[jamest (OP)]

Anne wants to know, 'If the universe is expanding, what is it expanding into?'

[paul cotter]

That is a good question and guess what? I can't answer it! The universe is by definition "all that there is", so by that definition there is nothing external to it, including any space as yet unoccupied. All we know for sure is that the universe is internally expanding and that expansion involves the space itself expanding rather than the contents flying apart. Some models reckon the process is similar to the surface of an expanding balloon but this model is a 2D one which does not accommodate our 3D universe.

[evan_au]

Another metaphor is cooking a raisin cake: all the raisins move away from each other in 3D.
- But the cake expands into the volume of the oven, so it doesn?t really answer the question.

We don?t know if the universe is finite or infinite. If the universe is infinite, the expansion is slightly easier to explain, because 2 x infinity = infinity
- This means that an infinite universe can expand into itself
- this is based on Cantor?s mathematics of infinite numbers, which is not really intuitive in our finite experience!
- Rationale: It is possible to create a 1 to 1 correspondence between a number z and number 2 x z, where z can range from minus infinity to plus infinity

[alancalverd]

Or you could start with an infinite vacuum, insert a finite number of atoms, and persuade them to move apart. If you define "universe" to mean the volume occupied by atoms, there is no conceptual problem.

[Halc]

If the universe is expanding, what is it expanding into?

The expansion of the universe is metric expansion of space itself, meaning that each volume of space is later larger, but nothing is actually significantly moving.  This means that the universe was always infinite, never bounded, and has no center, no edge where 'the universe is moving into previously unoccupied something'.  The big bang took place literally everywhere, not at some special location.

Another metaphor is cooking a raisin cake: all the raisins move away from each other in 3D.
- But the cake expands into the volume of the oven, so it doesn?t really answer the question.

Yes, the finite cake is a bounded model, so doesn't work.  It works if you consider it to be an infinite cake. The balloon surface is at least not bounded. There is no point on the surface of a balloon that is its center, but the mental image of it is still a 3D volume through which 2D space is moving.

Or you could start with an infinite vacuum, insert a finite number of atoms, and persuade them to move apart. If you define "universe" to mean the volume occupied by atoms, there is no conceptual problem.

No, this is exactly wrong.  That model has material moving through static space rather than space itself expanding. The finite atoms would have a center of mass, a point where the big bang took place. It would have atoms moving faster than light. All this is inconsistent with the consensus model of the expansion of space itself.

[alancalverd]

The finite atoms would have a center of mass, a point where the big bang took place.

Only if you wanted the big bang to have happened at a point.

If two atoms are moving apart faster than c, the center of mass concept is meaningless as they cannot receive gravitational influences from each other. But in order to do so they cannot have been created at a common point since it would require infinite energy to accelerate them to > c.

[varsigma]

The nice thing about logic is, you can look at it forwards and backwards.

In the latter case, the universe is contracting, and, Einstein's theories predict it contracts to a point. Except maybe not.

But the take away is that you imagine the quite large universe getting smaller. It doesn't have anywhere to leave an empty space behind it, that it might expand back into. Except that one is only true if there is a maximum of three spatial dimensions. Distances are not numbers, so they aren't much help here.