Into what is the universe expanding?

According to Stephen Hawking the discovery that the universe is expanding is one of the great intellectual revolutions of the 20th century. (see A Brief History of Time, 1998, p.41) Given that this is the case it seems legitimate to ask, as you do, into what is it expanding into. I must confess, given my interest in the relationship between philosophy and science, this is a question that occupied my mind for a time. My interest concerned the issue of the expansion of time in the immediate aftermath of the singularity which we call the ‘big bang’. According to Bill Bryson, most of what we know about the early moments of the universe is thanks to a theory first advanced by Alan Guth, a particle physicist at Stanford University. According to Guth, at one ten millionth of a trillionth of a trillionth of a second, gravity emerged. (see A Short History of Nearly Everything, 2003, p.36) What this means is that in less than the blink of an eye after the ‘big bang’ the universe was at the very least a hundred billion light years across. For me, the immediate consequence of this revelation is that, if the smallest measurable unit of time is equivalent to the figure stated above, then this figure is representative of the speed of that moment in time that we know as ‘the present’. Moreover, since it is clear that this instance is ungraspable by the mind, it follows that in reality we humans can never have the slightest notion of what it is to live in ‘the now’. For us ‘the present’ is both an illusion and a delusion. Rather than experiencing the present the mind is enveloped in a phenomenological membrane that is always playing catch up with the continuum of phenomena - of things as they appear to the mind - that are being filtered through the intuitions space and time, the category of cause and effect, natural inclinations, inherited dispositions, social conditioning, worldly experience, persona prejudices, memories, expectations and ambitions. Given that we can know little or nothing of that which is supposed to be so near to us, the question arises as to what can we know about that which is as remote as the outer regions of the universe? The answer to this is simple: that is, we cannot know anything.

Since this is rather a bald statement I believe it should be followed by some explanation. According to Stephen Hawking there are three models of the universe that explain the expansion of the universe. In the first model the universe is expanding sufficiently slowly that the gravitational attraction between the different galaxies causes the expansion to slow down and, in time, stop. The galaxies then begin to move towards one towards one another as the universe contracts. That is, it starts at zero, expands to a maximum, and then contracts to zero again. (op.cit., p.45) Clearly in such a case the universe is not expanding into anything outside itself. In the second model, the universe is expanding so quickly that the gravitational pull, whilst it may slow it down to some degree, it can never stop it. That is, it starts at zero and eventually the galaxies are moving apart at a steady speed. In the third model, the universe is expanding only as fast as it must to avoid collapsing into itself. In this case the expansion begins at zero and continues indefinitely. However, whilst the speed at which the galaxies move apart gets increasingly smaller, it never quite reaches zero. (see ibid.)

The thing that should be noted about the first model is that in it the universe is not infinite in space, but neither does space have any boundary. Gravity is so strong that space is bent round onto itself, rather like the surface of the Earth, where, if one were to keep going in a given direction one would eventually return to the where one had departed. However, as Hawking points out, whilst this first model may make good science fiction, because it can be shown that the universe itself would recollapse to zero size before one would it return to one’s point of departure. (see ibid., p.47) Since one would need to travel faster than the speed of light to reach the starting point before the universe came to an end, this model is a non-runner (excuse the pun).

In the first model, which expands and contracts, space is bent in on itself, and therefore finite in extent. In the second model, which expands forever, space is bent the other way, making space infinite. In the third model, space is flat, and therefore also infinite. The question is, of course, which model describes our universe. According to Hawking, present evidence suggests that the universe will more than likely continue to expand forever, but all we can be really certain of is that if it were to collapse, it would not be for at least another ten thousand years, since it has already been expanding for at least that long. (ibid., p.48). Since mankind will have long outlived its usefulness on this Earth before this time, there is little need for this statistic to concern us.

So where does all this leave us in relation to the question, "into what is the universe expanding?/ The answer of course is that for all their ingenuity, the models leave us none the wiser. We simply cannot know into what the universe expanding.