Read The Fabric of the Cosmos: Space, Time, and the Texture of Reality Online
Authors: Brian Greene
Tags: #Science, #Cosmology, #Popular works, #Astronomy, #Physics, #Universe
The Fabric of the Cosmos: Space, Time, and the Texture of Reality (35 page)
The time line in Figure 9.2 places the phase transitions we've discussed in historical context and hence gives us a firmer grasp of the sequence of events the universe has gone through from the big bang to the egg on your kitchen counter. But crucial information is still hidden within the fuzzy patch. Remember, knowing how things begin—the order of the stack of pages of
War and Peace,
the pressurized carbon dioxide molecules in your bottle of Coke, the state of the universe at the big bang—is essential to understanding how they evolve. Entropy can increase only if it is given room to increase. Entropy can increase only if it starts out low. If the pages of
War and Peace
begin thoroughly jumbled, further tosses will merely leave them jumbled; if the universe started out in a thoroughly disordered, high-entropy state, further cosmic evolution would merely maintain the disorder.
The history illustrated in Figure 9.2 is manifestly not a chronicle of eternal, unchanging disorder. Even though particular symmetries have been lost through cosmic phase transitions, the overall entropy of the universe has steadily increased. In the beginning, therefore, the universe must have been highly ordered. This fact allows us to associate "forward" in time with the direction of increasing entropy, but we still need to figure out an explanation for the incredibly low entropy—the incredibly high state of uniformity—of the newly born universe. This requires that we go even farther back than we have so far and try to understand more of what went on at the beginning—during the fuzzy patch in Figure 9.2—a task to which we now turn.
WHAT BANGED?
A common misconception is that the big bang provides a theory of cosmic origins. It doesn't. The big bang is a theory, partly described in the last two chapters, that delineates cosmic evolution from a split second after whatever happened to bring the universe into existence, but
it says nothing at all about time zero itself
. And since, according to the big bang theory, the bang is what is supposed to have happened at the beginning, the big bang leaves out the bang. It tells us nothing about what banged, why it banged, how it banged, or, frankly, whether it ever really banged at all.
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In fact, if you think about it for a moment, you'll realize that the big bang presents us with quite a puzzle. At the huge densities of matter and energy characteristic of the universe's earliest moments, gravity was by far the dominant force. But gravity is an
attractive
force. It impels things to come together. So what could possibly be responsible for the
outward
force that drove space to expand? It would seem that some kind of powerful repulsive force must have played a critical role at the time of the bang, but which of nature's forces could that possibly be?
For many decades this most basic of all cosmological questions went unanswered. Then, in the 1980s, an old observation of Einstein's was resurrected in a sparkling new form, giving rise to what has become known as
inflationary cosmology.
And with this discovery, credit for the bang could finally be bestowed on the deserving force:
gravity.
It's surprising, but physicists realized that in just the right environment gravity can be repulsive, and, according to the theory, the necessary conditions prevailed during the earliest moments of cosmic history. For a time interval that would make a nanosecond seem an eternity, the early universe provided an arena in which gravity exerted its repulsive side with a vengeance, driving every region of space away from every other with unrelenting ferocity. So powerful was the repulsive push of gravity that not only was the bang identified, it was revealed to be bigger—much bigger—than anyone had previously imagined. In the inflationary framework, the early universe expanded by an astonishingly huge factor compared with what is predicted by the standard big bang theory, enlarging our cosmological vista to a degree that dwarfed last century's realization that ours is but one galaxy among hundreds of billions.
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In this and the next chapter, we discuss inflationary cosmology. We will see that it provides a "front end" for the standard big bang model, offering critical modifications to the standard theory's claims about events during the universe's earliest moments. In doing so, inflationary cosmology resolves key issues that are beyond the reach of the standard big bang, makes a number of predictions that have been and in the near future will continue to be experimentally tested, and, perhaps most strikingly, shows how quantum processes can, through cosmological expansion, iron tiny wrinkles into the fabric of space that leave a visible imprint on the night sky. And beyond these achievements, inflationary cosmology gives significant insight into how the early universe may have acquired its exceedingly low entropy, taking us closer than ever to an explanation of the arrow of time.
After putting the finishing touches on general relativity in 1915, Einstein applied his new equations for gravity to a variety of problems. One was the long-standing puzzle that Newton's equations couldn't account for the so-called precession of the perihelion of Mercury's orbit—the observed fact that Mercury does not trace the same path each time it orbits the sun: instead, each successive orbit shifts slightly relative to the previous. When Einstein redid the standard orbital calculations with his new equations, he derived the observed perihelion precession precisely, a result he found so thrilling that it gave him heart palpitations.
