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

by Brian Greene

Well, not necessarily. Even as far back as the early decades of the twentieth century, a prescient series of papers by the German mathematician Theodor Kaluza and by the Swedish physicist Oskar Klein suggested that there might be dimensions that are proficient at evading detection. Their work envisioned that unlike the familiar spatial dimensions that extend over great, possibly infinite, distances, there might be additional dimensions that are tiny and curled up, making them difficult to see.

The Kaluza-Klein proposal suggested that a similar distinction, between dimensions that are big and easily seen, and others that are tiny and thus more difficult to reveal, might apply to the fabric of space

This line of thought establishes that the suggestion of “extra” spatial dimensions, however unfamiliar, is not absurd. That’s a good start, but it invites an essential question: Why, back in the 1920s, would someone invoke such an exotic idea? Kaluza’s motivation came from an insight he had shortly after Einstein published the general theory of relativity. He found that with a single stroke of the pen—literally—he could modify Einstein’s equations to make them apply to a universe with one additional dimension of space. And when he analyzed those modified equations, the results were so thrilling that, as his son has recounted, Kaluza discarded his normally reserved demeanor, pounded his desk with both hands, shot to his feet, and erupted into an aria from The Marriage of Figaro.10 Within the modified equations, Kaluza found the ones Einstein had already used successfully to describe gravity in the familiar three dimensions of space and one of time. But because his new formulation included an additional dimension of space, Kaluza found an additional equation. Lo and behold, when Kaluza derived this equation he recognized it as the very one Maxwell had discovered half a century earlier to describe the electromagnetic field.

Can string theory do better? One of the most beautiful features of string theory (and the facet that most impressed me when I learned the subject) is that particle properties are determined by the size and shape of the extra dimensions.

The lack of a unique specification of the extra dimensions is the main stumbling block preventing string theorists from making definitive predictions.

Quantum field theory has been rightly lauded as hugely successful, and yet it can’t explain the fundamental particle properties. If string theory also can’t explain the particle properties but goes beyond quantum field theory in one key measure, by embracing gravity, that alone would be a monumental achievement.

Indeed, in Chapter 6 we’ll see that in a cosmos replete with parallel worlds—as suggested by one modern reading of string theory—it may be plainly wrongheaded to hope that mathematics would pick out a unique form for the extra dimensions. Instead, much as the many different forms for DNA provide for the abundant variety of life on earth, so the many different forms for the extra dimensions may provide for the abundant variety of universes populating a string-based multiverse.

If a typical string is as small as Figure 4.2 suggests, to probe its extended structure—the very characteristic that distinguishes it from a point—you’d need an accelerator some million billion times more powerful than even the Large Hadron Collider. Using known technology, such an accelerator would need to be about as large as the galaxy, and would consume enough energy each second to power the entire world

The choice of fields and energy curves in quantum field theory is tantamount to the choice of the extra dimensional shape in string theory. The particular challenge facing string theory, though, is that the mathematics linking particle properties (such as their masses and charges) to the shape of the extra dimensions is extraordinarily intricate.

This makes it difficult to work backwards—to use experimental data to guide the choice of the extra dimensions, much as such data guide the choices of fields and energy curves in quantum field theory. One day we may have the theoretical dexterity to use experimental data to fix the form of string theory’s extra dimensions, but not yet.

A singularity is any physical setting, real or hypothetical, that is so extreme (huge mass, small size, enormous spacetime curvature, punctures or rips in the spacetime fabric) that quantum mechanics and general relativity go haywire, generating results akin to the error message displayed on a calculator when you divide any number by zero.

This suggests that a new kind of geometry, based not on points but rather on loops, should be linked to string physics.

