The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos

by Brian Greene

  Figure 5.2 From close up, the image looks like Albert Einstein. From farther away, it looks like Marilyn Monroe. (The image was created by Aude Oliva of the Massachusetts Institute of Technology.)

  Witten argued, and others since have filled in important details, that all five string theories are linked through a network of such dualities.3 Their overarching union, called M-theory (we’ll see why in a moment), combines insights from all five formulations, stitched together through the various duality relationships, to gain a far more refined understanding of each. One such insight, central to the theme we’re pursuing, showed that there’s much more to string theory than strings.

  Branes

  When I started studying string theory, I asked the very question that many in the years since have asked me: Why are strings considered so special? Why focus solely on fundamental ingredients that have only length? After all, the theory itself requires that the arena within which its ingredients exist—the spatial universe—has nine dimensions, so why not consider entities shaped like two-dimensional sheets or three-dimensional blobs or their higher-dimensional cousins? The answer I learned as a graduate student in the 1980s, and explained frequently when I lectured on the subject through the mid-1990s, was that the mathematics describing fundamental constituents with more than one spatial dimension suffered from fatal inconsistencies (such as quantum processes that would have negative probabilities, a meaningless mathematical result). But when the same mathematics was applied to strings, the inconsistencies canceled themselves out, leaving a cogent description.†4 Strings were definitely in a class of their own.

  Or so it seemed.

  Armed with the newfound calculational methods, physicists started analyzing their equations much more precisely and produced a range of unexpected results. One of the most surprising established that the rationale for excluding anything but strings was rickety. Theorists realized that the mathematical problems encountered when studying higher-dimensional ingredients, such as discs and blobs, were artifacts of the approximations being used. Using the more precise methods, a small army of theorists established that ingredients with various numbers of spatial dimensions do lurk in string theory’s mathematical shadows.5 The perturbative techniques were too coarse to expose these ingredients but the new methods finally could. By the late 1990s, it was abundantly clear that string theory was not just a theory that contained strings.

  The analyses revealed objects, shaped like Frisbees or flying carpets, with two spatial dimensions: membranes (one meaning of the “M” of M-theory), also called two-branes. But there was more. The analyses revealed objects with three spatial dimensions, so-called three-branes; objects with four spatial dimensions, four-branes, and so on, all the way up to nine-branes. The mathematics made clear that all of these entities could vibrate and wiggle, much like strings; indeed, in this context, strings are best thought of as one-branes—a single entry on an unexpectedly long list of the theory’s basic building blocks.

  An allied revelation, just as flabbergasting to those who’d spent the better part of their professional lives working on the subject, was that the number of spatial dimensions the theory requires is not actually nine. It’s ten. And if we fold in the dimension of time, the total number of spacetime dimensions is eleven. How could this be? Remember the “(D–10) times Trouble” consideration, recounted in Chapter 4, underlying the conclusion that string theory needs ten spacetime dimensions. The mathematical analysis that produced that equation was, once again, based on a perturbative approximation scheme that assumed the string coupling was small. Surprise, surprise, that approximation missed one of the theory’s spatial dimensions. The reason, Witten showed, is that the size of the string coupling directly controls the size of the hitherto unknown tenth spatial dimension. By taking the coupling small, researchers had unwittingly made this spatial dimension small, too—so small as to be invisible to the mathematics itself. The more precise methods rectified this failing, revealing a string/M-theory universe with ten dimensions of space and one of time, for a total of eleven spacetime dimensions.

  I remember well the dazed and wide-eyed looks everywhere at the international string theory conference, held at the University of Southern California in 1995, at which Witten first announced some of these results, the first shot in what is now called the Second String Theory Revolution.* For the multiverse story, it is the branes that are central. Using them, researchers have been led by the hand to another variety of parallel universes.

  Branes and Parallel Worlds

  We typically imagine that strings are ultra-small; that very feature makes testing the theory such a challenge. However, I noted in Chapter 4 that strings are not necessarily minute. Rather, a string’s length is controlled by its energy. The energies associated with the masses of electrons, quarks, and other known particles are so tiny that the corresponding strings would indeed be minuscule. But inject enough energy into a string, and you could cause it to stretch large. We don’t have anywhere near the capacity to do this here on earth, but that’s a limitation of our technological development. If string theory is right, an advanced civilization would be able to pump strings up to whatever size it liked. Natural cosmological phenomena also have the capacity to produce long strings; for example, strings can wrap around a portion of space and get caught up in the cosmological expansion, stretching long in the process. One of the possible experimental signatures outlined in Table 4.1 looks for gravitational waves that such long strings may emit as they vibrate far away in space.

  Like strings, higher-dimensional branes can be big. And this opens up a wholly new way in which string theory can describe the cosmos. To grasp what I mean, picture first a long string, as long as an overhead electric cable that runs as far as the eye can see. Next, picture a large two-brane, like an enormous tablecloth or a gargantuan flag, whose surface extends indefinitely. These are both easy to visualize because we can picture them located within the three dimensions of common experience.

