The Fabric of the Cosmos: Space, Time, and the Texture of Reality - Brian Greene (2004)
Part I. REALITY’S ARENA
Chapter 1. Roads to Reality
SPACE, TIME, AND WHY THINGS ARE AS THEY ARE
None of the books in my father’s dusty old bookcase were forbidden. Yet while I was growing up, I never saw anyone take one down. Most were massive tomes—a comprehensive history of civilization, matching volumes of the great works of western literature, numerous others I can no longer recall—that seemed almost fused to shelves that bowed slightly from decades of steadfast support. But way up on the highest shelf was a thin little text that, every now and then, would catch my eye because it seemed so out of place, like Gulliver among the Brobdingnagians. In hindsight, I’m not quite sure why I waited so long before taking a look. Perhaps, as the years went by, the books seemed less like material you read and more like family heirlooms you admire from afar. Ultimately, such reverence gave way to teenage brashness. I reached up for the little text, dusted it off, and opened to page one. The first few lines were, to say the least, startling.
“There is but one truly philosophical problem, and that is suicide,” the text began. I winced. “Whether or not the world has three dimensions or the mind nine or twelve categories,” it continued, “comes afterward”; such questions, the text explained, were part of the game humanity played, but they deserved attention only after the one true issue had been settled. The book was The Myth of Sisyphus and was written by the Algerian-born philosopher and Nobel laureate Albert Camus. After a moment, the iciness of his words melted under the light of comprehension. Yes, of course, I thought. You can ponder this or analyze that till the cows come home, but the real question is whether all your ponderings and analyses will convince you that life is worth living. That’s what it all comes down to. Everything else is detail.
My chance encounter with Camus’ book must have occurred during an especially impressionable phase because, more than anything else I’d read, his words stayed with me. Time and again I’d imagine how various people I’d met, or heard about, or had seen on television would answer this primary of all questions. In retrospect, though, it was his second assertion—regarding the role of scientific progress—that, for me, proved particularly challenging. Camus acknowledged value in understanding the structure of the universe, but as far as I could tell, he rejected the possibility that such understanding could make any difference to our assessment of life’s worth. Now, certainly, my teenage reading of existential philosophy was about as sophisticated as Bart Simpson’s reading of Romantic poetry, but even so, Camus’ conclusion struck me as off the mark. To this aspiring physicist, it seemed that an informed appraisal of life absolutely required a full understanding of life’s arena—the universe. I remember thinking that if our species dwelled in cavernous outcroppings buried deep underground and so had yet to discover the earth’s surface, brilliant sunlight, an ocean breeze, and the stars that lie beyond, or if evolution had proceeded along a different pathway and we had yet to acquire any but the sense of touch, so everything we knew came only from our tactile impressions of our immediate environment, or if human mental faculties stopped developing during early childhood so our emotional and analytical skills never progressed beyond those of a five-year-old—in short, if our experiences painted but a paltry portrait of reality—our appraisal of life would be thoroughly compromised. When we finally found our way to earth’s surface, or when we finally gained the ability to see, hear, smell, and taste, or when our minds were finally freed to develop as they ordinarily do, our collective view of life and the cosmos would, of necessity, change radically. Our previously compromised grasp of reality would have shed a very different light on that most fundamental of all philosophical questions.
But, you might ask, what of it? Surely, any sober assessment would conclude that although we might not understand everything about the universe—every aspect of how matter behaves or life functions—we are privy to the defining, broad-brush strokes gracing nature’s canvas. Surely, as Camus intimated, progress in physics, such as understanding the number of space dimensions; or progress in neuropsychology, such as understanding all the organizational structures in the brain; or, for that matter, progress in any number of other scientific undertakings may fill in important details, but their impact on our evaluation of life and reality would be minimal. Surely, reality is what we think it is; reality is revealed to us by our experiences.
To one extent or another, this view of reality is one many of us hold, if only implicitly. I certainly find myself thinking this way in day-to-day life; it’s easy to be seduced by the face nature reveals directly to our senses. Yet, in the decades since first encountering Camus’ text, I’ve learned that modern science tells a very different story. The overarching lesson that has emerged from scientific inquiry over the last century is that human experience is often a misleading guide to the true nature of reality. Lying just beneath the surface of the everyday is a world we’d hardly recognize. Followers of the occult, devotees of astrology, and those who hold to religious principles that speak to a reality beyond experience have, from widely varying perspectives, long since arrived at a similar conclusion. But that’s not what I have in mind. I’m referring to the work of ingenious innovators and tireless researchers—the men and women of science—who have peeled back layer after layer of the cosmic onion, enigma by enigma, and revealed a universe that is at once surprising, unfamiliar, exciting, elegant, and thoroughly unlike what anyone ever expected.