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Einstein also applied general relativity to the question of how sharply the path of light emitted by a distant star would be bent by spacetime's curvature as it passed by the sun on its way to earth. In 1919, two teams of astronomers—one camped out on the island of Principe off the west coast of Africa, the other in Brazil— tested this prediction during a solar eclipse by comparing observations of starlight that just grazed the sun's surface (these are the light rays most affected by the sun's presence, and only during an eclipse are they visible) with photographs taken when the earth's orbit had placed it between these same stars and the sun, virtually eliminating the sun's gravitational impact on the starlight's trajectory. The comparison revealed a bending angle that, once again, confirmed Einstein's calculations. When the press caught wind of the result, Einstein became a world-renowned celebrity overnight. With general relativity, it's fair to say, Einstein was on a roll.
Yet, despite the mounting successes of general relativity, for years after he first applied his theory to the most immense of all challenges—understanding the entire universe—Einstein absolutely refused to accept the answer that emerged from the mathematics. Before the work of Friedmann and Lemaître discussed in Chapter 8, Einstein, too, had realized that the equations of general relativity showed that the universe could not be static; the fabric of space could stretch or it could shrink, but it could not maintain a fixed size. This suggested that the universe might have had a definite beginning, when the fabric was maximally compressed, and might even have a definite end. Einstein stubbornly balked at this consequence of general relativity, because he and everyone else "knew" that the universe was eternal and, on the largest of scales, fixed and unchanging. Thus, notwithstanding the beauty and the successes of general relativity, Einstein reopened his notebook and sought a modification of the equations that would allow for a universe that conformed to the prevailing prejudice. It didn't take him long. In 1917 he achieved the goal by introducing a new term into the equations of general relativity: the
cosmologi
cal constant.
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Einstein's strategy in introducing this modification is not hard to grasp. The gravitational force between any two objects, whether they're baseballs, planets, stars, comets, or what have you, is attractive, and as a result, gravity constantly acts to draw objects toward one another. The gravitational attraction between the earth and a dancer leaping upward causes the dancer to slow down, reach a maximum height, and then head back down. If a choreographer wants a static configuration in which the dancer floats in midair, there would have to be a repulsive force between the dancer and the earth that would precisely balance their gravitational attraction: a static configuration can arise only when there is a perfect cancellation between attraction and repulsion. Einstein realized that exactly the same reasoning holds for the entire universe. In just the same way that the attractive pull of gravity acts to slow the dancer's ascent, it also acts to slow the expansion of space. And just as the dancer can't achieve stasis—it can't hover at a fixed height—without a repulsive force to balance the usual pull of gravity, space can't be static—space can't hover at a fixed overall size—without there also being some kind of balancing repulsive force. Einstein introduced the cosmological constant because he found that with this new term included in the equations, gravity could provide just such a repulsive force.
But what physics does this mathematical term represent? What is the cosmological constant, from what is it made, and how does it manage to go against the grain of usual attractive gravity and exert a repulsive outward push? Well, the modern reading of Einstein's work—one that goes back to Lemaître—interprets the cosmological constant as an exotic form of energy that uniformly and homogeneously fills all of space. I say "exotic" because Einstein's analysis didn't specify where this energy might come from and, as we'll shortly see, the mathematical description he invoked ensured that it could not be composed of anything familiar like protons, neutrons, electrons, or photons. Physicists today invoke phrases like "the energy of space itself" or "dark energy" when discussing the meaning of Einstein's cosmological constant, because if there were a cosmological constant, space would be filled with a transparent, amorphous presence that you wouldn't be able to see directly; space filled with a cosmological constant would still look dark. (This resembles the old notion of an aether and the newer notion of a Higgs field that has acquired a nonzero value throughout space. The latter similarity is more than mere coincidence since there is an important connection between a cosmological constant and Higgs fields, which we will come to shortly.) But even without specifying the origin or identity of the cosmological constant, Einstein was able to work out its gravitational implications, and the answer he found was remarkable.
To understand it, you need to be aware of one feature of general relativity that we have yet to discuss. In Newton's approach to gravity, the strength of attraction between two objects depends solely on two things: their masses and the distance between them. The more massive the objects and the closer they are, the greater the gravitational pull they exert on each other. The situation in general relativity is much the same, except that Einstein's equations show that Newton's focus on mass was too limited. According to general relativity, it is not just the mass (and the separation) of objects that contributes to the strength of the gravitational field.
Energy
and
pressure
also contribute. This is important, so let's spend a moment to see what it means.
Imagine that it's the twenty-fifth century and you're being held in the Hall of Wits, the newest Department of Corrections experiment employing a meritocratic approach to disciplining white-collar felons. The convicts are each given a puzzle, and they can regain their freedom only by solving it. The guy in the cell next to you has to figure out why
Gilligan's
Island
reruns made a surprise comeback in the twenty-second century and have been the most popular show ever since, so he's likely to be calling the Hall home for quite some time. Your puzzle is simpler. You are given two identical solid gold cubes—they are the same size and each is made from precisely the same quantity of gold. Your challenge is to find a way to make the cubes register different weights when gently resting on a fixed, exquisitely accurate scale, subject to one stipulation: you're not allowed to change the amount of matter in either cube, so there's to be no chipping, scraping, soldering, shaving, etc. If you posed this puzzle to Newton, he'd immediately declare it to have no solution. According to Newton's laws, identical quantities of gold translate into identical masses. And since each cube will rest on the same, fixed scale, earth's gravitational pull on them will be identical. Newton would conclude that the two cubes must register an identical weight, no ifs, ands, or buts.
