When subjected to spectral analysis, the wavelength of the light of the majority of stars is increased, shifted toward the red end of the spectrum. This lengthening of wavelength, the red-shift, may be a result of the Doppler effect. By this interpretation, the red-shift indicates that the greatest numbers of stars in the universe are moving away from us.
This red-shift effect, or increase in wavelength, may also result when radiation loses energy by moving against a gravitational field, suggesting the alternate hypothesis that the light of stars loses energy as it travels against the gravitational field of the Milky Way Galaxy. The presently accepted theory of the Big Sang is based in part upon the Doppler interpretation of the red-shift. Since the distances between all the stars appears to be constantly increasing, this, according to the theory of the Big Bang, suggests that Space itself is expanding.
But at this point, we have made a leap in the logic. The red-shift is describing the behavior of stars and other sources of radiant energy, The statement is: A) "The red-shift suggests that the majority of stars are moving away from us." But this statement is not equivalent to the statement: B) "Space is expanding." These are two different statements, and though A) may suggest B), A) does not does not prove B), and neither is B) a necessary consequence of A). Alternate hypothesis are available to us.
Which brings us close to a number of suspiciously semantic issues. When I walk away from you, the distance between us increases. We may say that the space between us has increased, though distance and space are not precisely the same thing. We would not say that the distance between us has expanded, because distance is a measure in two dimensions where expansion is a term we use to describe a four-dimensional event. Neither, in this case, would we say that the space (as a `thing-in-itself') between us has expanded. We are using the word space in two different senses here, and this may be giving rise to some ambiguities. In one sense, we are speaking of space as a synonym for distance. In this sense, the word space is being used as an adjective, describing the relationship between objects (as in `the space between us'). Distance does not exist of its own right. We must have objects for distance to occur.
With the word `Distance', we are describing the behavior of objects, and our discussion has nothing to do with `Space' itself. When I walk away from you, the space between us is doing nothing. It is not actively increasing its own volume, and neither is it being acted upon. Our relative motions have no effect on `Space'.
In the second sense, when we describe space as `expanding' our discussion slides insensibly into `Space' as a noun. The word `Expand' is an active verb. We ascribe verbs to nouns (for verbs and nouns are functions of the same entity). If it is expanding, `Space' must be a noun. When we use the word Space in this sense, we are using it in the sense of an area of volume, as in the space of a living room, a football arena, my space, and your space.
But we don't know that space is expanding. The red-shift may suggest the expansion of space, but certainly, does not prove it and we have grounds for raising a number of questions here. We may ask for a precise description of the logic that brings us from a discussion of the behavior of stars to a discussion of the behavior of space. We may ask for the steps that bring us from discussion of distance (adjective) between objects to a discussion of Space in itself (noun). We may ask the question "Since my movement away from you increases the distance between us, but leaves the Space unchanged, what is the mechanism or the logic that makes stars or other objects indicators of the behavior of space itself?"
We have many areas of doubt. The red-shift does suggest that space may be expanding, but it leaves open many other possibilities as well. It leaves open the possibility of influences other than the Doppler effect playing a role in our observations. It leaves open the possibility that we have been stumbling over semantics for decades, it leaves open the possibility that Space is not expanding. It leaves open the possibility that `Space' is an adjective, and does not exist until needed by a noun. It also leaves open the possibility that there simply is no such thing as Space at all.