dimensional space-time into anything else to quantify it. You create non need a medium too you lot create non need a larger space. Einstein’s theory is only self-contained amongst a four-dimensional, internally curved space-time.

While you lot create non have to embed space-time inward a higher-dimensional apartment space, you lot can. Indeed it tin move mathematically proved that you lot tin embed whatever curved 4 dimensional space-time into a 10 dimensional apartment space-time. The argue physicists don’t unremarkably create this is that these additional dimensions are superfluous too they don’t assistance the math either.

Black hole embedding diagram.
Only the surface itself has physical meaning.
The surrounding infinite is for visual purposes.
[Image source: Quora]  

We do, however, on occasion occupation what is called an “embedding diagram”, which
tin move useful to visualize the extrinsic curved sort of for certain slices of space-time. This is, for example, what gives ascent to the sentiment that when thing collapses to a dark hole, infinite develops a long pharynx amongst a bubble that eventually pinches off. But delight proceed inward heed that these are but visual aids. They bring their uses every bit such, but 1 has to move really careful inward interpreting them because they depend on the chosen embedding.

Now you lot enquire what does the universe expand into? It doesn’t expand into anything, it exactly expands. That the universe expands is a controversy close what happens within the universe, supported yesteryear measurements within the universe. It’s an only internal notion that does non require us to beak of an exterior of the universe or a medium into which it is embedded.

Thanks for an interesting question!