  If a three-brane is enormous, perhaps infinitely big, the situation changes. A three-brane of this sort would fill the space we occupy, like water filling a huge fish tank. Such ubiquity suggests that rather than think of the three-brane as an object that happens to be situated within our three spatial dimensions, we should envision it as the very substrate of space itself. Just as fish inhabit the water, we would inhabit a space-filling three-brane. Space, at least the space we directly inhabit, would be far more corporeal than generally imagined. Space would be a thing, an object, an entity—a three-brane. As we run and walk, as we live and breathe, we move in and through a three-brane. String theorists call this the braneworld scenario.

  It is here that parallel universes make their stringy entrance.

  I’ve been focusing on the relationship between three-branes and three spatial dimensions because I wanted to make contact with the familiar domain of everyday reality. But in string theory, there are more than just three spatial dimensions. And a higher-dimensional expanse offers ample room for accommodating more than one three-brane. Starting conservatively, imagine that there are two enormous three-branes. You may find it difficult to picture this. I certainly do. Evolution has prepared us to identify objects, those presenting opportunity as well as danger, that sit squarely within three-dimensional space. Consequently, although we can easily picture two ordinary three-dimensional objects inhabiting a region of space, few of us can picture two coexisting but separate three-dimensional entities, each of which could fully fill three-dimensional space. For ease in discussing the braneworld scenario, then, let’s suppress one spatial dimension in our visualizations and think about life on a giant two-brane. And for a definite mental image, think of the two-brane as a giant, extraordinarily thin slice of bread.*

  To use this metaphor effectively, imagine that the slice of bread includes the entirety of what we’ve traditionally called the universe—the Orion, Horsehead, and Crab nebulae; the entire Milky Way; the Andromeda, Sombrero, and Whirlpool Gala
xies; and so on—everything within our three-dimensional spatial expanse, however distant, as sketched in Figure 5.3a. To visualize a second three-brane we just need to picture a second enormous slice of bread. Where? Place it next to ours, just shifted slightly away in the extra dimensions (Figure 5.3b). To visualize three or four or any other number of three-branes is equally easy. Just add slices to the cosmic loaf. And while the loaf metaphor emphasizes a collection of branes all aligned with one another, it’s easy to imagine yet more general possibilities. The branes can be oriented any which way, and branes of any other dimensionality, higher or lower, can be included just the same.

  Figure 5.3 (a) In the braneworld scenario, what we have traditionally thought to be the entire cosmos is imagined to reside within a three-dimensional brane. For visual ease, we suppress one dimension and show the braneworld as having two spatial dimensions; we also show only a finite piece of branes that may extend infinitely far. (b) The higher-dimensional expanse of string theory can accommodate many parallel braneworlds.

  The same fundamental laws of physics would apply all across the collection of branes, since they all emerge from a single theory, string/M-theory. But, much as with the bubble universes in the Inflationary Multiverse, environmental details such as the value of this or that field permeating a brane, or even the number of spatial dimensions defining a brane, can profoundly affect its physical features. Some braneworlds might be much like our own, filled with galaxies, stars, and planets, while others might be very different. On one or more of those branes there might be self-aware beings who, like us, once thought that their slice—their expanse of space—was the entirety of the cosmos. In string theory’s braneworld scenario, we would now recognize this as a parochial perspective. In the braneworld scenario, our universe is just one of many that populate the Brane Multiverse.

  When the Brane Multiverse was first floated in the string theory community, the immediate response focused on an obvious question. If there are giant branes right next door, entire parallel universes hovering nearby like slices of rye cozying up to their neighbors, why don’t we see them?

  Sticky Branes and Gravity’s Tentacles

  Strings come in two shapes, loops and snippets. I haven’t addressed this distinction because it’s not essential for understanding many of the theory’s overarching features. But for braneworlds the distinction between loops and snippets is crucial, and a simple question reveals why. Can strings fly off a brane? The answer: A loop can. A snippet can’t.

  As first realized by renowned string theorist Joe Polchinski, it all has to do with the endpoints of a string snippet. The equations that convinced physicists that branes were part of string theory also revealed that strings and branes have a particularly intimate relationship. Branes are the only locations where the endpoints of string snippets can reside, as in Figure 5.4. The math showed that if you try to remove a string’s endpoint from a brane, you are attempting the impossible, like seeking to make π smaller or the square root of 2 bigger. Physically, it’s like trying to remove the north or south pole from the ends of a bar magnet. It just can’t be done. String snippets can freely move within and through a brane, effortlessly gliding from here to there, but they can’t leave it.