The fact is, the vast majority of phenomena, from the motion of planets to the interactions of particles, are just too complex to be described mathematically with complete precision. Instead, the task of the theoretical physicist is to figure out which complications in a given context can be discarded, yielding a manageable mathematical formulation that still captures essential details. In predicting the course of the earth you’d better include the effects of the sun’s gravity; if you include the moon’s too, all the better, but the mathematical complexity rises significantly. (In the nineteenth century, the French mathematician Charles-Eugène Delaunay published two 900-page volumes related to intricacies of the sun-earth-moon gravitational dance.) If you try to go further and account fully for the influence of all the other planets, the analysis becomes overwhelming. Luckily, for many applications, you can safely disregard all but the sun’s influence, since the effect of other bodies in the solar system on earth’s motion is nominal. Such approximations illustrate my earlier assertion that the art of physics lies in deciding what to ignore.

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.

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

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.

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.

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.

for the Brane Multiverse it means a possibly short distance away but the separation is through another dimension.

If we are on such a gliding brane, and there are other branes nearby, what would happen if we slammed into one of them? Although there are details that have not yet been fully worked out, you can be certain that a collision between two branes—a collision between two universes—would be violent. The simplest possibility would be two parallel three-branes coming closer and closer together till finally they collided straight-on, much like two cymbals crashing. The tremendous energy harbored in their relative motion would yield a fiery rush of particles and radiation that would obliterate any organized structures that either

To a group of researchers including Paul Steinhardt, Neil Turok, Burt Ovrut, and Justin Khoury, this cataclysm rang not just of an end but of a beginning. An intensely hot, thoroughly dense environment in which particles stream this way and that sounds much like the conditions just after the big bang. Perhaps, then, when two branes collide they wipe out whatever structures may have coalesced during either of their histories, from galaxies to planets to people, while setting the stage for a cosmic rebirth. Indeed, a three-brane filled with a blistering plasma of particles and radiation responds just as an ordinary three-dimensional spatial expanse would: it expands. And as it does, the environment cools, allowing particles to clump, ultimately yielding the next generation of stars and galaxies. Some have suggested that an apt name for this reprocessing of universes would be the big splat.

Evocative though it may be, “splat” misses a central feature of brane collisions. Steinhardt and his collaborators have argued that when branes collide, they don’t stick together. They bounce apart. The gravitational force they exert on each other then gradually slows their relative motion; eventually, they reach a maximum separation from which they start approaching once again. As the branes fall back together, each builds up speed, they collide, and through the ensuing firestorm the conditions on each brane are reset once again, initiating a new era of cosmological evolution. The essenc...

One of the oldest prescientific cosmologies, the Hindu tradition, envisions a nested complex of cosmological cycles within cycles, which, according to some interpretations, stretch from millions to trillions of years.

Part of the appeal of a cyclical cosmology is its apparent ability to avoid the knotty issue of how the universe began. If the universe goes through cycle after cycle, and if the cycles have always happened (and perhaps always will), then the problem of an ultimate beginning is sidestepped. Each cycle has its own beginning, but the theory provides a concrete physical cause: the termination of the previous cycle. And if you ask about the beginning of the entire cycle of universes, the answer is simply that there was no such beginning, because the cycles have been repeating for eternity.

Then in the 1950s, the Dutch astrophysicist Herman Zanstra called attention to a problematic feature of cyclical models, one that was implicit in Tolman’s analysis a couple of decades earlier. Zanstra showed

that there couldn’t have been an infinite number of cycles preceding our own. The wrench in the cosmological works was the Second Law of Thermodynamics. This law, which we’ll discuss more fully in Chapter 9, establishes that disorder—entropy—increases over time. It’s something we routinely experience. Kitchens, however ordered in the morning, have a way of becoming disordered by nightfall; the same goes for laundry bins, desktops, and playrooms. In these everyday settings, the increase in entropy is a mere nuisance; in cyclic cosmology, the increase in entropy is pivotal. As Tolman himself had realized, the equations of general relativity link the entropy content of the universe with the duration of a given cycle. More entropy means more disordered particles squeezed together when the universe shrinks; that generates a more powerful rebound, space expands further, and so the cycle lasts longer. Looking back from today, the Second Law then implies that ever-earlier cycles would have had ever-less entropy (because the Second Law says that entropy increases toward the future, it must decrease toward the past),* and would thus have had ever-shorter durations. Working this out mathematically, Zanstra showed that sufficiently far back in time the cycles would have been so short that they would have ceased. They would have had a beginning.

