GRAVITY WAVES, INFLATION, AND YOU
(Adapted from You Are Here: A User's Guide to the Universe. Click this if you'd prefer to read a PDF version.)
The publication of You Are Here: A User’s Guide to the Universe coincided with one of the most exciting bits of science news in decades: confirmation of Einstein’s prediction that spacetime itself ripples.
I hear you ask: Who cares? And I say: You do! You see, the really exciting thing about the discovery of gravity waves is not the waves themselves, but what they imply: that the theory called “inflationary cosmology,” dreamed up in 1979 by Alan Guth of MIT, is probably true.
Still not with me? Think this is esoteric nerd-food? Believe me: we all have to live in the same universe, and inflationary theory has done something truly outrageous to the place. It really is worth understanding what the fuss is about.
Here’s the three-sentence version:
Patterns in the gravity waves detected by the BICEP2 facility at the South Pole mean that inflation theory is probably true, and it follows that the universe is bigger than we thought it was. Much much much much much much much bigger. So much-much bigger, in fact, that if you suffer from vertigo you should either stop reading now or keep a plastic bag handy.
According to standard Big Bang Theory, “the universe” erupted out of essentially nothing 13.7 billion years ago. This was not an explosion—something that occurs in space—but an expansion of space. Think of pudding with raisins in it: as the pudding bakes, and inflates, all the raisins get further from each other. Since nothing travels faster than light, the furthest raisin we can see in any direction is 13.7 billion light years away (a bit less, in fact) and therefore our raisin (and every other raisin) seems to be at the center of a bubble roughly 27 billion light years in diameter.
OK, scratch that: even this “observable universe” is in fact quite a bit bigger. If light came from an object 13 billion years ago, then that object isn’t 13 billion light years away now. It was 13 billion light years away when the light we detect was emitted—but the universe has continued to expand since then. Think of a friend 13 feet away, throwing you a ball. If she’s standing on a rubber sheet that’s being stretched as the ball flies through the air, she may be 20 feet away by the time you catch it. Using the same idea, we can calculate that the radius of our “observable universe” (also called our “Hubble volume”) is more than 45 billion light years.
Notice that we’ve already severed the connection between “the universe” (= everything) and “the observable universe” (= what our telescopes reveal). The limit on how far out (or ‘back’) we can see lies in physical law, and has nothing to do with how much universe is “really out there.” The edge of the observable universe is an edge in time, not space. There could be galaxies further than 45 billion light years away; if there are, we simply wouldn’t know about it, since the universe hasn’t been around long enough for their light to reach us.
Well, are there any galaxies further out? Is the universe bigger than the observable universe?
That’s where inflationary cosmology comes in. In the late 1970s, physicists were looking for GUTs, “grand unified theories” that would combine general relativity (Einstein’s theory of gravitation) with quantum mechanics (the leading theory of everything else), thus making sense of all the forces of nature in one framework. (I’ll skip the suspense: more than a generation later they’re still sitting on the pot, purple in the face, grunting and straining. Nothing but gas has yet been produced.) A key question for GUTs is: what happens to particles at higher and higher energies? That’s why they keep building really huge, really expensive machines. Now, 10^14 GeV (100 billion electron volts) is barely enough energy to keep a flashlight running while you put the dog out—but Guth wanted to know what happens when you light that much gunpowder under a single elementary particle.
Simple calculations show how to do this. You just build a particle accelerator bigger than the solar system. Unfortunately the National Science Foundation doesn’t have that kind of money, so the only available ‘lab’ is the first 10^-35 of a second after the Big Bang. At that time, particles typically came equipped with 10^14 GeV of energy apiece.
That’s how physicists like MIT’s Alan Guth came to wish they knew a bit more cosmology. And that’s how he came to be familiar with all sorts of problems about the ‘standard’ Big Bang theory that the cosmologists were frankly pretty embarrassed by. One, called the flatness problem, puzzled Guth in particular. (In a very small nutshell: “How can the universe be essentially the same in all directions, when the bits of it 13 billion light years to our left can never have communicated with the bits 13 billion light years to our right?”) One day, a neat solution to the flatness problem—and other problems—popped into Guth’s head.
