by Brian Greene
For example, I’m pretty sure that if you were to bring Newton up to date by giving him a five-minute primer on general relativity, explaining the outlines of warped space and the expanding universe, he’d find your subsequent description of the inflationary proposal preposterous. Newton would sternly maintain that regardless of fancy math and newfangled Einsteinian language, gravity is still an attractive force. And so, he would emphasize with a pound on the table, gravity acts to pull objects together, slowing any cosmic divergence. Expansion that starts out dawdling, then sharply quickens for a brief period, might solve the horizon problem, but it’s a fiction. Newton would declare that just as gravitational attraction implies that the speed of a batted baseball diminishes as the ball moves upward, it similarly implies that the cosmic expansion must slow over time. Sure, if the expansion drops all the way to zero and then turns into cosmic contraction, the implosion can speed up over time, much as the ball’s speed can increase when it starts its downward journey. But the speed of the outward spatial expansion can’t increase.
Newton’s making a mistake, but you can’t blame him. The burden lies with the cursory summary you gave him of general relativity. Don’t get me wrong. It’s understandable that, given only five minutes (one of which was spent explaining baseball), you focused on curved spacetime as the source of gravity. Newton himself had called attention to the fact that there was no known mechanism for transmitting gravity, and he always viewed that as a yawning hole in his own theory. Naturally, you wanted to show him Einstein’s resolution. But Einstein’s theory of gravity did much more than merely fill a gap in Newtonian physics. Gravity in general relativity differs in its essence from gravity in Newton’s physics, and in the present context, there is one feature that cries out for emphasis.
In Newton’s theory, gravity arises solely from an object’s mass. The bigger the mass, the bigger the object’s gravitational pull. In Einstein’s theory, gravity arises from an object’s mass (and energy) but also from its pressure. Weigh a sealed bag of potato chips. Weigh it again, but this time squeeze the bag so that the air inside is under higher pressure. According to Newton, the weight will be the same, because there’s been no change in mass. According to Einstein, the squeezed bag will weigh slightly more, because although the mass is the same there’s been an increase in pressure.4 In everyday circumstances we’re not aware of it, because for ordinary objects the effect is fantastically tiny. Even so, general relativity, and the experiments that have shown it to be correct, makes it perfectly clear that pressure contributes to gravity.
This deviation from Newton’s theory is critical. Air pressure, whether the air is in a bag of potato chips, an inflated balloon, or the room where you’re now reading, is positive, meaning that the air pushes outward. In general relativity, positive pressure, like positive mass, contributes positively to gravity, resulting in increased weight. But whereas mass is always positive, there are situations in which pressure can be negative. Think of a stretched rubber band. Rather than pushing outward, the rubber band’s straining molecules pull inward, exerting what physicists call negative pressure (or, equivalently, tension). And much as general relativity shows that positive pressure gives rise to attractive gravity, it shows that negative pressure gives rise to the opposite: repulsive gravity.
Repulsive gravity?
This would blow Newton’s mind. For him, gravity was only attractive. But your mind should remain intact: you’ve already encountered this strange clause in general relativity’s contract with gravity. Remember Einstein’s cosmological constant, discussed in the previous chapter? I declared there that by infusing space with a uniform energy, a cosmological constant generates repulsive gravity. But in that earlier encounter, I didn’t explain why this happens. Now I can. A cosmological constant not only endows the spatial fabric with a uniform energy determined by the constant’s value (the number on the third line of the apocryphal relativity tax form), but it also fills space with a uniform negative pressure (we will see why in a moment). And, as above, when it comes to the gravitational force each produces, negative pressure does the opposite of positive mass and positive pressure. It yields repulsive gravity.*
In Einstein’s hands, repulsive gravity was used for a single erroneous purpose. He proposed finely adjusting the amount of negative pressure that permeates space to ensure that the repulsive gravity produced would exactly counter the attractive gravity exerted by the universe’s more familiar material contents, yielding a static universe. As we’ve seen, he subsequently renounced this move. Six decades later, the developers of the inflationary theory proposed a kind of repulsive gravity that differed from Einstein’s version much as the finale of Mahler’s Eighth differs from the drone of a tuning fork. Rather than a moderate and steady outward push that would stabilize the universe, the inflationary theory envisions a gargantuan surge of repulsive gravity that’s astoundingly short and thunderingly intense. Regions of space had ample time before the burst to come to the same temperature, but then, riding the surge, covered the great distances necessary to reach their observed positions in the sky.
At this point, Newton would surely shoot you another disapproving look. Ever the skeptic, he would find another problem with your explanation. After catching up on the more intricate details of general relativity by racing through one of the standard textbooks, he would accept the strange fact that gravity can—in principle—be repulsive. But, he’d ask, what’s all this talk of negative pressure permeating space? It’s one thing to use the inward pull of a stretched rubber band as an example of negative pressure. It’s another to argue that billions of years ago, just around the time of the big bang, space was momentarily permeated by an enormous and uniform negative pressure. What thing, or process, or entity has the capacity to supply such a fleeting but pervasive negative pressure?
