The Hidden Reality Part 6

What would that mean?

Imagine you're puzzling over some fundamental feature of the universe, say the ma.s.s of an electron, .00054 (expressed as a fraction of the proton's ma.s.s), or the strength of the electromagnetic force, .0073 (expressed by its coupling constant), or, of primary interest to us here, the value of the cosmological constant, 1.38 10123 (expressed in Planck units). Your intention is to explain why these constants have the particular values they do. You try and try but come up emptyhanded. Take a step back, Carter says. Maybe you're failing for the same reason you'd fail to explain the earth-sun distance: there is no fundamental explanation. Just as there are many planets at many distances and we necessarily inhabit one whose orbit yields hospitable conditions, maybe there are many universes with many different values for the "constants" and we necessarily inhabit the one in which the values are conducive to our existence. (expressed in Planck units). Your intention is to explain why these constants have the particular values they do. You try and try but come up emptyhanded. Take a step back, Carter says. Maybe you're failing for the same reason you'd fail to explain the earth-sun distance: there is no fundamental explanation. Just as there are many planets at many distances and we necessarily inhabit one whose orbit yields hospitable conditions, maybe there are many universes with many different values for the "constants" and we necessarily inhabit the one in which the values are conducive to our existence.

In this way of thinking, to ask why the constants have their particular values is to ask the wrong kind of question. There is no law dictating their values; their values can and do vary across the multiverse. Our intrinsic selection bias ensures that we find ourselves in that part of the multiverse in which the constants have the values with which we're familiar simply because we're unable to exist in the parts of the multiverse where the values are different.

Note that the reasoning would fall flat if our universe were unique because you could still ask the "lucky coincidence" or "deeper explanation" questions. Much as a potent explanation for why the shop has your shoe size requires that the shelves be stocked with many different sizes, and much as a potent explanation for why there's a planet situated at a bio-friendly distance from its host star requires planets...o...b..ting their stars at many different distances, so a potent explanation of nature's constants requires a vast a.s.sortment of universes endowed with many different values for those constants. Only in this setting-a multiverse, and a robust one at that-does anthropic reasoning have the capacity to make the mysterious mundane.*

Clearly, then, the degree to which you are swayed by the anthropic approach depends on the degree to which you are convinced of its three essential a.s.sumptions: (1) our universe is part of a multiverse; (2) from universe to universe in the multiverse, the constants take on a broad range of possible values; and (3) for most variations of the constants away from the values we measure, life as we know it would fail to take hold.

In the 1970s, when Carter put forward these ideas, the notion of parallel universes was anathema to many physicists. Certainly, there's still ample reason to be skeptical. But we've seen in the previous chapters that although the case for any particular version of the multiverse is surely tentative, there's reason for giving this new view of reality serious consideration, a.s.sumption 1. Many scientists now are. Regarding a.s.sumption 2, we've also seen that, for example, in the Inflationary and Brane Multiverses, we would indeed expect physical features, such as the constants of nature, to vary from universe to universe. Later in this chapter we'll look at this point more closely.

But what about a.s.sumption 3, concerning life and the constants?

Life, Galaxies, and Nature's Numbers.

For many of nature's constants, even modest variations would render life as we know it impossible. Make the gravitational constant stronger, and stars burn up too quickly for life on nearby planets to evolve. Make it weaker and galaxies don't hold together. Make the electromagnetic force stronger, and hydrogen atoms repel each other too strongly to fuse and supply power to stars.13 But what about the cosmological constant? Does life's existence depend on its value? This is the issue Steven Weinberg took up in his 1987 paper. But what about the cosmological constant? Does life's existence depend on its value? This is the issue Steven Weinberg took up in his 1987 paper.

Because the formation of life is a complex process about which our understanding is in its earliest stages, Weinberg recognized that it was hopeless to determine how one or another value of the cosmological constant directly impacts the myriad steps that breathe life into matter. But rather than give up, Weinberg introduced a clever proxy for the formation of life: the formation of galaxies. Without galaxies, he reasoned, the formation of stars and planets would be thoroughly compromised, with a devastating impact on the chance that life might emerge. This approach was not only eminently reasonable but also useful: it s.h.i.+fted the focus to determining the impact that cosmological constants of various sizes would have on galaxy formation, and that was a problem Weinberg could solve.

The essential physics is elementary. While precise details of galaxy formation are an active area of research, the broad-brush process involves a kind of astrophysical s...o...b..ll effect. A clump of matter forms here or there, and by virtue of being more dense than its surroundings, it exerts a greater gravitational pull on nearby matter and thus grows larger still. The cycle continues feeding on itself to ultimately produce a swirling ma.s.s of gas and dust, from which stars and planets coalesce. Weinberg's realization was that a cosmological constant with a value large enough would disrupt the clumping process. The repulsive gravity it would generate, if sufficiently strong, would thwart galactic formation by making the initial clumps-which were small and fragile-stream apart before they had time to become robust by attracting surrounding matter.

Weinberg worked out the idea mathematically and found that a cosmological constant any larger than a few hundred times the current cosmological density of matter, a few protons per cubic meter, would disrupt the formation of galaxies. (Weinberg also considered the impact of a negative cosmological constant. The constraints in that case are even tighter, because a negative value increases the attractive pull of gravity and makes the whole universe collapse before stars even have time to ignite.). If you imagine, then, that we're part of a multiverse and that the cosmological constant's value varies over a wide range from universe to universe, much as planet-star distances vary over a wide range from solar system to solar system-the only universes that could have galaxies, and hence the only universes we could inhabit, are ones in which the cosmological constant is no larger than Weinberg's limit, which in Planck units is about 10121.

After years of failed efforts by the community of physicists, this was the first theoretical calculation to result in a value for the cosmological constant that was not absurdly larger than limits inferred from observational astronomy. Nor did it contradict a belief widely held at the time of Weinberg's work, that the cosmological constant vanished. Weinberg took this apparent progress one step further by encouraging an even more aggressive interpretation of his result. He suggested that we should expect to find ourselves in a universe with a cosmological constant whose value is as small as it needs to be for us to exist, but not a whole lot smaller. A much smaller constant, he reasoned, would call for an explanation that goes beyond mere compatibility with our existence. That is, it would require precisely the kind of explanation that physics had valiantly sought but so far failed to find. This led Weinberg to suggest that more refined measurements might one day reveal that the cosmological constant doesn't vanish but, instead, has a value near or at the upper limit that he'd calculated. As we've seen, within a decade of Weinberg's paper, the observations of the Supernova Cosmology Project and the High-Z Supernova Search Team proved this suggestion prophetic.