These developments are anything but details. Breakthroughs in physics have forced, and continue to force, dramatic revisions to our conception of the cosmos. I remain as convinced now as I did decades ago that Camus rightly chose life’s value as the ultimate question, but the insights of modern physics have persuaded me that assessing life through the lens of everyday experience is like gazing at a van Gogh through an empty Coke bottle. Modern science has spearheaded one assault after another on evidence gathered from our rudimentary perceptions, showing that they often yield a clouded conception of the world we inhabit. And so whereas Camus separated out physical questions and labeled them secondary, I’ve become convinced that they’re primary. For me, physical reality both sets the arena and provides the illumination for grappling with Camus’ question. Assessing existence while failing to embrace the insights of modern physics would be like wrestling in the dark with an unknown opponent. By deepening our understanding of the true nature of physical reality, we profoundly reconfigure our sense of ourselves and our experience of the universe.
The central concern of this book is to explain some of the most prominent and pivotal of these revisions to our picture of reality, with an intense focus on those that affect our species’ long-term project to understand space and time. From Aristotle to Einstein, from the astrolabe to the Hubble Space Telescope, from the pyramids to mountaintop observatories, space and time have framed thinking since thinking began. With the advent of the modern scientific age, their importance has only been heightened. Over the last three centuries, developments in physics have revealed space and time as the most baffling and most compelling concepts, and as those most instrumental in our scientific analysis of the universe. Such developments have also shown that space and time top the list of age-old scientific constructs that are being fantastically revised by cutting-edge research.
To Isaac Newton, space and time simply were—they formed an inert, universal cosmic stage on which the events of the universe played themselves out. To his contemporary and frequent rival Gottfried Wilhelm von Leibniz, “space” and “time” were merely the vocabulary of relations between where objects were and when events took place. Nothing more. But to Albert Einstein, space and time were the raw material underlying reality. Through his theories of relativity, Einstein jolted our thinking about space and time and revealed the principal part they play in the evolution of the universe. Ever since, space and time have been the sparkling jewels of physics. They are at once familiar and mystifying; fully understanding space and time has become physics’ most daunting challenge and sought-after prize.
The developments we’ll cover in this book interweave the fabric of space and time in various ways. Some ideas will challenge features of space and time so basic that for centuries, if not millennia, they’ve seemed beyond questioning. Others will seek the link between our theoretical understanding of space and time and the traits we commonly experience. Yet others will raise questions unfathomable within the limited confines of ordinary perceptions.
We will speak only minimally of philosophy (and not at all about suicide and the meaning of life). But in our scientific quest to solve the mysteries of space and time, we will be unrestrained. From the universe’s smallest speck and earliest moments to its farthest reaches and most distant future, we will examine space and time in environments familiar and far-flung, with an unflinching eye seeking their true nature. As the story of space and time has yet to be fully written, we won’t arrive at any final assessments. But we will encounter a series of developments—some intensely strange, some deeply satisfying, some experimentally verified, some thoroughly speculative—that will show how close we’ve come to wrapping our minds around the fabric of the cosmos and touching the true texture of reality.
Historians differ on exactly when the modern scientific age began, but certainly by the time Galileo Galilei, René Descartes, and Isaac Newton had had their say, it was briskly under way. In those days, the new scientific mind-set was being steadily forged, as patterns found in terrestrial and astronomical data made it increasingly clear that there is an order to all the comings and goings of the cosmos, an order accessible to careful reasoning and mathematical analysis. These early pioneers of modern scientific thought argued that, when looked at the right way, the happenings in the universe not only are explicable but predictable. The power of science to foretell aspects of the future—consistently and quantitatively—had been revealed.
Early scientific study focused on the kinds of things one might see or experience in everyday life. Galileo dropped weights from a leaning tower (or so legend has it) and watched balls rolling down inclined surfaces; Newton studied falling apples (or so legend has it) and the orbit of the moon. The goal of these investigations was to attune the nascent scientific ear to nature’s harmonies. To be sure, physical reality was the stuff of experience, but the challenge was to hear the rhyme and reason behind the rhythm and regularity. Many sung and unsung heroes contributed to the rapid and impressive progress that was made, but Newton stole the show. With a handful of mathematical equations, he synthesized everything known about motion on earth and in the heavens, and in so doing, composed the score for what has come to be known as classical physics.