Others still have taken a more radical tack. Maybe, they suggest, the decades of fruitless attempts to pin down the form for the extra dimensions are telling us something. Maybe, these radicals brazenly continue, we need to take seriously all of the possible shapes and fluxes emerging from string theory’s mathematics. Maybe, they urge, the reason the mathematics contains all these possibilities is that they’re all real, each shape being the extra-dimensional part of its own separate universe. And maybe, grounding a seemingly wild flight of fancy in observational data, this is just what’s needed to address perhaps the thorniest problem of all: the cosmological constant.

The tiny number printed above was first measured in 1998 by two teams of astronomers making meticulous observations of exploding stars in distant galaxies. Since then, the work of many has corroborated the teams’ result. What is the number, and why such a fuss? Evidence is mounting that it’s what I referred to earlier as the entry on the third line of the general relativity tax form: Einstein’s cosmological constant, which specifies the amount of invisible dark energy permeating the fabric of space.

When these astronomers began their work, neither group was focused on measuring the cosmological constant. Instead, the teams had set their sights on measuring another cosmological feature, the rate at which the expansion of space is slowing. Ordinary attractive gravity acts to pull every object closer to every other, so it causes the expansion speed to decrease. The precise rate of slowdown is central to predicting what the universe will be like in the far future. A big slowdown would mean that the expansion of space would diminish all the way to zero and then reverse its motion, leading to a period of spatial contraction. Unabated, this might result in a big crunch—a reverse of the big bang—or perhaps a bounce, as in the cyclical models introduced in the previous chapter. A small slowdown would yield a very different outcome. Much as a ball with a high speed can escape the earth’s gravity and head ever farther outward, if the speed of spatial expansion were high enough, and the rate of its slowdown sufficiently meager, space could expand forever. By measuring the cosmic slowdown, the two groups sought the ultimate fate of the cosmos.

The approach of each team was straightforward: measure how fast space was expanding at various times in the past, and by comparing those speeds determine the rate at which the expansion has been slowing over the course of cosmic history. Okay. But how would you do this? As with many questions in astronomy, the answer comes down to careful measurements of light. Galaxies are luminous beacons whose motion traces the spatial expansion. If we could determine how fast

galaxies at a range of distances were receding from us when, long ago, they emitted the light we now see, we could determine how fast space was expanding at a variety of moments in the past. By comparing those speeds, we’d learn the rate of cosmic slowdown. That’s the essential idea. To fill in the details, we need to address two primary questions. From today’s observations of faraway galax...

When you look at stars in the night sky, the parallax is too small to be reliably measured; your eyes are just too close together to yield a significant difference in angle. But there’s a clever way around this: measure the position of a star on two occasions, some six months apart, thus using the two locations of the earth in place of the two locations of your eyes. The larger separation of the observing locations increases the

parallax; it’s still small, but in some cases is big enough to be measured. Back in the early 1800s there was an intense competition among a group of scientists to be the first to measure such stellar parallax; in 1838, the German astronomer and mathematician Friedrich Bessel won the bragging rights, successfully measuring the parallax to a star called 61 Cygni, in the constellation Cygnus. The angular difference turned out to be .000084 degrees, placing the star about 10 light-years away.

The hitch, and it’s not a small one, lies in establishing the intrinsic brightness of astrophysical objects.

The bloated dwarf star collapses, setting off an explosion so violent that the light generated rivals the combined output of the other 100 billion or so stars residing in the galaxy it inhabits.

The challenge in using Type Ia supernovae, however, is that in a typical galaxy they take place only once every few hundred years: How do you catch them in the act?