But to a.s.sess fully this unconventional explanatory framework, we need to examine Weinberg's reasoning more closely. Weinberg is imagining a sprawling multiverse so diverse in population that it just has has to contain at least one universe with the cosmological constant we've observed. But what kind of multiverse will guarantee, or at least make it highly likely, that this is the case? to contain at least one universe with the cosmological constant we've observed. But what kind of multiverse will guarantee, or at least make it highly likely, that this is the case?

To think this through, consider first an a.n.a.logous problem with simpler numbers. Imagine you work for the notorious film producer Harvey W. Einstein, who has asked you to put out a casting call for the lead in his new indie, Pulp Friction Pulp Friction. "How tall do you want him?" you ask. "I dunno. Taller than a meter, less than two. But you better make sure whatever height I decide, there's someone who fits the bill." You're tempted to correct your boss, noting that because of quantum uncertainty he really doesn't need to have every every height represented but, thinking back on what happened to the surly little talking fly who tried that, you refrain. height represented but, thinking back on what happened to the surly little talking fly who tried that, you refrain.

Now you face a decision. How many actors should you have at the audition? You reason: If W. measures heights to a centimeter's accuracy, there are a hundred different possibilities between one and two meters. So you need at least a hundred actors. But since some actors who show up may have the same height, leaving other heights unrepresented, you'd better gather more than a hundred. To be safe, maybe you should put out a call for a few hundred actors. That's a lot, but fewer than what you'd need if W. measured heights to a millimeter's accuracy. In that case, there'd be a thousand different heights between one and two meters, so to be safe you'd need to gather a few thousand actors.

The same reasoning is relevant for the case of universes with different cosmological constants. a.s.sume that all the universes in a multiverse have cosmological constant values between zero and one (in the usual Planck units); smaller values lead to universes that collapse, larger values would strain the applicability of our mathematical formulations, compromising all understanding. So just as the actors' heights had a range of one (in meters), the universes' cosmological constants have a range of one (in Planck units). As for accuracy, the a.n.a.log of W. using centimeter ticks, or millimeter ticks, is the precision with which we can measure the cosmological constant. Today's accuracy is about 10124 (in Planck units). In the future, our accuracy will no doubt improve, but as we'll see, that will hardly affect our conclusions. Then just as there are 10 (in Planck units). In the future, our accuracy will no doubt improve, but as we'll see, that will hardly affect our conclusions. Then just as there are 102 different possible heights s.p.a.ced at least 10 different possible heights s.p.a.ced at least 102 meters apart (1 centimeter) in a one-meter range, and 10 meters apart (1 centimeter) in a one-meter range, and 103 different possible heights s.p.a.ced at least 10 different possible heights s.p.a.ced at least 103 meters apart (1 millimeter), so there are 10 meters apart (1 millimeter), so there are 10124 different values of the cosmological constant s.p.a.ced at least 10 different values of the cosmological constant s.p.a.ced at least 10124 apart between the values 0 and 1. apart between the values 0 and 1.

To ensure that every possible cosmological constant is realized, we'd therefore need a multiverse with at least 10124 different universes. But as with the actors, we need to account for possible duplicates, universes that may have the same cosmological constant value. And so to play it safe and make it highly likely that every possible cosmological constant value is realized, we should have a multiverse with far more than 10 different universes. But as with the actors, we need to account for possible duplicates, universes that may have the same cosmological constant value. And so to play it safe and make it highly likely that every possible cosmological constant value is realized, we should have a multiverse with far more than 10124 universes, say a million times more, bringing it to a nice even 10 universes, say a million times more, bringing it to a nice even 10130 universes. I'm being cavalier because when we're talking about numbers this large, the exact values hardly matter. No familiar example of anything-not the number of cells in your body (10 universes. I'm being cavalier because when we're talking about numbers this large, the exact values hardly matter. No familiar example of anything-not the number of cells in your body (1013); not the number of seconds since the big bang (1018); not the number of photons in the observable part of the universe (1088)-comes even remotely close to the number of universes we're contemplating. The bottom line is that Weinberg's approach for explaining the cosmological constant works only if we're part of a multiverse in which there are a huge number of different universes; their cosmological constants must fill out some 10124 distinct values. Only with that many different universes is there a high likelihood that there's one with a cosmological constant that matches ours. distinct values. Only with that many different universes is there a high likelihood that there's one with a cosmological constant that matches ours.

Are there theoretical frameworks that naturally yield such a spectacular profusion of universes with different cosmological constants?14 From Vice to Virtue.

There are. We encountered such a framework in the previous chapter. A count of the different possible forms for the extra dimensions in string theory, when including fluxes that can thread through them, came to about 10500. This dwarfs 10124. Multiply 10124 by a few hundred orders of magnitude and 10 by a few hundred orders of magnitude and 10500 still dwarfs it. Subtract 10 still dwarfs it. Subtract 10124 from 10 from 10500, and then subtract it again, and again, and do so a billion times over, and you'd barely make a dent. The result would still be nearly 10500.

Critically, the cosmological constant does indeed vary from one such universe to another. Just as magnetic flux carries energy (it can move things), so the fluxes threading holes in Calabi-Yau shapes also have energy, whose quant.i.ty is quite sensitive to the shape's geometrical details. If you have two different Calabi-Yau shapes with different fluxes penetrating different holes, their energies will generally be different too. And since a given Calabi-Yau shape is attached to every point in the familiar three large dimensions of s.p.a.ce, much as circular loops of pile attach to every point on the large extended base of a carpet, the energy the shape contains would uniformly fill the three large dimensions, much as soaking the individual fibers in a carpet's pile would make the entire carpet backing uniformly heavy. Thus, should one or another of the 10500 different dressed-up Calabi-Yau shapes const.i.tute the requisite extra dimensions, different dressed-up Calabi-Yau shapes const.i.tute the requisite extra dimensions, the energy it contains would contribute to the cosmological constant the energy it contains would contribute to the cosmological constant. Results obtained by Raphael Bousso and Joe Polchinski made this observation quant.i.tative. They argued that the various cosmological constants supplied by the 10500 or so different possible forms for the extra dimensions are distributed uniformly across a broad range of values. or so different possible forms for the extra dimensions are distributed uniformly across a broad range of values.