In the decades following Newton’s work, his equations were developed into an elaborate mathematical structure that significantly extended both their reach and their practical utility. Classical physics gradually became a sophisticated and mature scientific discipline. But shining clearly through all these advances was the beacon of Newton’s original insights. Even today, more than three hundred years later, you can see Newton’s equations scrawled on introductory-physics chalkboards worldwide, printed on NASA flight plans computing spacecraft trajectories, and embedded within the complex calculations of forefront research. Newton brought a wealth of physical phenomena within a single theoretical framework.
But while formulating his laws of motion, Newton encountered a critical stumbling block, one that is of particular importance to our story (Chapter 2). Everyone knew that things could move, but what about the arena within which the motion took place? Well, that’s space, we’d all answer. But, Newton would reply, what is space? Is space a real physical entity or is it an abstract idea born of the human struggle to comprehend the cosmos? Newton realized that this key question had to be answered, because without taking a stand on the meaning of space and time, his equations describing motion would prove meaningless. Understanding requires context; insight must be anchored.
And so, with a few brief sentences in his Principia Mathematica, Newton articulated a conception of space and time, declaring them absolute and immutable entities that provided the universe with a rigid, unchangeable arena. According to Newton, space and time supplied an invisible scaffolding that gave the universe shape and structure.
Not everyone agreed. Some argued persuasively that it made little sense to ascribe existence to something you can’t feel, grasp, or affect. But the explanatory and predictive power of Newton’s equations quieted the critics. For the next two hundred years, his absolute conception of space and time was dogma.
The classical Newtonian worldview was pleasing. Not only did it describe natural phenomena with striking accuracy, but the details of the description—the mathematics—aligned tightly with experience. If you push something, it speeds up. The harder you throw a ball, the more impact it has when it smacks into a wall. If you press against something, you feel it pressing back against you. The more massive something is, the stronger its gravitational pull. These are among the most basic properties of the natural world, and when you learn Newton’s framework, you see them represented in his equations, clear as day. Unlike a crystal ball’s inscrutable hocus-pocus, the workings of Newton’s laws were on display for all with minimal mathematical training to take in fully. Classical physics provided a rigorous grounding for human intuition.
Newton had included the force of gravity in his equations, but it was not until the 1860s that the Scottish scientist James Clerk Maxwell extended the framework of classical physics to take account of electrical and magnetic forces. Maxwell needed additional equations to do so and the mathematics he employed required a higher level of training to grasp fully. But his new equations were every bit as successful at explaining electrical and magnetic phenomena as Newton’s were at describing motion. By the late 1800s, it was evident that the universe’s secrets were proving no match for the power of human intellectual might.
Indeed, with the successful incorporation of electricity and magnetism, there was a growing sense that theoretical physics would soon be complete. Physics, some suggested, was rapidly becoming a finished subject and its laws would shortly be chiseled in stone. In 1894, the renowned experimental physicist Albert Michelson remarked that “most of the grand underlying principles have been firmly established” and he quoted an “eminent scientist”—most believe it was the British physicist Lord Kelvin—as saying that all that remained were details of determining some numbers to a greater number of decimal places.1 In 1900, Kelvin himself did note that “two clouds” were hovering on the horizon, one to do with properties of light’s motion and the other with aspects of the radiation objects emit when heated,2 but there was a general feeling that these were mere details, which, no doubt, would soon be addressed.
Within a decade, everything changed. As anticipated, the two problems Kelvin had raised were promptly addressed, but they proved anything but minor. Each ignited a revolution, and each required a fundamental rewriting of nature’s laws. The classical conceptions of space, time, and reality—the ones that for hundreds of years had not only worked but also concisely expressed our intuitive sense of the world— were overthrown.
The relativity revolution, which addressed the first of Kelvin’s “clouds,” dates from 1905 and 1915, when Albert Einstein completed his special and general theories of relativity (Chapter 3). While struggling with puzzles involving electricity, magnetism, and light’s motion, Einstein realized that Newton’s conception of space and time, the corner-stone of classical physics, was flawed. Over the course of a few intense weeks in the spring of 1905, he determined that space and time are not independent and absolute, as Newton had thought, but are enmeshed and relative in a manner that flies in the face of common experience. Some ten years later, Einstein hammered a final nail in the Newtonian coffin by rewriting the laws of gravitational physics. This time, not only did Einstein show that space and time are part of a unified whole, he also showed that by warping and curving they participate in cosmic evolution. Far from being the rigid, unchanging structures envisioned by Newton, space and time in Einstein’s reworking are flexible and dynamic.