The solution was ludicrous, and it had some even more ludicrous consequences, but it was still kind of interesting. Theorists will be theorists. No need to worry, right?
When Archimedes discovered the principle of buoyancy (“A floating object displaces its own weight in water”) he leapt out of his bath and ran naked through the streets of Syracuse shrieking Eureka—which, as everyone knows, is Greek for “I found the soap.” Guth was not in the bath when he had his Eureka moment, so he had to make do with writing SPECTACULAR REALIZATION on a sheet of paper and drawing a big box around the words. What he had seen was this: many of the problems with ‘standard’ Big Bang theory vanish if you assume that the universe went through a brief but aggressive period of ‘inflation’ in the first fraction of a second of time.
Of course, in one sense the universe is ‘inflating’ right now: it’s still expanding. But what Guth meant was different. He meant that for a certain incredibly brief instant the dimension of space expanded faster than the speed of light.
Impossible? No. Einstein’s equations tell us that nothing can traverse space (get from A to B) faster than light. But relativity doesn’t say anything about how fast A can get away from B—that is, how fast space itself can expand. So Guth’s idea, however counterintuitive, doesn’t violate any known physical laws.
There were also some good technical reasons to take inflation seriously, but it did sound a bit phony at first; it had the ring of a cleverly-engineered solution designed specifically to sweep problems under the carpet.
The shy phase didn’t last. Like all good scientific theories, inflation led to specific predictions, and predictions led to huge grant proposals and large, complicated, satellite-based experiments. The theory passed the tests brilliantly. That’s when cosmologists started to mull over the possibility that some version of Guth’s idea was probably not just clever mathematics but rather a description of our world.
While the scientific community was still digesting this, and getting a bad case of heartburn as a result, along came Russian cosmologist Andre Linde. Linde saw a problem with Guth’s theory, and came up with a solution. The solution was inflation in a new form, which Linde calls “chaotic inflation.” The new theory was even more persuasive—and had consequences even more ludicrous than the old one.
The “inflationary epoch” (yes, they really call it that) occurred only for the first zepto-fragment of a second. In fact it ended at 10^-35 of the first second—which is a bit like planning to read the whole Library of Congress, then giving up after the first letter of the first word. Even if the universe had been expanding at the speed of light, 10^-35 of a second is so brief that the universe could have gotten only a teeny bit bigger. But inflation theory says that in this time it actually doubled in size every fraction of a trillionth of a second—not just getting a bit bigger overall, or ten times as big, but growing from sub-sub-sub-atomic size to the size of a baseball.
Doesn’t seem like much, does it? But the original “universe seed” is to a baseball as the piece of grit in your eye is to the current observable universe. Only more so.
According to various versions of Linde’s theory, inflation means the radius of the universe now is at least 10^100, or possibly 10^40,000, or possibly “ten to the ten to the twelve” times as big as we thought.
Since all these numbers are perfectly insane, let’s look first at the most insane of all. In the end, as you’ll see, it doesn’t make a whole lot of difference. “Ten to the ten to the twelve” (10 raised to the power of 10^12) might not look very impressive to a non-mathematician. That’s a pity, because in fact it’s a number that makes a term like “mind-bendingly humongous” seem almost hysterically inadequate. And ‘hysterical’ is the word: once you start to understand “10 raised to 10^12”, sobbing with horrified laughter is a perfectly reasonable response. “10 raised to 10^12” is, in the most literal sense of the word, monstrous. To borrow a phrase from Shakespeare, it beggars all description. But hey, let’s have a go.
“10 raised to 10^12 times bigger” is not 12 times bigger. Nor is it “10 x 12” (= 120) times bigger. Nor is it “10 raised to the 12” (= one trillion) times bigger.
A trillion times bigger—that would be headline stuff! But no. The Linde Universe is “10 raised to the ‘10 to the 12th power’” times bigger. That’s ten raised to the power of a trillion (10^1,000,000,000,000) times bigger.