The genius of inflation’s pioneers was to provide an answer. They showed that the negative pressure required for an antigravity burst naturally emerges from a novel mechanism involving ingredients known as quantum fields. For our story, the details are crucial because the manner in which inflationary expansion comes about is central to the version of parallel universes it yields.
Quantum Fields
In Newton’s day, physics concerned itself with the motion of objects you can see—stones, cannonballs, planets—and the equations he developed closely reflected this focus. Newton’s laws of motion are a mathematical embodiment of how such tangible bodies move when they’re pushed, pulled, or shot through the air. For more than a century, this was a wonderfully fruitful approach. But in the early 1800s, the English scientist Michael Faraday initiated a transformation in thinking with the elusive but demonstrably powerful concept of the field.
Take a strong refrigerator magnet and place it an inch above a paper clip. You know what happens. The clip jumps up and sticks to the magnet’s surface. This demonstration is so commonplace, so thoroughly familiar, that it’s easy to overlook how bizarre it is. Without touching the paper clip, the magnet can make it move. How is this possible? How can an influence be exerted in the absence of any contact with the clip itself? These and a multitude of related considerations led Faraday to postulate that though the magnet proper does not touch the paper clip, the magnet produces something that does. That something is what Faraday called a magnetic field.
We can’t see the fields produced by magnets; we can’t hear them; none of our senses are attuned to them. But that reflects physiological limitations, nothing more. As a flame generates heat, so a magnet generates a magnetic field. Lying beyond the physical boundary of the solid magnet, the magnet’s field is a “mist” or “essence” that fills space and does the magnet’s bidding.
Magnetic fields are but one kind of field. Charged particles give rise to another: electric fields, such as those responsible for the shock you sometimes receive when you reach for a metal doorknob in a room with wall-to-wall wool carpeting. Unexpectedly, Faraday’s experiments showed that electric and magnetic
fields are intimately related: he found that a changing electric field generates a magnetic field, and vice versa. In the late 1800s, James Clerk Maxwell put mathematical might behind these insights, describing electric and magnetic fields in terms of numbers assigned to each point in space; the numbers’ values reflect the field’s ability, at that location, to exert influence. Places in space where the magnetic field’s numerical values are large, for instance an MRI’s cavity, are places where metal objects will feel a strong push or pull. Places in space where the electric field’s numerical values are large, for instance the inside of a thundercloud, are places where powerful electrical discharges such as lightning may occur.
Maxwell discovered equations, which now bear his name, that govern how the strength of electric and magnetic fields varies from point to point in space and moment to moment in time. These very same equations govern the sea of rippling electric and magnetic fields, so-called electromagnetic waves, within which we’re all immersed. Turn on a cell phone, a radio, or a wireless computer, and the signals received represent a tiny portion of the thicket of electromagnetic transmissions silently rushing by and through you every second. Most stunning of all, Maxwell’s equations revealed that visible light itself is an electromagnetic wave, one whose rippling patterns our eyes have evolved to see.
In the second half of the twentieth century, physicists united the field concept with their burgeoning understanding of the microworld encapsulated by quantum mechanics. The result, quantum field theory, provides a mathematical framework for our most refined theories of matter and nature’s forces. Using it, physicists have established that in addition to electric and magnetic fields, there exists a whole panoply of others with names like strong and weak nuclear fields and electron, quark, and neutrino fields. One field that to date remains wholly hypothetical, the inflaton field, provides a theoretical basis for inflationary cosmology.*
Quantum Fields and Inflation
Fields carry energy. Qualitatively, we know this because fields accomplish tasks that require energy, such as causing objects (like paper clips) to move. Quantitatively, the equations of quantum field theory show us how, given the numerical value of a field at a particular location, to calculate the amount of energy it contains. Typically, the larger the value, the larger the energy. A field’s value can vary from place to place, but should it be constant, taking the same value everywhere, it would fill space with the same energy at every point. Guth’s critical insight was that such uniform field configurations fill space not only with uniform energy but also with uniform negative pressure. And with that, he found a physical mechanism to generate repulsive gravity.
To see why a uniform field yields negative pressure, think first about a more ordinary situation that involves positive pressure: the opening of a bottle of Dom Pérignon. As you slowly remove the cork, you can feel the positive pressure of the champagne’s carbon dioxide pushing outward, driving the cork from the bottle and into your hand. A fact you can directly verify is that this outward exertion drains a little energy from the champagne. You know those vapor tendrils you see near the bottle’s neck when the cork is out? They form because the energy expended by the champagne in pushing against the cork results in a drop in temperature, which, much as with your breath on a wintry day, causes surrounding water vapor to condense.
Now imagine replacing the champagne with something less festive but more pedagogical—a field whose value is uniform throughout the bottle. When you remove the cork this time, your experience will be very different. As you slide the cork outward, you make a little extra volume inside the bottle available for the field to permeate. Since a uniform field contributes the same energy at every location, the larger the volume the field fills, the greater the total energy the bottle contains. Which means that, unlike with champagne, the act of removing the cork adds energy to the bottle.
