What is the meaning of the “expansion of space”?

When we say that "the space between galaxies is expanding," what do we really mean? For instance, if I think of space as being a Cartesian grid, then when space expands should I think of it as adding more grid-points or as making the distance between the grid-points larger? Or is this a flawed picture of space-time even when far from significant mass densities?

It seems to me that it must be the case that we are "adding more grid-points" because otherwise we would not observe the expansion since anything that occupied that part of the grid (e.g. light, my hand, etc.) would also expand by a corresponding amount (otherwise, after a sufficient amount of expansion, we would be able to observe sub-atomic scale processes as being macroscopic in scale). But if it is the case that we are adding more grid-points, then the "expansion" of space seems like a misnomer: shouldn't it be called the "creation" of space?

That being said, either case (adding grid-points or stretching distances) could conceivably be the same process depending on the nature of space-time (i.e. if it were discrete but dense - like the Rationals - rather than either strictly discrete (Integers) or strictly continuous (Reals)... I hope that analogy makes sense).

So what is really going on in intergalactic space? What is the meaning of its expansion? Does it correspond to creating more space, stretching the space that's already there, or something more subtle?

• Though it isn't an exact duplicate, my answer to Does time expand with space? includes a description of what we mean by the expansion of space. – John Rennie Jan 27 '14 at 18:50
• What it sounds like is that the meaning of space's expansion is that our measuring sticks find larger distances between points in space at later times (which is of course just a way of quantifying the statement "space is expanding"). That is a pretty unsatisfying answer. But is that really the best explanation that the theory has: space is expanding means the distance between two points increases with time? Surely there is some deeper insight into what the theory has to say about how space itself is changing when it is the case that our measuring sticks find greater distances at greater times. – Geoffrey Jan 27 '14 at 19:11
• I can see (what I think is) your point. The trouble is that the deeper insight you are straining for is very deep. The behaviour of spacetime is linked to a fundamental symmetry called general covariance. Spacetime is expanding because it has to in order to respect this symmetry. – John Rennie Jan 28 '14 at 8:58

• So here's the rub: if this is the case, then after a very long time shouldn't the expansion of space imply that vacuum processes which used to occur at very small length scales would now be macroscopically observable? Since vacuum fluctuations are controlled by the fields which are functions of space, then what is keeping the distances over which pair-produced particles (for example) can exist from expanding also (in other words, raising the value of $\hbar$)? Is it just the case that expansionist theories break down in that limit, or am I missing some subtlety? – Geoffrey Jan 31 '14 at 3:32