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John Derbyshire

With things on the surface of the Earth obviously going to hell in a hand basket, there is some consolation to be found in contemplating the rest of the universe. I don’t know that healthy people, other than salaried cosmologists, ought to do too much of this, but it is salutary once in a while to try to get one’s mind around the whole shebang. It puts all those ugly headlines into perspective, soothing and calming the mind. Out, then, into the cosmos!

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I am not going to offer a course in elementary astronomy. If you can’t remember the difference between planets, stars and galaxies, you can pick up the essentials from “The Galaxy Song” at the end of the movie Monty Python’s The Meaning of Life. These fundamentals have been known for decades. In recent months, however, cosmologists have been able to add a great deal to our understanding. Some long-standing mysteries have been clarified, some once-popular theories knocked on the head, some margins of error narrowed. All this has been made possible by a very clever little NASA satellite known as WMAP — the Wilkinson Microwave Anisotropy Probe, launched in June 2001.*

What WMAP is doing up there above our heads is looking at the oldest light in the universe. The light that comes to us from the Sun is about 8½ minutes old; the light that comes to us from Pluto is 5½ hours old; the light from the Pole Star is around 430 years old. The most distant thing you can see in the night sky is the M31 galaxy, whose light is nearly 3 million years old when it reaches us. WMAP is looking at light way, way older than that: light over 13 billion years old. This was the first light in the universe, the light that shone when (to state the matter approximately) there was first enough space for light to shine. What WMAP can do much, much better than we have ever been able to do before is examine the variations in this ancient light, the patches of greater or lesser luminosity. In this way, the satellite can tell us new and interesting things about the very early universe — for that, of course, is where this ancient light originated. This is light from a short time — a mere 380,000 years — after the Big Bang.

The Big Bang concept is widely misunderstood. It was not a case of a blob of stuff suddenly exploding outward into an empty blackness beyond itself. There was no empty blackness; there was no “beyond.” The Big Bang theory, confirmed by all of WMAP’s observations, says this:

In the remote past, the universe — the entire universe — was much hotter and denser than it is now.

At some period before that, it was so hot and dense that ordinary matter could not possibly have existed.

At some period before that, it was so hot and dense that our current understanding of physics is unable to describe it.

There is very little point in asking what the situation was before that. The word “before” has meaning only when time is doing its usual thing — advancing from the past into the future at a steady clip — and preferably when we have some means to actually measure time. In the remotest, hottest, densest state of the universe, time (along with space, matter and energy) was doing something unfamiliar, something we really don’t understand very well. There was, in any case, nothing around with which we could measure time: no swinging pendulums or moving clock-hands, no vibrating atoms, no decaying particles. Far back in that zone — very close to what physicists call “the initial singularity” — our understanding breaks down completely. There we bump up against Ludwig Wittgenstein, the philosopher who said: “Of that of which we cannot speak, we must perforce be silent.” ** Pictures of a spiky bright starburst exploding into blackness are a childish misrepresentation of this profound mystery.

When was that state of affairs? How far back can our understanding take us? Answer: about 13.7 billion years. That is “the age of the universe,” according to the WMAP observations. At that distance in time, we know that the universe was fantastically hotter and denser than it is now. At some point shortly before that, conditions were so extreme our understanding cannot encompass them.

Now, 13.7 billion years is not actually a very great age. Our own Earth is around 4.55 billion years old, almost precisely one-third the age of the universe. The Sun is a little older — the Earth and other planets are a sort of scum left over from the Sun’s condensation. These are big numbers, but in a way they are comforting. Taken together with the WMAP findings, they indicate that the entire universe operates on a scale of time that we can grasp imaginatively. The earth is very old, but we can come to mental terms with its age. We can handle rocks that were formed very early in Earth’s history; we can construct a plausible picture of the development of living things across most of that history. (Life seems to have got going almost as soon as the new Earth was cool enough to bear it.) That the universe is merely three times older than this means that the universe is Earth-scale in time. It might easily have been not three, but three trillion, or three googol***, times older than our home planet. That would present us with serious conceptual difficulties.

The WMAP observations indicate that the future of the universe may also be on this same friendly scale. Space and time may only have another 21 billion years of existence, according to one theory arising from those observations. WMAP has determined that only 4 percent of the universe is made of ordinary matter. An invisible stuff known as “dark matter” makes up another 23 percent, with the balance — 73 percent — consisting of “dark energy.” Now, just as ordinary matter and energy generate gravitational fields, which are always attractive, so dark energy generates antigravity, invariably repulsive. Depending on some parameters not yet known with enough precision, the average density of dark energy may increase as the universe ages, leading to a runaway expansion or “Big Rip,” with everything accelerating away from everything else until the cosmos becomes infinitely large and time comes to a stop 21 billion years from now. As unappealing as this sounds, it is no worse, and a good deal speedier, than the previously favored theory of The End, in which everything drained away into black holes over a time span of googols of years. Again, we are at least operating with Earth-size numbers.

