by Brian Greene
What are the conditions necessary for inflation? We've seen that inflation is the inevitable result of the inflaton field's value getting stuck, for just a moment and within just a tiny region, on the high-energy plateau in its potential energy bowl. Our charge, therefore, is to determine how likely this starting configuration for inflation actually is. If initiating inflation proves easy, we'll be in great shape. But if the necessary conditions are extraordinarily unlikely to be attained, we will merely have shifted the question of time's arrow one step further back—to finding the explanation for the low-entropy inflaton field configuration that got the ball rolling.
I'll first describe current thinking on this issue in the most optimistic light, and then return to essential elements of the story that remain cloudy.
Boltzmann Redux
As mentioned in the previous chapter, the inflationary burst is best thought of as an event occurring in a preexisting universe, rather than being thought of as the creation of the universe itself. Although we don't have an unassailable understanding of what the universe was like during such a preinflationary era, let's see how far we can get if we assume that things were in a thoroughly ordinary, high-entropy state. Specifically, let's imagine that primordial, preinflationary space was riddled with warps and bumps, and that the inflaton field was also highly disordered, its value jumping to and fro like the frog in the hot metal bowl.
Now, just as you can expect that if you patiently play a fair slot machine, sooner or later the randomly spinning dials will land on triple diamonds, we expect that sooner or later a chance fluctuation within this highly energetic, turbulent arena of the primordial universe will cause the inflaton field's value to jump to the correct, uniform value in some small nugget of space, initiating an outward burst of inflationary expansion. As explained in the previous section, calculations show that the nugget of space need only have been tiny—on the order of 10 -26 centimeters across—for the ensuing cosmological expansion (inflationary expansion followed by standard big bang expansion) to have stretched it larger than the universe we see today. Thus, rather than assuming or simply declaring that conditions in the early universe were right for inflationary expansion to take place, in this way of thinking about things an ultramicroscopic fluctuation weighing a mere twenty pounds, occurring within an ordinary, unremarkable environment of disorder, gave rise to the necessary conditions.
What's more, just as the slot machine will also generate a wide variety of nonwinning results, in other regions of primordial space other kinds of inflaton fluctuations would also have happened. In most, the fluctuation wouldn't have had the right value or have been sufficiently uniform for inflationary expansion to occur. (Even in a region that's a mere 10 -26 centimeters across, a field's value can vary wildly.) But all that matters to us is that there was one nugget that yielded the space-smoothing inflationary burst that provided the first link in the low-entropy chain, ultimately leading to our familiar cosmos. As we see only our one big universe, we only need the cosmic slot machine to pay out once. 5
Since we are tracing the universe back to a statistical fluctuation from primordial chaos, this explanation for time's arrow shares certain features with Boltzmann's original proposal. Remember from Chapter 6 that Boltzmann suggested that everything we now see arose as a rare but every so often expectable fluctuation from total disorder. The problem with Boltzmann's original formulation, though, was that it could not explain why the chance fluctuation had gone so far overboard and produced a universe hugely more ordered than it would need to be even to support life as we know it. Why is the universe so vast, having billions and billions of galaxies, each with billions and billions of stars, when it could have drastically cut corners by having, say, just a few galaxies, or even only one?
From the statistical point of view, a more modest fluctuation that produced some order but not as much as we currently see would be far more likely. Moreover, since on average entropy is on the rise, Boltzmann's reasoning suggests that it would be much more likely that everything we see today just now arose as a rare statistical jump to lower entropy. Recall the reason: the farther back the fluctuation happened, the lower the entropy it would have had to attain (entropy starts to rise after any dip to low entropy, as in Figure 6.4, so if the fluctuation happened yesterday, it must have dipped down to yesterday's lower entropy, and if it happened a billion years ago, it must have dipped down to that era's even lower entropy). Hence, the farther back in time, the more drastic and improbable the required fluctuation. Thus, it is much more likely that the jump just happened. But if we accept this conclusion, we can't trust memories, records, or even the laws of physics that underlie the discussion itself—a completely intolerable position.
The tremendous advantage of the inflationary incarnation of Boltzmann's idea is that a small fluctuation early on—a modest jump to the favorable conditions, within a tiny nugget of space—inevitably yields the huge and ordered universe we are aware of. Once inflationary expansion set in, the little nugget was inexorably stretched to scales at least as large as the universe we currently see, and hence there is no mystery as to why the universe didn't cut corners; there is no mystery why the universe is vast and is populated by a huge number of galaxies. From the get-go, inflation gave the universe an amazing deal. A jump to lower entropy within a tiny nugget of space was leveraged by inflationary expansion into the vast reaches of the cosmos. And, of utmost importance, the inflationary stretching didn't just yield any old large universe. It yielded our large universe—inflation explains the shape of space, it explains the large-scale uniformity, and it even explains the "smaller"-scale inhomogeneities such as galaxies and temperature variations in the background radiation. Inflation packages a wealth of explanatory and predictive power in a single fluctuation to low entropy.