This is just what the doctor ordered. Having 10500 tick marks distributed across a range from 0 to 1 ensures that many of them lie extremely close to the value of the cosmological constant astronomers have measured during the past decade. It may be hard to find the explicit examples among the 10 tick marks distributed across a range from 0 to 1 ensures that many of them lie extremely close to the value of the cosmological constant astronomers have measured during the past decade. It may be hard to find the explicit examples among the 10500 possibilities, because even if today's fastest computers took a single second to a.n.a.lyze each form for the extra dimensions, after a billion years only a paltry 10 possibilities, because even if today's fastest computers took a single second to a.n.a.lyze each form for the extra dimensions, after a billion years only a paltry 1032 examples would have been examined. But this reasoning suggests strongly that they exist. examples would have been examined. But this reasoning suggests strongly that they exist.

Certainly, a collection of 10500 different possible forms for the extra dimensions is about as far from a unique universe as anyone imagined string theory research would ever take us. And for those who've held strongly to Einstein's dream of finding a unified theory describing one single universe-ours-these developments came with significant discomfort. But a.n.a.lysis of the cosmological constant casts the situation in a different light. Rather than despair because a unique universe seems not to emerge, we are encouraged to celebrate: string theory makes the least plausible part of Weinberg's explanation of the cosmological constant-the requirement that there be many more than 10 different possible forms for the extra dimensions is about as far from a unique universe as anyone imagined string theory research would ever take us. And for those who've held strongly to Einstein's dream of finding a unified theory describing one single universe-ours-these developments came with significant discomfort. But a.n.a.lysis of the cosmological constant casts the situation in a different light. Rather than despair because a unique universe seems not to emerge, we are encouraged to celebrate: string theory makes the least plausible part of Weinberg's explanation of the cosmological constant-the requirement that there be many more than 10124 different universes-suddenly seem plausible. different universes-suddenly seem plausible.

The Final Step, in Brief.

The elements of a tantalizing story seem to be coming together. But a gap remains in the reasoning. It's one thing for string theory to allow for a huge number of possible distinct universes. It's another to claim that string theory ensures that all of the possible universes to which it can give rise are actually out there, parallel worlds populating a vast multiverse. As emphasized most emphatically by Leonard Susskind-who was inspired by the pioneering work of Shamit Kachru, Renata Kallosh, Andrei Linde, and Sandip Trivedi-if we weave eternal inflation into the tapestry, the gap can be filled.15 I'll now explain this final step, but in case you're reaching saturation and just want the punch line, here's a three-sentence summary. The Inflationary Multiverse-the ever-expanding Swiss cheese cosmos-contains a vast, ever-increasing number of bubble universes. The idea is that when inflationary cosmology and string theory are melded, the process of eternal inflation sprinkles string theory's 10500 possible forms for the extra dimensions across the bubbles-one form for the extra dimensions per bubble universe-providing a cosmological framework that realizes all possibilities. By this reasoning, we live in that bubble whose extra dimensions yield a universe, cosmological constant and all, that's hospitable to our form of life and whose properties agree with observations. possible forms for the extra dimensions across the bubbles-one form for the extra dimensions per bubble universe-providing a cosmological framework that realizes all possibilities. By this reasoning, we live in that bubble whose extra dimensions yield a universe, cosmological constant and all, that's hospitable to our form of life and whose properties agree with observations.

In the remainder of the chapter, I will flesh out the details, but if you're ready to move on, feel free to jump ahead to the chapter's last section.

The String Landscape.

In explaining inflationary cosmology back in Chapter 3 Chapter 3, I used a variation on a common metaphor. A mountain's peak represents the highest value of energy contained in an inflaton field suffusing s.p.a.ce. The act of rolling down the mountain and coming to rest at a low point in the terrain represents the inflaton shedding this energy, which in the process is converted to particles of matter and radiation.

Let's revisit three aspects of the metaphor, updating them with insights we've since acquired. First, we've learned that the inflaton is only one source of the energy that may fill s.p.a.ce; other contributions come from the quantum jitters of any and all fields-electromagnetic, nuclear, and so on. To revise the metaphor accordingly, alt.i.tude will now reflect the combined energy uniformly suffusing s.p.a.ce contributed by all sources.

Second, the original metaphor envisioned the base of the mountain, where the inflaton finally comes to rest, as being at "sea level," alt.i.tude zero, meaning the inflaton has shed all its energy (and pressure). But with our revised metaphor, the height of the mountain's base should represent the combined energy suffusing s.p.a.ce from all sources after inflation has drawn to a close. This is another name for that bubble universe's cosmological constant. The mystery in explaining our cosmological constant thus translates into the mystery of explaining the alt.i.tude of our mountain's base-why is it so close to, but not exactly at, sea level?

Finally, we initially considered the simplest of mountainous terrains, a peak leading smoothly to a base, where the inflaton would ultimately settle (see Figure 3.1 Figure 3.1). We then went a step further, taking account of other ingredients (Higgs fields) whose evolution and final resting places would influence the physical features manifest in the bubble universes (see Figure 3.6 Figure 3.6). In string theory, the range of possible universes is richer still. The shape of the extra dimensions determines the physical features within a given bubble universe, and so the possible "resting places," the various valleys in Figure 3.6b Figure 3.6b, now represent the possible shapes the extra dimensions can take. To accommodate the 10500 possible forms for these dimensions, the mountain terrain therefore needs a lush a.s.sortment of valleys, ledges, and outcroppings, as represented in possible forms for these dimensions, the mountain terrain therefore needs a lush a.s.sortment of valleys, ledges, and outcroppings, as represented in Figure 6.4 Figure 6.4. Any such feature in the terrain where a ball could come to rest represents a possible shape into which the extra dimensions could relax; the alt.i.tude at that location represents the cosmological constant of the corresponding bubble universe. Figure 6.4 Figure 6.4 ill.u.s.trates what's called the ill.u.s.trates what's called the string landscape string landscape.

With this more refined understanding of the mountain-or landscape-metaphor, we now consider how quantum processes affect the form of the extra dimensions in this setting. As we will see, quantum mechanics lights up the landscape.