Both the Supernova Cosmology Project and the High-Z Supernova Search Team tackled this obstacle in a manner reminiscent of epidemiological studies: accurate information about even relatively rare conditions can be gained if you study large populations. Similarly, by using telescopes equipped with wide-field-of-view detectors capable of simultaneously examining thousands of galaxies, the researchers were able to locate dozens of Type Ia supernovae, which could then be closely observed with more conventional telescopes. On the basis of how bright each appeared, the teams were able to calculate the distance to dozens of galaxies situated billions of light-years away—thus accomplishing the first step in the task they’d set for themselves.

Much of observational astronomy relies on the very same considerations. Astronomers use telescopes to gather light from distant objects, and from the colors they find—the particular wavelengths of light they measure—they can identify the chemical composition of the sources. An early demonstration occurred during the solar eclipse of 1868, when the French astronomer Pierre Janssen and, independently, the English astronomer Joseph Norman Lockyer examined light from the outermost shell of the sun, peeking just beyond the moon’s rim, and found a mysterious bright emission with a wavelength that no one could reproduce in the laboratory using known substances. This led to the bold—and correct—suggestion that the light was emitted by a new, hitherto unknown element. The unknown substance was helium, which thus claims the singular distinction of being the only element discovered in the sun before it was found on earth. Such work established convincingly that, much as you can be uniquely identified by the pattern of lines making up your fingerprint, so an atomic species is uniquely identified by the pattern of wavelengths of the light it emits (and also absorbs).

Our cosmic destiny turns on the shape of this graph. With accelerated expansion, space will continue to spread indefinitely, dragging away distant galaxies ever farther and ever faster. A hundred billion years from now, any galaxies not now resident in our neighborhood (a gravitationally bound cluster of about a dozen galaxies called our “local group”) will exit our cosmic horizon and enter a realm permanently beyond our capacity to see. Unless future astronomers have records handed down to them from an earlier era, their cosmological theories will seek explanations for an island universe, with galaxies numbering no more than students in a backwoods school, floating in a static sea of darkness. We live in a privileged age. Insights the universe giveth, accelerated expansion will taketh away.

To many researchers, the discovery of a nonzero cosmological constant

is the single most surprising observational result to have emerged in their lifetimes.

So there is no fundamental reason why the earth is 93 million miles from the sun. A planet’s orbital distance from its host star is due to the vagaries of historical happenstance, the innumerable detailed features of the swirling gas cloud from which a particular solar system coalesced; it’s a contingent fact that’s unavailable for fundamental explanation. Indeed, these astrophysical processes have produced planets throughout the cosmos, orbiting their respective suns at a vast assortment of distances. We find ourselves on one such planet situated 93 million miles from our sun because that’s a planet on which our form of life could evolve. Failure to take account of this selection bias would lead one to search for a deeper answer. But that’s a fool’s errand.

Carter’s paper emphasized the importance of paying heed to such bias, an accounting he called the anthropic principle (an unfortunate name, because the idea would apply equally well to any form of intelligent life that makes and analyzes observations, not just to humans). No one took exception to this element of Carter’s argument. The controversial part was his suggestion that the anthropic principle might cast its net not just over things in the universe, like planetary distances, but over the universe itself.

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 10500 possibilities, because even if today’s fastest computers took a single second to analyze 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.

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.

The core physics relies on a process known as quantum tunneling. Imagine a particle, an electron for instance, encountering a solid barrier, say a slab of steel ten feet thick, that classical physics predicts it can’t penetrate. A hallmark of quantum mechanics is that the rigid classical 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 shine: 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 bump” separating its current value from the one it seeks, as in Figure 6.5? Coleman and De Luccia found that much as is the case for a single particle, a universe can do what classical physics forbids: it can jitter its way—it can quantum tunnel—through the barrier and reach the lower energy configuration.

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.

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 assuming 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, space 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.

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