And so Boltzmann may well have been right. Everything we see may have resulted from a chance fluctuation out of a highly disordered state of primeval chaos. In this realization of his ideas, though, we can trust our records and we can trust our memories: the fluctuation did not happen just now. The past really happened. Our records are records of things that took place. Inflationary expansion amplifies a tiny speck of order in the early universe—it "wound up" the universe to a huge expanse with minimal gravitational entropy—so the 14 billion years of subsequent unwinding, of subsequent clumping into galaxies, stars, and planets, presents no puzzle.
In fact, this approach even tells us a bit more. Just as it's possible to hit the jackpot on a number of slot machines on the floor of the Bellagio, in the primordial state of high entropy and overall chaos there was no reason why the conditions necessary for inflationary expansion would arise only in a single spatial nugget. Instead, as Andrei Linde has proposed, there could have been many nuggets scattered here and there that underwent space-smoothing inflationary expansion. If that were so, our universe would be but one among many that sprouted—and perhaps continue to sprout—when chance fluctuations made the conditions right for an inflationary burst, as illustrated in Figure 11.2. As these other universes would likely be forever separate from ours, it's hard to imagine how we would ever establish whether this "multiverse" picture is true. However, as a conceptual framework, it's both rich and tantalizing. Among other things, it suggests a possible shift in how we think about cosmology: In Chapter 10, I described inflation as a "front end" to the standard big bang theory, in which the bang is identified with a fleeting burst of rapid expansion. But if we think of the inflationary sprouting of each new universe in Figure 11.2 as its own bang, then inflation itself is best viewed as the overarching cosmological framework within which big bang-like evolutions happen, bubble by bubble. Thus, rather than inflation's being incorporated into the standard big bang theory, in this approach the standard big bang would be incorporated into inflation.
Figure 11.2 Inflation can occur repeatedly, sprouting new universes from older ones.
Inflation and the Egg
So why do you see an egg splatter but
not unsplatter? Where does the arrow of time that we all experience come from? Here is where this approach has taken us. Through a chance but every so often expectable fluctuation from an unremarkable primordial state with high entropy, a tiny, twenty-pound nugget of space achieved conditions that led to a brief burst of inflationary expansion. The tremendous outward swelling resulted in space's being stretched enormously large and extremely smooth, and, as the burst drew to a close, the inflaton field relinquished its hugely amplified energy by filling space nearly uniformly with matter and radiation. As the inflaton's repulsive gravity diminished, ordinary attractive gravity became dominant. And, as we've seen, attractive gravity exploits tiny inhomogeneities caused by quantum jitters to cause matter to clump, forming galaxies and stars and ultimately leading to the formation of the sun, the earth, the rest of the solar system, and the other features of our observed universe. (As discussed, some 7 billion or so years ATB, repulsive gravity once again became dominant, but this is only relevant on the largest of cosmic scales and has no direct impact on smaller entities like individual galaxies or our solar system, where ordinary attractive gravity still reigns.) The sun's relatively low-entropy energy was used by low-entropy plant and animal life forms on earth to produce yet more low-entropy life forms, slowly raising the total entropy through heat and waste. Ultimately, this chain produced a chicken that produced an egg— and you know the rest of the story: the egg rolled off your kitchen counter and splattered on the floor as part of the universe's relentless drive to higher entropy. It's the low-entropy, highly ordered, uniformly smooth nature of the spatial fabric produced by inflationary stretching that is the analog of having the pages of War and Peace all in their proper numerical arrangement; it is this early state of order—the absence of severe bumps or warps or gargantuan black holes—that primed the universe for the subsequent evolution to higher entropy and hence provided the arrow of time we all experience. With our current level of understanding, this is the most complete explanation for time's arrow that has been given.
The Fly in the Ointment?
To me, this story of inflationary cosmology and time's arrow is lovely. From a wild and energetic realm of primordial chaos, there emerged an ultramicroscopic fluctuation of uniform inflaton field weighing far less than the limit for carry-on luggage. This initiated inflationary expansion, which set a direction to time's arrow, and the rest is history.
But in telling this story, we've made a pivotal assumption that's as yet unjustified. To assess the likelihood of inflation's being initiated, we've had to specify the characteristics of the preinflationary realm out of which inflationary expansion is supposed to have emerged. The particular realm we've envisioned—wild, chaotic, energetic—sounds reasonable, but delineating this intuitive description with mathematical precision proves challenging. Moreover, it is only a guess. The bottom line is that we don't know what conditions were like in the supposed preinflationary realm, in the fuzzy patch of Figure 10.3, and without that information we are unable to make a convincing assessment of the likelihood of inflation's initiating; any calculation of the likelihood depends sensitively on the assumptions we make. 6
With this hole in our understanding, the most sensible summary is that inflation offers a powerful explanatory framework that bundles together seemingly disparate problems—the horizon problem, the flatness problem, the origin-of-structure problem, the low-entropy-of-the-early-universe problem—and offers a single solution that addresses them all. This feels right. But to go to the next step, we need a theory that can cope with the extreme conditions characteristic of the fuzzy patch— extremes of heat and colossal density—so that we will stand a chance of gaining sharp, unambiguous insight into the earliest moments of the cosmos.