Figure 6.4 The string landscape can be visualized schematically as a mountainous terrain in which different valleys represent different forms for the extra dimensions, and alt.i.tude represents the cosmological constant's value The string landscape can be visualized schematically as a mountainous terrain in which different valleys represent different forms for the extra dimensions, and alt.i.tude represents the cosmological constant's value.

Quantum Tunneling in the Landscape.

While Figure 6.4 Figure 6.4 is necessarily schematic (each of the different Higgs fields in is necessarily schematic (each of the different Higgs fields in Figure 3.6 Figure 3.6 has its own axis; similarly each of the roughly 500 different field fluxes that can thread a Calabi-Yau shape should also have its own axis-but sketching mountains in a 500-dimensional s.p.a.ce is a challenge), it correctly suggests that universes with different forms for the extra dimensions are part of a connected terrain. has its own axis; similarly each of the roughly 500 different field fluxes that can thread a Calabi-Yau shape should also have its own axis-but sketching mountains in a 500-dimensional s.p.a.ce is a challenge), it correctly suggests that universes with different forms for the extra dimensions are part of a connected terrain.16 And when quantum physics is taken into account, using results discovered independently of string theory by the legendary physicist Sidney Coleman in collaboration with Frank De Luccia, the connections between the universes allow for dramatic trans.m.u.tations. And when quantum physics is taken into account, using results discovered independently of string theory by the legendary physicist Sidney Coleman in collaboration with Frank De Luccia, the connections between the universes allow for dramatic trans.m.u.tations.

The core physics relies on a process known as quantum tunneling quantum tunneling. Imagine a particle, an electron for instance, encountering a solid barrier, say a slab of steel ten feet thick, that cla.s.sical physics predicts it can't penetrate. A hallmark of quantum mechanics is that the rigid cla.s.sical notion of "can't penetrate" often translates into the softer quantum declaration of "has a small but nonzero probability of penetrating." The reason is that the quantum jitters of a particle allow it, every so often, to suddenly materialize on the other side of an otherwise impervious barrier. The moment at which such quantum tunneling happens is random; the best we can do is predict the likelihood that it will take place during one interval or another. But the math says that if you wait long enough, penetration through just about any barrier will happen. And it does happen. If it didn't, the sun wouldn't s.h.i.+ne: for hydrogen nuclei to get close enough to fuse, they must tunnel through the barrier created by the electromagnetic repulsion of their protons.

Coleman and De Luccia, and many who have since followed their lead, scaled quantum tunneling up from single particles to an entire universe that's faced with a similar "impenetrable" barrier separating its current configuration from another that's possible. To get a feel for their result, imagine two possible universes that are otherwise identical save for a field, uniformly suffusing each, whose energy is higher in one, lower in the other. In the absence of a barrier, the higher energy-field value rolls to the lower, like a ball rolling down a hill as we've seen in the discussion of inflationary cosmology. But what happens if the field's energy curve has a "mountainous b.u.mp" separating its current value from the one it seeks, as in Figure 6.5 Figure 6.5? Coleman and De Luccia found that much as is the case for a single particle, a universe can do what cla.s.sical physics forbids: it can jitter its way-it can quantum tunnel-through the barrier and reach the lower energy configuration.

Figure 6.5 An example of a field's energy curve that has two values-two troughs or valleys-where the field naturally comes to rest. A universe suffused with the higher-energy field value can quantum tunnel to the lower value. The process involves a small randomly located region of s.p.a.ce in the original universe acquiring the lower field value; the region then expands, converting an ever-wider domain from the higher to the lower energy An example of a field's energy curve that has two values-two troughs or valleys-where the field naturally comes to rest. A universe suffused with the higher-energy field value can quantum tunnel to the lower value. The process involves a small randomly located region of s.p.a.ce in the original universe acquiring the lower field value; the region then expands, converting an ever-wider domain from the higher to the lower energy.

But because we are talking about a universe and not just a single particle, the tunneling process is more involved. It's not that the field's value throughout all of s.p.a.ce tunnels simultaneously through the barrier, Coleman and De Luccia argued; rather, a "seed" tunneling event would create a small, randomly located bubble suffused with the smaller field energy. The bubble would then grow, much like Vonnegut's ice-nine, ever enlarging the domain in which the field had tunneled to the lower energy.

These ideas can be applied directly to the string landscape. Imagine that the universe has a particular form for the extra dimensions, which corresponds to the left valley in Figure 6.6a Figure 6.6a. Because of this valley's high alt.i.tude, the three familiar spatial dimensions are permeated by a large cosmological constant-yielding strong repulsive gravity-and so are rapidly inflating. This expanding universe, together with its extra dimensions, is ill.u.s.trated on the left side of Figure 6.6b Figure 6.6b. Then, at some random location and moment, a tiny region of s.p.a.ce tunnels through the intervening mountain to the valley on the right side of Figure 6.6a Figure 6.6a. Not that the tiny region of s.p.a.ce moves (whatever that would mean); rather, the form of the extra dimensions (its shape, size, fluxes it carries) in this little region changes. The extra dimensions in the tiny region trans.m.u.te, acquiring the form a.s.sociated to the right valley in Figure 6.6a Figure 6.6a. This new bubble universe lies within the original, as ill.u.s.trated in Figure 6.6b Figure 6.6b.

The new universe will rapidly expand and continue to transform the extra dimensions as it spreads. But since the new universe's cosmological constant has decreased-its alt.i.tude in the landscape is lower than the original-the repulsive gravity it experiences is weaker, and so it won't expand as fast as the original universe. We thus have an expanding bubble universe, with the new form for the extra dimensions, contained in even faster expanding bubble universe, with the original form for the extra dimensions.17 The process can repeat. At other locations inside the original universe as well as inside the new one, further tunneling events cause additional bubbles to open up, creating regions with yet different forms for the extra dimensions (Figure 6.7). In due course, the expanse of s.p.a.ce will be riddled with bubbles inside of bubbles inside of bubbles-each undergoing inflationary expansion, each with a different form for the extra dimensions, and each with a smaller cosmological constant than the larger bubble universe within which it formed.