With your twenty-fifth-century high school knowledge of general relativity, though, you see a way out. General relativity shows that the strength of the gravitational attraction between two objects does not just depend on their masses
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(and their separation), but also on any and all additional contributions to each object's total
energy.
And so far we have said nothing about the temperature of the golden cubes. Temperature is a measure of how quickly, on average, the atoms of gold that make up each cube are moving to and fro—it's a measure of how energetic the atoms are (it reflects their
kinetic
energy). Thus, you realize that if you heat up one cube, its atoms will be more energetic, so it will weigh a bit more than the cooler cube. This is a fact Newton was unaware of (an increase of 10 degrees Celsius would increase the weight of a one-pound cube of gold by about a millionth of a billionth of a pound, so the effect is minuscule), and with this solution you win release from the Hall.
Well, almost. Because your crime was particularly devious, at the last minute the parole board decides that you must solve a second puzzle. You are given two identical old-time Jack-in-the-box toys, and your new challenge is to find a way to make each have a different weight. But in this go-around, not only are you forbidden to change the amount of mass in either object, you are also required to keep both at exactly the same temperature. Again, were Newton given this puzzle, he would immediately resign himself to life in the Hall. Since the toys have identical masses, he would conclude that their weights are identical, and so the puzzle is insoluble. But once again, your knowledge of general relativity comes to the rescue: On one of the toys you compress the spring, tightly squeezing Jack under the closed lid, while on the other you leave Jack in his popped-up posture. Why? Well, a compressed spring has more energy than an uncompressed one; you had to exert energy to squeeze the spring down and you can see evidence of your labor because the compressed spring exerts pressure, causing the toy's lid to strain slightly outward. And, again, according to Einstein,
any
additional energy affects gravity, resulting in additional weight. Thus, the closed Jack-in-the-box, with its compressed spring exerting an outward pressure, weighs a touch more than the open Jack-in-the-box, with its uncompressed spring. This is a realization that would have escaped Newton, and with it you finally
do
earn back your freedom.
The solution to that second puzzle hints at the subtle but critical feature of general relativity that we're after. In his paper presenting general relativity, Einstein showed mathematically that the gravitational force depends not only on mass, and not only on energy (such as heat), but also on any
pressures
that may be exerted. And this is the essential physics we need if we are to understand the cosmological constant. Here's why. Outward-directed pressure, like that exerted by a compressed spring, is called
positive pressure.
Naturally enough, positive pressure makes a positive contribution to gravity. But, and this is the critical point, there are situations in which the pressure in a region, unlike mass and total energy, can be
negative,
meaning that the pressure sucks inward instead of pushing outward. And although that may not sound particularly exotic, negative pressure can result in something extraordinary from the point of view of general relativity:
whereas positive pressure contributes to ordinary
attractive gravity, negative pressure contributes to "negative" gravity, that
is, to repulsive gravity!
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With this stunning realization, Einstein's general relativity exposed a loophole in the more than two-hundred-year-old belief that gravity is always an attractive force. Planets, stars, and galaxies, as Newton correctly showed, certainly do exert an attractive gravitational pull. But when pressure becomes important (for ordinary matter under everyday conditions, the gravitational contribution of pressure is negligible) and, in particular, when pressure is negative (for ordinary matter like protons and electrons, pressure is positive, which is why the cosmological constant can't be composed of anything familiar) there is a contribution to gravity that would have shocked Newton.
It's repulsive.
This result is central to much of what follows and is easily misunderstood, so let me emphasize one essential point. Gravity and pressure are two related but separate characters in this story. Pressures, or more precisely, pressure differences, can exert their own, nongravitational forces. When you dive underwater, your eardrums can sense the pressure difference between the water pushing on them from the outside and the air pushing on them from the inside. That's all true. But the point we're now making about pressure and gravity is completely different. According to general relativity, pressure can indirectly exert another force—it can exert a gravitational force—because pressure contributes to the gravitational field. Pressure, like mass and energy, is a source of gravity. And remarkably, if the pressure in a region is negative, it contributes a gravitational
push
to the gravitational field permeating the region, not a gravitational pull.
This means that when pressure is negative, there is competition between ordinary attractive gravity, arising from ordinary mass and energy, and exotic repulsive gravity, arising from the negative pressure. If the negative pressure in a region is negative enough, repulsive gravity will dominate; gravity will push things apart rather than draw them together. Here is where the cosmological constant comes into the story. The cosmological term Einstein added to the equations of general relativity would mean that space is uniformly suffused with energy but, crucially, the equations show that this energy has a uniform, negative pressure. What's more, the gravitational repulsion of the cosmological constant's negative pressure overwhelms the gravitational attraction coming from its positive energy, and so repulsive gravity wins the competition:
a cosmo
logical constant exerts an overall repulsive gravitational force.
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