This is a number far, far too big to write down in ordinary notation. It’s also far too big to make sense of, but maybe we can try to get a little sense of just how little sense of it we can get...?
A quick refresher on the power of powers is in order here. Pick a seriously big number: say, the number of protons and neutrons in the observable universe. That’s said to be somewhere around 10^80, which is 1 followed by 80 zeroes. Definitely more than you have in the bank. But remember that, the way powers of ten work, a trillion universes like ours (10^12 of them) would have 10^80 x 10^12 = 10^(80+12) = 10^92 protons and neutrons.
So if you can imagine the difference in scale between (a) a single proton, and (b) a trillion of our universes—which, of course, you can’t—you’ve not even taken the first step up the mountain towards imagining the scale of the Linde Universe.
Suppose instead that we attempt to get a grip on the idea by using a model. A really really tiny model. Let’s shrink our vast “observable universe,” all 100 billion galaxies or so—to the size of a grain of sand. Or: let’s reduce everything further, to the point at which the observable universe is the size of that speck-within-a-speck-within-a-speck, the proton.
The observable universe is about 10^26-meters. The proton is about 42 orders of magnitude (42 zeroes, if you like) smaller, at 10^-15 meters.
So, if we reduce the Linde Universe by the same amount, to create a “Linde Miniverse” that’s also 42 orders of magnitude smaller--
Instead of being 10^1,000,000,000,000 times bigger than the observable universe, the Linde Miniverse is only 10^1,000,000,000,000 divided by 10^42 times bigger.
Which is 10^(1,000,000,000,000-42) times bigger.
Which is 10^999,999,999,958 times bigger.
Here’s an admittedly paradoxical way to put this: At least from the human point of view, the Linde Universe is so utterly and absurdly gargantuan that shrinking it to a millionth of a trillionth of a trillionth of a trillionth of its original size doesn’t really make any difference to how big it is.
Now admittedly, on some of Linde’s models the whole universe is much smaller than this: a mere pathetic 10^100 times bigger than the observable universe, for instance. In which case our proton-sized micro-universe sits in a Linde Miniverse that’s a mere pathetic 10^(100-42) = 10^58 times bigger than the observable universe.
In ordinary language, that’s ten billion trillion trillion trillion trillion times bigger.
Give up yet? Had enough? It gets worse!
First, 10^100 and 10^1,000,000,000,000 are to some extent figures pulled out of thin air: the real power might be smaller or larger—or it might be, as Alexander Vilenkin and others have theorized, that space is simply infinite. (This isn’t ‘just a theory.’ Some measurements of tiny irregularities in the Cosmic Microwave Background make sense if space is infinite and are hard to explain if it isn’t.)
Second, Guth, Linde, and Vilenkin all doubt whether our universe, however big it may be, is all there is. On the contrary, in fact: inflation theory strongly suggests that our universe is just one “bubble” of spacetime among others—nothing more than a single fragment of fizz in the champagne glass of creation. If this is right, then there are other universes out there. Or out somewhere: these are not just other regions of space but in a deeper sense separate spaces, and there may be new ones fizzing into existence all the time.
In a new twist on the idea of the Creation, both theorists have also suggested that, given a microscopic fraction of matter as a seed, and the right technology, an advanced civilization might be able to ‘grow’ new universes at will. As Guth puts it, with characteristic dark humor, our universe may have originated on a bench in someone’s basement. It’s rather disturbing to think that the God of the Creation might have been a minimally competent twelve-year-old in some other universe, and that our universe might be a bench-top experiment gone wrong.
What if space is infinite? And what if, as the evidence suggests, this infinite space has matter evenly distributed through it? Quantum theory says space comes in little lumps called Planck volumes. (They make a proton look vast: they are 10^20 times smaller.) Like a Rubik’s cube, a space divided up into Planck lengths can only have a (gargantuan, but) finite possible arrangement of matter and energy.
So everything that can happen does happen.
Calculations by cosmologist Max Tegmark indicate that there must be a “Twin Earth” within 10^(10^28) meters from us that’s identical to the Earth in every single detail of its entire history except that your name is Obadiah.