The result is a more intricate version of the Swiss cheese multiverse we found in our earlier encounter with eternal inflation. In that version, we had two types of regions: the "cheesy" ones that were undergoing inflationary expansion and the "holes" that weren't. This was a direct reflection of the simplified landscape with a single mountain whose base we a.s.sumed to be at sea level. The richer string theory landscape, with its sundry peaks and valleys corresponding to different values of the cosmological constant, gives rise to the many different regions in Figure 6.7 Figure 6.7-bubbles inside of bubbles inside of bubbles, like a sequence of Matryosta dolls, each painted by a different artist. Ultimately, the relentless series of quantum tunnelings through the mountainous string landscape realizes every possible form for the extra dimensions in one or another bubble universe. This is the Landscape Multiverse Landscape Multiverse.

Figure 6.6 (a) A quantum tunneling event, within the string landscape A quantum tunneling event, within the string landscape. (b) (b) The tunneling creates a small region of s.p.a.ce-represented by the smaller and darker bubble-within which the form of the extra dimensions has changed The tunneling creates a small region of s.p.a.ce-represented by the smaller and darker bubble-within which the form of the extra dimensions has changed.

Figure 6.7 The tunneling process can repeat, yielding a vast nested sequence of expanding bubble universes, each with a different form for the extra dimensions The tunneling process can repeat, yielding a vast nested sequence of expanding bubble universes, each with a different form for the extra dimensions.

The Landscape Multiverse is just what we need for Weinberg's explanation of the cosmological constant. We've argued that the string landscape ensures that there are, in principle, possible possible forms for the extra dimensions that would have a cosmological constant in the ballpark of the observed value: there are valleys in the string landscape whose tiny alt.i.tude is on par with the tiny but nonzero cosmological constant that the supernovae observations revealed. When the string landscape combines with eternal inflation, all possible forms for the extra dimensions, including those with such a small cosmological constant, are brought to life. Somewhere within the vast nested sequence of bubbles const.i.tuting the Landscape Multiverse, there are universes whose cosmological constant is about 10 forms for the extra dimensions that would have a cosmological constant in the ballpark of the observed value: there are valleys in the string landscape whose tiny alt.i.tude is on par with the tiny but nonzero cosmological constant that the supernovae observations revealed. When the string landscape combines with eternal inflation, all possible forms for the extra dimensions, including those with such a small cosmological constant, are brought to life. Somewhere within the vast nested sequence of bubbles const.i.tuting the Landscape Multiverse, there are universes whose cosmological constant is about 10123, the minuscule number that launched this chapter. And according to this line of thought, it is in one of those bubbles that we live.

The Rest of Physics?

The cosmological constant is but one feature of the universe we inhabit. It is arguably among the most puzzling, since its small measured value is so famously at odds with the numbers that emerge from the most straightforward estimates using established theory. This chasm draws singular focus to the cosmological constant and underlies the urgency of finding a framework, however exotic, with the capacity to explain it. Proponents of the interlocking set of ideas laid out above argue that the string multiverse does just that.

But what about all the other features of our universe-the existence of three kinds of neutrinos, the particular ma.s.s of the electron, the strength of the weak nuclear force, and so on? While we can at least imagine calculating these numbers, no one has as yet managed to do so. You might wonder whether their values, too, are ripe for a multiverse-based explanation. Indeed, researchers surveying the string landscape have found that these numbers, like the cosmological constant, also vary from place to place, and hence-at least in our current understanding of string theory-are not uniquely determined. This leads to a perspective very different from what dominated in the early days of research on the subject. It suggests that trying to calculate the properties of the fundamental particles, like trying to explain the distance between the earth and the sun, may be misguided. Like planetary distances, some or all of the properties would vary from one universe to the next.

For this line of thinking to be credible, though, we need at a bare minimum to know not only that there are bubble universes in which the cosmological constant has the right value, but also that in at least one such bubble the forces and the particles agree with what scientists in our universe have measured. We need to be sure that our universe, in all its detail, is somewhere in the landscape. This is the goal of a vibrant field called string model building string model building. The research program amounts to hunting around the string landscape and examining possible forms for the extra dimensions mathematically, in search of universes that most resemble ours. It's a formidable challenge, because the landscape is too large and intricate to be fully studied in any systematic way. Progress requires sharp calculational skills as well as intuition regarding which pieces to a.s.semble-the extra-dimensional shape, its size, the field fluxes cycling its holes, the presence of various branes, and so on. Those who lead this charge combine the best of rigorous science with an artistic sensibility. To date, no one has found an example that reproduces the features of our universe exactly. But with some 10500 possibilities awaiting exploration, the consensus is that our universe has a home somewhere in the landscape. possibilities awaiting exploration, the consensus is that our universe has a home somewhere in the landscape.

Is This Science?

In this chapter we've turned a logical corner. Until now, we've been exploring the implications for reality, writ large, of various developments in fundamental physics and cosmology research. I delight in the possibility that copies of the earth exist in the far reaches of s.p.a.ce, or that our universe is one of many bubbles in an inflating cosmos, or that we live on one of many braneworlds const.i.tuting a giant cosmic loaf. These are undeniably provocative and alluring ideas.

But with the Landscape Multiverse, we've invoked parallel universes in a different way. In the approach we've just followed, the Landscape Multiverse is not merely broadening our view of what might be out there. Instead, an array of parallel universes, worlds that may be beyond our ability to visit or see or test or influence, now and perhaps always, are directly invoked to provide insight into observations we make here, in this universe.

Which raises an essential question: Is this science?

*One point of language. For the most part, I use the terms "cosmological constant" and "dark energy" interchangeably. When I need a little more precision, I take the value of the cosmological constant to denote the amount amount of dark energy suffusing s.p.a.ce. As noted earlier, physicists often use the term "dark energy" a bit more liberally, to mean anything that can look like or masquerade as a cosmological constant over reasonably long time scales, but might slowly change and hence not truly be constant. of dark energy suffusing s.p.a.ce. As noted earlier, physicists often use the term "dark energy" a bit more liberally, to mean anything that can look like or masquerade as a cosmological constant over reasonably long time scales, but might slowly change and hence not truly be constant.

*It's also how 3D movie technology works: by suitably choosing the spatial offsets on the screen of nearly duplicate images, the filmmaker causes your brain to interpret the resulting parallaxes as different distances, creating the illusion of a 3D environment.

*If s.p.a.ce is infinitely big, you might wonder what it means to say that the universe is larger now than it was in the past. The answer is that "larger" refers to the distances between galaxies today compared with the distances between those same galaxies in the past. The expansion of the universe means the galaxies are now farther apart, which is reflected mathematically in the universe's scale factor being larger. In the case of an infinite universe, "larger" does not refer to the overall size of s.p.a.ce, since once infinite always infinite. But for ease of language, I will continue to refer to the changing size of the universe, even in the case of infinite s.p.a.ce, with the understanding that I'm referring to the changing distances between galaxies.