How could that be? Where would the energy come from? Well, think about what happens if the bottle’s contents, rather than pushing the cork outward, pull the cork inward. This would require you to pull on the cork to remove it, an exertion of effort that in turn would transfer energy from your muscles to the contents of the bottle. To explain the increase in the bottle’s energy we thus conclude that, unlike champagne, which pushes outward, a uniform field sucks inward. That’s what we mean by a uniform field’s resulting in a negative—not positive—pressure.
Although there’s no sommelier uncorking the cosmos, the same conclusion holds: if there’s a field—the hypothetical inflaton field—that has a uniform value throughout a region of space, it will fill that region not only with energy but also with negative pressure. And, as is now familiar, such negative pressure yields repulsive gravity, which drives an ever-quickening expansion of space. When Guth slotted into Einstein’s equations the likely numerical values for the inflaton’s energy and pressure consonant with the extreme environment of the early universe, the mathematics revealed that the resulting repulsive gravity would be stupendous. It would easily be many orders of magnitude stronger than the repulsive force Einstein envisioned years earlier when he dallied with the cosmological constant, and would propel a spectacular spatial stretching. That alone was exciting. But Guth realized there was an indispensable bonus.
The same reasoning that explains why a uniform field has negative pressure applies as well to a cosmological constant. (If the bottle contains empty space endowed with a cosmological constant, then when you slowly remove the cork the extra space you make available within the bottle contributes extra energy. The only source for this extra energy is your muscles, which therefore must have strained against an inward, negative pressure supplied by the cosmological constant.) And, as with a uniform field, a cosmological constant’s uniform negative pressure also yields repulsive gravity. But the vital point here is not the similarities, per se, but the manner in which a cosmological constant and a uniform field differ.
A cosmological constant is just that—a constant, a fixed number inserted on the third line of general relativity’s tax form that would generate the same repulsive gravity today as it would have billions of years ago. By contrast, the value of a field can change, and generally will. When you turn on your microwave oven, you change the electromagnetic field filling its interior; when the technician flips the switch on an MRI machine, he or she changes the electromagnetic field threading the cavity. Guth realized that an inflaton field filling space could behave similarly—turning on for a burst and then turning off—which would allow repulsive gravity to operate during only a brief window of time. That’s essential. Observations establish that if the blistering growth of space happened at all, it must have happened billions of years ago and then sharply dropped off to the statelier-paced expansion evidenced by detailed astronomical measurements. So an all-important feature of the inflationary proposal is that the era of powerful repulsive gravity be transient.
The mechanism for turning on and then shutting off the inflationary burst relies on physics that Guth initially developed but that Linde, and Albrecht and Steinhardt, refined substantially. To get a feel for their proposal, think of a ball—better still, think of nearly round Eric Cartman—perched precariously on one of South Park’s snow-covered mountains. A physicist would say that because of his position, Cartman embodies energy. More precisely, he embodies potential energy, meaning that he has pent-up energy that’s ready to be tapped, most easily by his tumbling downward, which would transform the potential energy into the energy of motion (kinetic energy). Experience attests, and the laws of physics make precise, that this is typical. A system harboring potential energy will exploit any opportunity to release that energy. In short, things fall.
The energy carried by a field’s nonzero value is also potential energy: it, too, can be tapped, resulting in an incisive analogy with Cartman. Just as the increase in Cartman’s potential energy as he climbs the mountain is determined by the shape of the slope—in flatter regions his potential energy varies minimally as he walks, because
he gets hardly any higher, while in steeper regions his potential energy rises sharply—the potential energy of a field is described by an analogous shape, called its potential energy curve. Such a curve, as in Figure 3.1, determines how a field’s potential energy varies with its value.
Following inflation’s pioneers, let’s then imagine that in the earliest moments of the cosmos, space is uniformly filled with an inflaton field, whose value places it high up on its potential energy curve. Imagine further, these physicists urge us, that the potential energy curve flattens out into a gentle plateau (as in Figure 3.1), allowing the inflaton to linger near the top. Under these hypothesized conditions, what will happen?
Figure 3.1 The energy contained in an inflaton field (vertical axis) for given values of the field (horizontal axis).
Two things, both critical. While the inflaton is on the plateau, it fills space with a large potential energy and negative pressure, driving a burst of inflationary expansion. But, just as Cartman releases his potential energy by rolling down the slope, so the inflaton releases its potential energy by its value, throughout space, rolling to lower numbers. And as its value decreases, the energy and negative pressure it harbors dissipate, bringing an end to the period of blistering expansion. Just as important, the energy released by the inflaton field isn’t lost—instead, like a cooling vat of steam condensing into water droplets, the inflaton’s energy condenses into a uniform bath of particles that fill space. This two-step process—brief but rapid expansion, followed by energy conversion to particles—results in a huge, uniform spatial expanse that’s filled with the raw material of familiar structures like stars and galaxies.