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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?

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  • $\begingroup$ 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. $\endgroup$ – John Rennie Jan 27 '14 at 18:50
  • $\begingroup$ 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. $\endgroup$ – Geoffrey Jan 27 '14 at 19:11
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    $\begingroup$ 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. $\endgroup$ – John Rennie Jan 28 '14 at 8:58
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I could start this answer by saying that space isn't really the thing that's expanding; that it's the scale factor of the metric that's growing larger. But I won't because that's just an overcomplicated way of saying space is expanding. But to answer your question, the most correct way to think about it would be that the grid points are getting farther apart. It is not that we are adding more grid points.

You are correct that the "stretching" of space would apply to all things. For instance, we know that as light travels through space, the expansion causes its wavelength to expand correspondingly. The reason we do not expand with it though is that we have forces holding us together. The space between our atoms does not expand because the electromagnetic force is stronger and holds our atoms in relatively the same place. Similarly, the Sun's gravity holds Earth in its orbit in spite of the expansion. In fact, for all objects within our local cluster, gravity is strong enough to counteract the effect of the grid points separating.

TLDR: The expansion of space is more like "stretching" than adding new space

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    $\begingroup$ If a force is holding two objects together in spite of the space expanding from underneath them, this would mean that the objects are on a sort of treadmill. That is to say that the objects are moving towards each other, while seeming to be at the same distance since the space between them itself expanded. If that is the case, work is being done by the force, and the objects should lose potential energy, shouldn't they? $\endgroup$ – Sujoy Gupta Jan 30 '14 at 8:48
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    $\begingroup$ @SujoyGupta You could take that point of view, but remember that if work is being done by the force holding them, then work is also being done by the expansion to essentially keep them in the same location. The net effect cancels out and we are left with the fact that since the objects do not draw closer or pull apart, there is no net change in potential energy $\endgroup$ – Jim Jan 30 '14 at 15:38
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    $\begingroup$ 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? $\endgroup$ – Geoffrey Jan 31 '14 at 3:32
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    $\begingroup$ If space is stretching, then also our yardsticks are stretching with space. Would that not imply that also the laws of physics are "stretching", and therefore we would actually not notice any difference? I think it is more accurate to say that space is added, that is - in the words of the OP - grid points are added. $\endgroup$ – fishinear Dec 19 '15 at 9:45

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