*The Cambridge astrophysicist George Efstathiou was also one of the early pioneers who argued strongly and convincingly for a nonzero cosmological constant.

*In Chapter 7 Chapter 7, we will examine more thoroughly and more generally the challenges of testing theories that involve a multiverse; we will also more closely a.n.a.lyze the role of anthropic reasoning in yielding potentially testable outcomes.

CHAPTER 7.

Science and the Multiverse.

On Inference, Explanation, and Prediction.

When David Gross, co-recipient of the 2004 n.o.bel Prize in physics, inveighs against string theory's Landscape Multiverse, there's a fair chance he'll quote Winston Churchill's speech of October 29, 1941: "Never give in.... Never, never, never, never-in nothing, great or small, large or petty-never give in." When Paul Steinhardt, the Albert Einstein Professor in Science at Princeton University and co-discoverer of the modern form of inflationary cosmology, speaks of his distaste for the Landscape Multiverse, the rhetorical flourishes are more subdued, but you can be pretty sure a comparison to religion, an unfavorable one at that, will at some point appear. Martin Rees, the United Kingdom's Astronomer Royal, sees the multiverse as the natural next step in our deepening grasp of all there is. Leonard Susskind says those who ignore the possibility that we're part of a multiverse are merely averting their eyes from a vision they find overwhelming. And these are just a few examples. There are many others on both sides, vehement naysayers and enthusiastic devotees, and they don't always express their opinions in terms so lofty.

In the quarter century I've been working on string theory, I've never seen pa.s.sions run quite so high, or language turn quite so sharp, as in discussions of string theory's landscape and the multiverse to which it may give rise. And it's clear why. Many see these developments as a battleground for the very soul of science.

The Soul of Science.

While the Landscape Multiverse has been the catalyst, the arguments turn on issues central to any theory in which a multiverse plays a role. Is it scientifically justifiable to speak of a multiverse, an approach that invokes realms inaccessible not just in practice but, in many cases, even in principle? Is the notion of a multiverse testable or falsifiable? Can invoking a multiverse provide explanatory power of which we'd otherwise be deprived?

If the answer to these questions is no, as detractors insist is the case, then multiverse proponents are a.s.suming an unusual stance. Nontestable, nonfalsifiable proposals, invoking hidden realms beyond our capacity to access-these seem a far cry from what most of us would want to call science. And therein lies the spark that makes pa.s.sions flare. Proponents counter that although the manner in which a given multiverse connects with observation may be different from what we're used to-it may be more indirect; it may be less explicit; it may require fortune to s.h.i.+ne favorably on future experiments-in respectable proposals, such connections are not fundamentally absent. Unapologetically, this line of argument takes an expansive view of what our theories and observations can reveal, and how the insights can be verified.

Where you come down on the multiverse also depends on your view of science's core mandate. General summaries often emphasize that science is about finding regularities in the workings of the universe, explaining how the regularities both illuminate and reflect underlying laws of nature, and testing the purported laws by making predictions that can be verified or refuted through further experiment and observation. Reasonable though the description may be, it glosses over the fact that the actual process of science is a much messier business, one in which asking the right questions is often as important as finding and testing the proposed answers. And the questions aren't floating in some preexisting realm in which the role of science is to pick them off, one by one. Instead, today's questions are very often shaped by yesterday's insights. Breakthroughs generally answer some questions but then give rise to a host of others that previously could not even be imagined. In judging any development, including multiverse theories, we must take account not only of its capacity for revealing hidden truths but also of its impact on the questions we are led to address. The impact, that is, on the very practice of science. As will become clear, multiverse theories have the capacity to reshape some of the deepest questions scientists have wrestled with for decades. That prospect invigorates some and infuriates others.

Having set the scene, let's now systematically think through the legitimacy, testability, and utility of frameworks that imagine ours to be one of many universes.

Accessible Multiverses.

It's hard to achieve consensus on these issues partly because the multiverse concept isn't monolithic. We've already come upon five versions-Quilted, Inflationary, Brane, Cyclic, and Landscape-and in the chapters that follow we will encounter four more. Understandably, the generic generic notion of a multiverse has a reputation for lying beyond testability. After all, the typical a.s.sessment goes, we're considering universes other than our own, but since we have access only to this one, we might as well be talking about ghosts or the tooth fairy. Indeed, this is the central problem, with which we'll shortly grapple, but note first that some multiverses notion of a multiverse has a reputation for lying beyond testability. After all, the typical a.s.sessment goes, we're considering universes other than our own, but since we have access only to this one, we might as well be talking about ghosts or the tooth fairy. Indeed, this is the central problem, with which we'll shortly grapple, but note first that some multiverses do do allow for interactions between member universes. We've seen that in the Brane Multiverse untethered string loops can travel from one brane to another. And in the Inflationary Multiverse, bubble universes can find themselves in even more direct contact. allow for interactions between member universes. We've seen that in the Brane Multiverse untethered string loops can travel from one brane to another. And in the Inflationary Multiverse, bubble universes can find themselves in even more direct contact.

Recall that the s.p.a.ce between two bubble universes in the Inflationary Multiverse is permeated by an inflaton field whose energy and negative pressure remain high and which therefore undergoes inflationary expansion. This expansion drives the bubble universes apart. Even so, if the rate at which the bubbles themselves expand exceeds the rate at which the swelling s.p.a.ce propels them to separate, the bubbles will collide. Bearing in mind that inflationary expansion is c.u.mulative-the more swelling s.p.a.ce there is between two bubbles, the faster they're driven apart-we come to an interesting realization. If two bubbles form really really close together, there will be so little intervening s.p.a.ce that their rate of separation will be slower than their rate of expansion. That puts the bubbles on a collision course. close together, there will be so little intervening s.p.a.ce that their rate of separation will be slower than their rate of expansion. That puts the bubbles on a collision course.