As we will learn in the next chapter, this requires a theory that can overcome perhaps the greatest obstacle theoretical physics has faced during the last eighty years: a fundamental rift between general relativity and quantum mechanics. Many researchers believe that a relatively new approach called superstring theory may have accomplished this, but if superstring theory is right, the fabric of the cosmos is far stranger than almost anyone ever imagined.
IV - ORIGINS AND UNIFICATION
12 - The World on a String
THE FABRIC ACCORDING TO STRING THEORY
Imagine a universe in which to understand anything you'd need to understand everything. A universe in which to say anything about why a planet orbits a star, about why a baseball flies along a particular trajectory, about how a magnet or a battery works, about how light and gravity operate—a universe in which to say anything about anything—you would need to uncover the most fundamental laws and determine how they act on the finest constituents of matter. Thankfully, this universe is not our universe.
If it were, it's hard to see how science would have made any progress at all. Over the centuries, the reason we've been able to make headway is that we've been able to work piecemeal; we've been able to unravel mysteries step by step, with each new discovery going a bit deeper than the previous. Newton didn't need to know about atoms to make great strides in understanding motion and gravity. Maxwell didn't need to know about electrons and other charged particles to develop a powerful theory of electromagnetism. Einstein didn't need to address the primordial incarnation of space and time to formulate a theory of how they curve in the service of the gravitational force. Instead, each of these discoveries, as well as the many others that underlie our current conception of the cosmos, proceeded within a limited context that unabashedly left many basic questions unanswered. Each discovery was able to contribute its own piece to the puzzle, even though no one knew—and we still don't know—what grand synthesizing picture comprises all the puzzle's pieces.
A closely related observation is that although today's science differs sharply from that of even fifty years ago, it would be simplistic to summarize scientific progress in terms of new theories overthrowing their predecessors. A more correct description is that each new theory refines its predecessor by providing a more accurate and more wide-reaching framework. Newton's theory of gravity has been superseded by Einstein's general relativity, but it would be naïve to say that Newton's theory was wrong. In the domain of objects that don't move anywhere near as fast as light and don't produce gravitational fields anywhere near as strong as those of black holes, Newton's theory is fantastically accurate. Yet this is not to say that Einstein's theory is a minor variant on Newton's; in the course of improving Newton's approach to gravity, Einstein invoked a whole new conceptual schema, one that radically altered our understanding of space and time. But the power of Newton's discovery within the domain he intended it for (planetary motion, commonplace terrestrial motion, and so on) is unassailable.
We envision each new theory taking us closer to the elusive goal of truth, but whether there is an ultimate theory—a theory that cannot be refined further, because it has finally revealed the workings of the universe at the deepest possible level—is a question no one can answer. Even so, the pattern traced out during the last three hundred years of discovery gives tantalizing evidence that such a theory can be developed. Broadly speaking, each new breakthrough has gathered a wider range of physical phenomena under fewer theoretical umbrellas. Newton's discoveries showed that the forces governing planetary motion are the same as those governing the motion of falling objects here on earth. Maxwell's discoveries showed that electricity and magnetism are two sides of the same coin. Einstein's discoveries showed that space and time are as inseparable as Midas' touch and gold. The discoveries of a generation of physicists in the early twentieth century established that myriad mysteries of microphysics could be explained with precision using quantum mechanics. More recently, the discoveries of Glashow, Salam, and Weinberg showed that electromagnetism and the weak nuclear force are two manifestations of a single force—the electroweak force—and there is even tentative, circumstantial evidence that the strong nuclear force may join the electroweak force in a yet grander synthes
is. 1 Taking all this together, we see a pattern that goes from complexity to simplicity, a pattern that goes from diversity to unity. The explanatory arrows seem to be converging on a powerful, yet-to-be discovered framework that would unify all of nature's forces and all of matter within a single theory capable of describing all physical phenomena.
Albert Einstein, who for more than three decades sought to combine electromagnetism and general relativity in a single theory, is rightly credited with initiating the modern search for a unified theory. For long stretches during those decades, he was the sole searcher for such a unified theory, and his passionate yet solitary quest alienated him from the mainstream physics community. During the last twenty years, though, there has been a resurgence in the quest for a unified theory; Einstein's lonely dream has become the driving force for a whole generation of physicists. But with the discoveries since Einstein's time has come a shift in focus. Even though we don't yet have a successful theory combining the strong nuclear force and the electroweak force, all three of these forces (electromagnetic, weak, strong) have been described by a single uniform language based on quantum mechanics. But general relativity, our most refined theory of the fourth force, stands outside this framework. General relativity is a classical theory: it does not incorporate any of the probabilistic concepts of quantum theory. A primary goal of the modern unification program is therefore to combine general relativity and quantum mechanics, and to describe all four forces within the same quantum mechanical framework. This has proven to be one of the most difficult problems theoretical physics has ever encountered.
