The Over-and-Back Paradox
A paradox is something that can't possibly be true, but apparently is. The trick is to figure out how to resolve it. The "Over-and-Back Paradox" has to do with the true age of the universe relative to the age postulated by the Conventional Model of the Big Bang.
Recent Hubble telescope pictures show immature galaxies at a distance of about 14 billion light years from Earth. According to the Conventional Model, these are said to have been formed near the beginning of time. They have obviously evolved for a billion years or so, and their light has then been travelling towards us ever since. They have been moving all that time, so they are now even further away from us than they once were.
The Conventional Model says that space was added between these bodies and us fast enough to delay the time that the light took to reach us! However, we have no evidence that any space is being added inside the Solar System or inside the Milky Way! So why should we believe that space was added outside the Milky Way? In fact, galaxies seen as they were billions of years ago are much the same size and shape of nearby galaxies. In any event, we moved away from these bodies after the original creation event.
A reader of this essay objected to the statement, "added between", and corrected it to the words "space expanded", giving the familiar balloon analogy. He saw no reason that space could not have expanded even almost at the speed of light to fully explain this paradox. Let me remind this reader that if he were to also have a picture of a clown drawn on his balloon, and he blew it up, not only would the dots move apart, but the clown would expand and get bigger too! We have no evidence that galaxies or clusters have gotten bigger and their constituents have moved further apart. Hence, the balloon expansion is a false analogy. Please read the next section, recently added, for even wilder claims.
Impossible Size? Cornish Explains Further (Update, 8:25 a.m. Tuesday, May 25, 2004)
This article generated quite a few e-mails from readers who were perplexed or flat out could not believe the universe was just 13.7 billion years old yet 158 billion light-years wide. That suggests the speed of light has been exceeded, they argue. So SPACE.com asked Neil Cornish to explain further. Here is his response:
"The problem is that funny things happen in general relativity which appear to violate special relativity (nothing traveling faster than the speed of light and all that). Let's go back to Hubble's observation that distant galaxies appear to be moving away from us, and the more distant the galaxy, the faster it appears to move away. The constant of proportionality in that relationship is known as Hubble's constant."
"One seemingly paradoxical consequence of Hubble's observation is that galaxies sufficiently far away will be receding from us at a velocity faster than the speed of light. This distance is called the Hubble radius, and is commonly referred to as the horizon in analogy with a black hole horizon. In terms of special relativity, Hubble's law appears to be a paradox. But in general relativity we interpret the apparent recession as being due to space expanding (the old raisins in a rising fruit loaf analogy). The galaxies themselves are not moving through space (at least not very much), but the space itself is growing so they appear to be moving apart. There is nothing in special or general relativity to prevent this apparent velocity from exceeding the speed of light. No faster-than-light signals can be sent via this mechanism, and it does not lead to any paradoxes." !!!
Statement of the Actual Paradox
1) If the age of the universe is about 15 billion years, consistent with the inverse of the Hubble constant, then the light must have left those far galaxies when the mass that made those galaxies was relatively close to the mass that eventually made the Earth. Why did the light take so long to get here? Did it take the long way around, rather than the straight line distance? Did space really expand between us fast enough to almost outrun the light? The Conventional explanation is that is precisely what happened, and what we see is an apparent present distance of separation.
2) Alternately, let's assume that those far galaxies were really 14 billion light years away from us when the light left them. Then how did they get so far away, if they started out close to us? They weren't moving anywhere near the speed of light at the time we saw them. The Conventional explanation is that they weren't far away at all.
The two statements together form a paradox if we consider that no volumetric expansion of galaxies has been observed. Something is obviously wrong.
Resolution of the Paradox
There's only one possible scenario that resolves the paradox. The far galaxies must have been formed 15 billion years ago, and the light must have travelled to us for 14 billion years. The universe must then be at least 30 billion years old! It could be even much older than that, as much as 10 times or more as old.
But this does not agree with the Conventional Model! So now the question is, how did it happen? Maybe the Conventional Model is wrong! That leads us to consider using a new model that might be able to resolve the paradox by producing an older universe.