Expert: Courtney Seligman - 8/27/2011

Question
I have read and understand your answer of 8/13/2011 to the question about the age of the universe being 13.7 billion years old and the cosmic horizon of visible light being 42 billion light years. However, doesn't this seemingly violate the Theory of Relativity? If the farthest galaxies are 42 billion years away relative to us, but have only had 13.7 billion years to traverse that distance, were they not moving away from our relative positions at speeds greater than the speed of light?

Answer
(Sorry for the delay in replying. I wrote an answer several hours ago, but when I tried to 'send' it, my Internet connection died, and it took quite a while to figure out how to fix it.)

It is true that nothing (including light) can go faster than light, relative to the immediate surroundings. But the expansion of the Universe does not involve things moving relative to their surroundings. It involves an expansion of the empty space which contains those things.

When the objects we see as they were 13.7 billion years ago emitted the light by which we now see them, they were only a few thousands or hundreds of thousands of light years away from us. But the space between us and them was expanding at nearly the speed of light, so the light coming from them toward us couldn't make much headway. If, say, light was coming from a region moving away from us at 99% the speed of light, it would take a hundred years to get one light year closer to us. If it was coming from a region moving away from us at 99.9% the speed of light, it would take a thousand years to get one light year closer to us. So the time required for the light to move the few thousands or hundreds of thousands of light years from "there" to "here" stretched out to 13.7 billion years.

Now during that time, the objects which emitted the light were probably not moving relative to each other or the space containing them at any significant speed (usually, "peculiar" (non-Hubble-expansion) velocities are only a few hundred to at most a couple of thousand miles per second, which is nothing in comparison to the speed of light). But being originally in a region moving away from us at nearly the speed of light, they were rapidly carried away from us, to much larger distances. And obviously, if it took the light coming from their smaller distances billions of years to struggle through the expanding space between us and them, then they should have ended up (moving away at nearly the speed of light, not because of their own motion, but because of the expansion of space between us and them) at least that far.

In addition, as they got further away, there was more space between them and us than originally. This means that even though the expansion of space per unit of distance might have slowed (and in fact did slow) quite a bit, their original speed of motion away from us (equal to nearly the speed of light) would now be faster than ever, since there is far more space between us and them now than ever before.

Exactly how much space is between us and them at the present time is hard to say. It depends upon how the expansion rate of the Universe has changed over time (which can be estimated, by comparing "actual" distances, measured in one way or another, to distances estimated from redshifts), and the overall "shape" of space-time (which can be "spherical", "flat", or "hyperbolic"). The shape is not really known, but the best current estimate is that it is more or less "flat". If that is assumed to be absolutely correct, then calculations indicate that galaxies seen as they were 13.7 billion years ago have now been moved nearly 42 billion light years away by the expansion of the space between us and them. They themselves did not move that far; in fact, relative to the objects near them, they have probably moved by insignificant amounts. But the space between us and them, expanding faster and faster simply because there is more and more of it as time goes on, has carried them along with it, until they are about that distance.

Of course, the assumptions involved in the last paragraph, which are related to the calculation of the actual distance of the objects, may be slightly "off", in which case they could be a few billion years closer or further than that. But it really doesn't make any difference, because given their current distance, the space between us and them must be expanding at about 3 times the speed of light (not at any given place; just over the total space between us and them), so light from them traveling toward us is actually moving away from us at twice the speed of light, because the "ship" of light moving toward us is going slower than the "current" of expanding space, carrying it away from us.

I hope this makes things clear; but if there is anything still confusing you, just let me know.