  If these ideas are more than just interesting mathematics and we are in fact all living on a brane, you’re right now directly experiencing the viselike grip our brane exerts on string endpoints. Try to jump off our three-brane. Try again, harder. I suspect you’re still here. In a braneworld, the strings that make up you, and the rest of ordinary matter, are snippets. While you can jump up and down, throw a baseball from first to second, and send a sound wave from radio to ear, all with absolutely no resistance from the brane, you can’t depart the brane. When you try to jump off, the endpoints of your string snippets anchor you to the brane, unalterably. Our reality could be a floating slab in a higher-dimensional expanse, but we’d be permanently imprisoned, unable to venture out and explore the grander cosmos.

  Figure 5.4 Branes are the only locations where the endpoints of string snippets can reside.

  The same picture holds for the particles that transmit the three nongravitational forces. The analysis shows that they, too, arise from string snippets. Most notable among these are photons, the purveyors of the electromagnetic force. Visible light, which is a stream of photons, can therefore travel freely through the brane, from this text to your eyes, or from the Andromeda Galaxy to the Wilson Observatory, but it too is unable to escape. Another braneworld could be hovering millimeters away, but because light can’t travel across the gap, we would never see the slightest hint of its presence.

  The one force that’s different in this regard is gravity. The distinguishing feature of gravitons, noted in Chapter 4, is that they have spin-2, twice that of the particles arising from string snippets (such as photons) that convey the nongravitational forces. That gravitons have twice the spin of an individual string snippet means you can think of gravitons as being built of two such snippets, the two ends of one melding with those of the other, yielding a loop. And since loops have no endpoints, branes can’t trap them. Gravitons can therefore leave and reenter a braneworld. In a braneworld scenario, then, gravity provides our only means of probing beyond our three-dimensional spatial expanse.

  This realization plays a central role in some of the potential tests of string theory mentioned in Chapter 4 (Table 4.1). In the 1980s and 1990s, before branes entered the picture, physicists imagined that string theory’s extra dimensions were roughly Planck-sized (a radius of about 10–33 centimeters), the natural scale for a theory involving gravity and quantum mechanics. But the braneworld scenario encourages more expansive thinking. With our only probe beyond the three common dimensions being gravity—the feeblest of all forces—the extra dimensions can be a good deal larger and have still avoided detection. So far.

  If the extra dimensions exist, and are much larger than previously thought—perhaps a billion billion billion times larger (about 10–4 centimeters across)—then experiments that measure the strength of gravity, described in the second row of Table 4.1, stand a chance of detecting them. When objects attract each other gravitationally, they exchange streams of gravitons; the gravitons are invisible messengers that communicate gravity’s influence. The more gravitons the objects exchange, the stronger the mutual gravitational pull. When some of these streaming gravitons leak off our brane and flow into the extra dimensions, the gravitational attraction between objects will be diluted. The larger the extra dimensions, the more the dilution, and the weaker gravity appears. By carefully measuring the gravitational pull between two objects brought closer together than the size of the extra dimensions, experimenters envision intercepting the gravitons before they leak from our brane; if so, the experimenters should measure a strength for gravity that’s proportionately larger. Thus, although I didn’t mention it in Chapter 4, this approach for unmasking the extra dimensions relies on the braneworld scenario.

  A more modest increase in the size of the extra dimensions, to only about 10–18 centimeters across, would still make them potentially accessible to the Large Hadron Collider. As discussed in the third entry of Table 4.1, high-energy collisions between protons can eject debris into the extra dimensions, resulting in an apparent loss of energy in our dimensions that might be detectable. This experiment, too, relies on the braneworld scenario. Data attesting to missing energy would be explained by positing that our universe exists on a brane and arguing that debris with the capacity to fly off our brane—gravitons—had carried the energy away.

  The prospect of mini black holes, the fourth entry of Table 4.1, is yet another braneworld by-product. The Large Hadron Collider stands a chance of producing mini black holes in proton-proton collisions only if the intrinsic strength of gravity grows large when probed over short distances. As above, it is the braneworld scenario that makes this possible.

  The details cast these three experiments in a new light. Not only are these experiments seeking
evidence of exotic structures such as extra dimensions of space and tiny black holes, they are also seeking evidence that we’re living on a brane. In turn, a positive result would not only build a case for string theory’s braneworld scenario, but would also provide indirect evidence for universes beyond our own. If we can establish that we’re living on a brane, the mathematics gives us no reason to expect that ours is the only one.

  Time, Cycles, and the Multiverse

  The multiverses we’ve so far encountered, however different in detail, share one basic trait. In the Quilted, Inflationary, and Brane Multiverses, the other universes are all “out there” in space. For the Quilted Multiverse “out there” means far away in the everyday sense; for the Inflationary Multiverse it means beyond our bubble universe and across the rapidly expanding intervening realm; for the Brane Multiverse it means a possibly short distance away but the seperation is through another dimension. Evidence supporting the braneworld scenario would lead us to consider seriously another variety of multiverse, one that leverages not the opportunities afforded by space but those of time.6