This reasoning is borne out by the mathematics. In the Inflationary Multiverse, universes can collide. Moreover, a number of research groups (including Jaume Garriga, Alan Guth, and Alexander Vilenkin; Ben Freivogel, Matthew Kleban, Alberto Nicolis, and Kris Sigurdson; as well as Anthony Aguirre and Matthew Johnson) have established that whereas some collisions may violently disrupt each bubble universe's internal structure-not good for possible bubble dwellers like us-gentler brush-ups may also occur, avoiding disastrous consequences yet still yielding observable signatures. The calculations show that if we had such a fender-bender with another universe, the impact would send shock waves rippling through s.p.a.ce, generating modifications to the pattern of hot and cold regions in the microwave background radiation.1 Researchers are now working out the detailed fingerprint such a disruption would leave, laying the groundwork for observations that could one day provide evidence that our universe has collided with others-evidence that other universes are out there. Researchers are now working out the detailed fingerprint such a disruption would leave, laying the groundwork for observations that could one day provide evidence that our universe has collided with others-evidence that other universes are out there.

But, however exciting the prospect may be, what if no test seeking evidence of an interaction or an encounter with another universe proves successful? Taking a hardheaded perspective, where does the concept of a multiverse stand if we never find any experimental or observational signatures of other universes?

Science and the Inaccessible I: Can it be scientifically justifiable to invoke un.o.bservable universes?

Every theoretical framework comes with an a.s.sumed architecture-the theory's fundamental ingredients, and the mathematical laws that govern them. Besides defining the theory, this architecture also establishes the kinds of questions we can ask within the theory. Isaac Newton's architecture was tangible. His mathematics dealt with the positions and velocities of objects we directly encounter or can easily see, from rocks and b.a.l.l.s to the moon and sun. A great many observations confirmed Newton's predictions, giving us confidence that his mathematics did indeed describe how familiar objects move. James Clerk Maxwell's architecture introduced a significant step of abstraction. Vibrating electric and magnetic fields are not the kinds of things for which our senses have evolved a direct affinity. Although we see "light"-electromagnetic undulations whose wavelengths lie in the range our eyes can detect-our visual experiences don't directly trace the undulating fields the theory posits. Even so, we can build sophisticated equipment that measures these vibrations and that, together with the theory's abundance of confirmed predictions, builds an overwhelming case that we're immersed in a pulsating ocean of electromagnetic fields.

In the twentieth century, fundamental science came to increasingly rely on inaccessible features. s.p.a.ce and time, through their melded union, provide the scaffolding for special relativity. When subsequently endowed with Einsteinian malleability, they become the flexible backdrop of the general theory of relativity. Now, I've seen watches tick and I've used rulers to measure, yet I've never grasped s.p.a.cetime in the same way I grasp the arms of my chair. I feel the effects of gravity, but if you pressed me on whether I can directly affirm that I'm immersed in curved s.p.a.cetime, I find myself back in the Maxwellian situation. I'm convinced that the theories of special and general relativity are correct not because I have tangible access to their core ingredients but rather because when I accept their a.s.sumed frameworks, the mathematics makes predictions about things I can measure. And the predictions turn out to be extraordinarily accurate.

Quantum mechanics takes such inaccessibility still further. The central ingredient of quantum mechanics is the probability wave, governed by an equation discovered in the mid-1920s by Erwin Schrodinger. Even though such waves are its hallmark feature, we will see in Chapter 8 Chapter 8 that the architecture of quantum physics ensures that they're permanently and completely un.o.bservable. Probability waves give rise to predictions for where this or that particle is likely to be found, but the waves themselves slither outside the arena of everyday reality. that the architecture of quantum physics ensures that they're permanently and completely un.o.bservable. Probability waves give rise to predictions for where this or that particle is likely to be found, but the waves themselves slither outside the arena of everyday reality.2 Nevertheless, because the predictions succeed so well, generations of scientists have accepted such an odd situation: a theory introduces a radically new and vital construct that, according to the theory itself, is un.o.bservable. Nevertheless, because the predictions succeed so well, generations of scientists have accepted such an odd situation: a theory introduces a radically new and vital construct that, according to the theory itself, is un.o.bservable.

The common theme running through these examples is that a theory's success can be used as an after-the-fact justification for its basic architecture, even when that architecture remains beyond our ability to access directly. This is so thoroughly part of the daily experience of theoretical physicists that the language used and the questions formulated regularly refer, without the slightest hesitation, to things that are at the very least far less accessible than tables and chairs and some of which lie permanently outside the bounds of direct experience.*

When we go further and use a theory's architecture to learn about the phenomena it entails, yet other kinds of inaccessibility present themselves. Black holes emerge from the mathematics of general relativity, and astronomical observations have provided substantial evidence that they're not only real but commonplace. Even so, the interior of a black hole is an exotic environment. According to Einstein's equations, the black hole's edge, its event horizon, is a surface of no return. You can cross in, but you can't cross out. We committed exterior dwellers will never observe a black hole's interior, not just because of practical considerations but as a consequence of the very laws of general relativity. Yet, there's full consensus that the region on the other side of a black hole's event horizon is real.

The application of general relativity to cosmology provides even more extreme instances of inaccessibility. If you don't mind a one-way journey, the interior of a black hole is at least a possible destination. But realms lying beyond our cosmic horizon are unreachable, even if we were able to travel at nearly light speed. In an accelerating universe such as ours, this point becomes forcefully evident. Given the measured value of the cosmological speedup (and a.s.suming it will never change), any object more distant from us than about 20 billion light-years lies permanently outside what we can see, visit, measure, or influence. Farther than that distance, s.p.a.ce will always be receding from us so quickly that any attempt to breach the separation would be as fruitless as a kayaker navigating against a current flowing faster than she can paddle.

Objects that have always been beyond our cosmic horizon are objects that we have never observed and never will observe; conversely, they have never observed us, and never will. Objects that at some time in the past were within our cosmic horizon but have been dragged beyond it by spatial expansion are objects that we once could see but never will again. Yet I think we can agree that such objects are as real as anything tangible, and so are the realms they inhabit. It would surely be peculiar to argue that a galaxy that we could once see but that has since slipped over our cosmic horizon has entered a realm that's nonexistent, a realm that because of its permanent inaccessibility needs to be wiped off reality's map. Even though we can't observe or influence such realms, nor they us, they are properly included in our picture of what exists.3 These examples make clear that science is no stranger to theories that include elements, from basic ingredients to derived consequences, that are inaccessible. Our confidence in such intangibles relies on our confidence in the theory. When quantum mechanics invokes probability waves, its impressive ability to describe things we can measure, such as the behavior of atoms and subatomic particles, compels us to embrace the ethereal reality it posits. When general relativity predicts the existence of places we can't observe, its phenomenal successes in describing those things we can observe, such as the motion of planets and the trajectory of light, compels us to take the predictions seriously.