Space may also, like time, turn out to be on a scale we can just about comprehend. The simplest model of the universe, mathematically speaking, is one that is infinite in size and “flat.” That is, if you were to start off from Earth and travel through space in a straight line, you would (a) never return to your start point, and (b) always be among familiar types of matter and energy. The universe may indeed be like that, but WMAP is offering some hints that suggest otherwise. Our three-dimensional universe may do something analogous to what the two-dimensional surface of a sphere does — wrap round on itself, so that if you head off in a straight line in any direction (like an ant setting off southward from the north pole of a sphere), you return to your starting point in some definite time. It might even do something analogous to what the two-dimensional surface of a tire inner tube does — wrap round on itself in such a way that you get back to your starting point much faster in one direction (“across” the inner tube) than in another (“around” the inner tube). In either case the universe would be finite, as the surface of a sphere or an inner tube is, and probably not very large: billions of light-years, not googols of light-years, around. Physicists will be content with whatever has emerged when we have enough data to settle the matter; but on the whole they would prefer the universe finite, as infinity presents some knotty problems.

[Though not the problem the newspaper reports have been telling us about: the problem that, in an infinite universe, absolutely everything must happen. There would, these reports claim, somewhere in the remote reaches of an infinite universe, be another world exactly like our own in every respect, except that my name would be spelt "Darbyshire." This is not true. You can have an infinite universe in which certain things never happen. The set of numbers 2, 4, 6, 8, 10, 12, 14,... is infinite, but that doesn't mean you can find every conceivable kind of number in it. In fact, it contains no odd numbers at all. You can, in fact, have an infinite universe in which nothing ever happens — a sort of Virginia Woolf universe.]

You will often hear it said that the size and age of the universe are so large we cannot grasp them. The evidence coming in from WMAP suggests that this is not so. The entire age of the universe may be only 35 billion years, nearly forty percent of which has already elapsed. It may be only a few billion light years around, or across. These are big numbers against the scale of our everyday lives, but they are not breathtakingly unapproachable. They are very small potatoes by comparison with what they might have been. Mathematics has numbers far, far larger than this.**** The universe may not be infinite, nor even very large. It is entirely possible that one of the distant galaxies we can see with our telescopes is in fact our own galaxy, its light having traveled all the way round the cosmos and back to our eyes.

The late Isaac Asimov, in one of his beautiful little pop-science essays, described the progress of human understanding as a series of dethronements. We thought the Sun and planets all revolved round the Earth, then Copernicus showed us otherwise. We thought our star system was the only one (see H. G. Wells’s 1896 short story “Under the Knife” for this phase of our understanding), till Edwin Hubble proved that it was merely one among billions. We thought we human beings were a separate creation from the rest of the animal kingdom, but Darwin and his successors proved us wrong. Dethroned, dethroned, dethroned: this past 500 years has wrought havoc with humanity’s self-esteem. But look! — the Creator has given us a universe of modest duration and limited size to play in. We can’t do much with it at our present stage of development, but it is not inconceivable that our remote descendants, yours and mine, might spread out across it and master it. Sure, we are insignificant, but not quite as insignificant as we thought we were a couple of years ago.

* All told, WMAP will cost about $145m, spread over five years. For comparison, one Space Shuttle flight costs $550m. The satellite has been designed and built for NASA by a consortium of scholars, with Princeton University a principal player. David Wilkinson was a Princeton cosmologist who died last September. The satellite, originally just MAP, was re-named in his honor.
** In German: Wovon man nicht sprechen kann, darüber muss man schweigen. I have often envied the Germans for their having a single verb, the verb schweigen, that means “to be silent.” We could use a verb like that in English.
*** A googol is ten thousand trillion trillion trillion trillion trillion trillion trillion trillion. In its written form, it is a “1″ followed by a hundred zeros. The probability of you typing out the Wittgenstein quote above (ignoring the umlaut) by hitting the keys on a 50-key keyboard at random are about one in a googol.
**** The biggest one mentioned in Prime Obsession has ten to the power of ten billion trillion trillion digits, i.e. 1010,000,000,000,000,000,000,000,000,000,000,000 digits. That’s not the number, that’s the number of digits in the number. You didn’t think I was going to get through this without a plug for my book, did you?



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