So for confidence in a theory to grow we don't require that all of its features be verifiable; a robust and varied a.s.sortment of confirmed predictions is enough. Scientific work going back well over a century has accepted that a theory may invoke hidden, inaccessible elements-provided it also makes interesting, novel, and testable predictions about an abundance of observable phenomena.

This suggests that it's possible to mount a convincing argument for a theory involving a multiverse even if we can't obtain any direct evidence for universes beyond our own. If the experimental and observational evidence supporting a theory compels you to embrace it, and if the theory is founded on such a tight mathematical structure that there's no room for cherry-picking among its features, then you have to embrace all of it. And if the theory implies the existence of other universes, then that's the reality the theory requires you to take on board.

In principle, then-and make no mistake, my point here is one of principle-the mere invocation of inaccessible universes does not consign a proposal to stand outside science. To amplify this, imagine that one day we a.s.semble a convincing experimental and observational case for string theory. Perhaps a future accelerator is able to detect sequences of string vibrational patterns and evidence for extra dimensions, while astronomical observations detect stringy features in the microwave background radiation, as well as the signatures of long stretched strings undulating through s.p.a.ce. Suppose further that our understanding of string theory has progressed substantially, and we've learned that the theory absolutely, positively, incontrovertibly generates the Landscape Multiverse. Notwithstanding calls to the contrary, a theory with strong experimental and observational support, whose internal structure requires a multiverse, would lead us to conclude inexorably that the time for "giving in" had arrived.*

So to address the question heading this section, in the right scientific context it would not merely be respectable to invoke a multiverse; failing failing to do so would evidence nonscientific prejudice. to do so would evidence nonscientific prejudice.

Science and the Inaccessible II: So much for principle; where do we stand in practice?

The skeptic will rightly respond that it's one thing to make a point of principle about how the case for a given multiverse theory might be fas.h.i.+oned. It's another to a.s.sess whether any of the multiverse proposals we've described qualify as experimentally confirmed theories that come equipped with an absolute prediction of other universes. Do they?

The Quilted Multiverse arises from an infinite spatial expanse, a possibility that fits squarely within general relativity. The snag is that general relativity allows for an infinite spatial expanse but doesn't require require it, which in turn explains why, even though general relativity is an accepted framework, the Quilted Multiverse remains tentative. An infinite spatial expanse does emerge directly from eternal inflation-recall that each bubble universe when viewed from the inside appears infinitely large-but in this setting the Quilted Multiverse is rendered uncertain because the underlying proposal, eternal inflation, remains hypothetical. it, which in turn explains why, even though general relativity is an accepted framework, the Quilted Multiverse remains tentative. An infinite spatial expanse does emerge directly from eternal inflation-recall that each bubble universe when viewed from the inside appears infinitely large-but in this setting the Quilted Multiverse is rendered uncertain because the underlying proposal, eternal inflation, remains hypothetical.

The same consideration affects the Inflationary Multiverse, which also emerges from eternal inflation. Astronomical observations over the past decade have bolstered the physics community's confidence in inflationary cosmology but have nothing to say about whether the inflationary expansion is eternal. Theoretical studies show that although many versions are eternal, yielding bubble universe upon bubble universe, some entail but a single ballooning spatial expanse.

The Brane, Cyclic, and Landscape Multiverses are based on string theory, so they suffer multiple uncertainties. Remarkable as string theory may be, rich as its mathematical structure may have become, the dearth of testable predictions, and the concomitant absence of contact with observations or experiments, relegates it to the realm of scientific speculation. Moreover, with the theory still very much a work in progress, it's unclear which features will continue to play a primary role in future refinements. Will branes, the basis of the Brane and Cyclic Multiverses, remain central? Will the copious choices for the extra dimensions, the basis for the Landscape Multiverse, persist, or will we eventually find a mathematical principle that picks out one particular shape? We just don't know.

So, although it's conceivable that we could fas.h.i.+on a convincing argument for a multiverse theory that made little or no reference to its prediction of other universes, for the multiverse scenarios we've encountered that approach won't fly. At least not yet. To a.s.sess any of them, we will need to tackle their prediction of a multiverse head-on.

Can we? Can a theory's invocation of other universes yield testable predictions even if those universes lie beyond the reach of experiments and observations? Let's address this key question through a number of steps. We'll follow the pattern above, progressing from an "in principle" to an "in practice" perspective.

Predictions in a Multiverse I: If the universes const.i.tuting a multiverse are inaccessible, can they nevertheless meaningfully contribute to making predictions?

Some scientists who resist multiverse theories see the enterprise as an admission of failure, a full-fledged retreat from the long-sought goal of understanding why the universe we see has the properties it does. I empathize, being one of many who have worked for decades to realize string theory's tantalizing promise of calculating every fundamental observable feature of the universe, including the values of nature's constants. If we accept that we're part of a multiverse in which some or perhaps even all of the constants vary from one universe to another, then we accept that this goal is misguided. If the fundamental laws allow, say, the strength of the electromagnetic force to have many different values across the multiverse, then the very notion of calculating the the strength is meaningless, like asking a pianist to pick out strength is meaningless, like asking a pianist to pick out the the note. note.

But here's the question: Does variation in features mean that we lose all power to predict (or postdict) those intrinsic to our own universe? Not necessarily. Even though a multiverse precludes uniqueness, it's possible that a degree of predictive capability can be retained. It comes down to statistics.

Consider dogs. They don't have a unique weight. There are very light dogs, such as Chihuahuas, that can weigh under two pounds; there are very heavy dogs, such as Old English mastiffs, that can tip the scales at over two hundred pounds. Were I to challenge you to predict the weight of the next dog you pa.s.s in the street, it might seem that the best you could do would be to pick a random number within the range I've given. Yet, with a little information, you can make a more refined guess. If you get ahold of the dog population data in your neighborhood, such as the number of people who have this or that breed, the distribution of weights within each breed, and perhaps even information on the number of times per day different breeds typically need to be taken for a walk, you can figure out the weight of the dog you are most likely likely to encounter. to encounter.

This wouldn't be a sharp prediction; statistical insights often aren't. But depending on the distribution of dogs, you may be able to do much