The two theories of relativity are among humankind’s most precious achievements, and with them Einstein toppled Newton’s conception of reality. Even though Newtonian physics seemed to capture mathematically much of what we experience physically, the reality it describes turns out not to be the reality of our world. Ours is a relativistic reality. Yet, because the deviation between classical and relativistic reality is manifest only under extreme conditions (such as extremes of speed and gravity), Newtonian physics still provides an approximation that proves extremely accurate and useful in many circumstances. But utility and reality are very different standards. As we will see, features of space and time that for many of us are second nature have turned out to be figments of a false Newtonian perspective.
The second anomaly to which Lord Kelvin referred led to the quantum revolution, one of the greatest upheavals to which modern human understanding has ever been subjected. By the time the fires subsided and the smoke cleared, the veneer of classical physics had been singed off the newly emerging framework of quantum reality.
A core feature of classical physics is that if you know the positions and velocities of all objects at a particular moment, Newton’s equations, together with their Maxwellian updating, can tell you their positions and velocities at any other moment, past or future. Without equivocation, classical physics declares that the past and future are etched into the present. This feature is also shared by both special and general relativity. Although the relativistic concepts of past and future are subtler than their familiar classical counterparts (Chapters 3 and 5), the equations of relativity, together with a complete assessment of the present, determine them just as completely.
By the 1930s, however, physicists were forced to introduce a whole new conceptual schema called quantum mechanics. Quite unexpectedly, they found that only quantum laws were capable of resolving a host of puzzles and explaining a variety of data newly acquired from the atomic and subatomic realm. But according to the quantum laws, even if you make the most perfect measurements possible of how things are today, the best you can ever hope to do is predict the probability that things will be one way or another at some chosen time in the future, or that things were one way or another at some chosen time in the past. The universe, according to quantum mechanics, is notetched into the present; the universe, according to quantum mechanics, participates in a game of chance.
Although there is still controversy over precisely how these developments should be interpreted, most physicists agree that probability is deeply woven into the fabric of quantum reality. Whereas human intuition, and its embodiment in classical physics, envision a reality in which things are always definitely one way or another, quantum mechanics describes a reality in which things sometimes hover in a haze of being partly one way and partly another. Things become definite only when a suitable observation forces them to relinquish quantum possibilities and settle on a specific outcome. The outcome that’s realized, though, cannot be predicted—we can predict only the odds that things will turn out one way or another.
This, plainly speaking, is weird. We are unused to a reality that remains ambiguous until perceived. But the oddity of quantum mechanics does not stop here. At least as astounding is a feature that goes back to a paper Einstein wrote in 1935 with two younger colleagues, Nathan Rosen and Boris Podolsky, that was intended as an attack on quantum theory.3 With the ensuing twists of scientific progress, Einstein’s paper can now be viewed as among the first to point out that quantum mechanics— if taken at face value—implies that something you do over here can be instantaneously linked to something happening over there, regardless of distance. Einstein considered such instantaneous connections ludicrous and interpreted their emergence from the mathematics of quantum theory as evidence that the theory was in need of much development before it would attain an acceptable form. But by the 1980s, when both theoretical and technological developments brought experimental scrutiny to bear on these purported quantum absurdities, researchers confirmed that there can be an instantaneous bond between what happens at widely separated locations. Under pristine laboratory conditions, what Einstein thought absurd really happens (Chapter 4).
The implications of these features of quantum mechanics for our picture of reality are a subject of ongoing research. Many scientists, myself included, view them as part of a radical quantum updating of the meaning and properties of space. Normally, spatial separation implies physical independence. If you want to control what’s happening on the other side of a football field, you have to go there, or, at the very least, you have to send someone or something (the assistant coach, bouncing air molecules conveying speech, a flash of light to get someone’s attention, etc.) across the field to convey your influence. If you don’t—if you remain spatially isolated—you will have no impact, since intervening space ensures the absence of a physical connection. Quantum mechanics challenges this view by revealing, at least in certain circumstances, a capacity to transcend space; long-range quantum connections can bypass spatial separation. Two objects can be far apart in space, but as far as quantum mechanics is concerned, it’s as if they’re a single entity. Moreover, because of the tight link between space and time found by Einstein, the quantum connections also have temporal tentacles. We’ll shortly encounter some clever and truly wondrous experiments that have recently explored a number of the startling spatio-temporal interconnections entailed by quantum mechanics and, as we’ll see, they forcefully challenge the classical, intuitive worldview many of us hold.
Despite these many impressive insights, there remains one very basic feature of time—that it seems to have a direction pointing from past to future—for which neither relativity nor quantum mechanics has provided an explanation. Instead, the only convincing progress has come from research in an area of physics called cosmology.
To open our eyes to the true nature of the universe has always been one of physics’ primary purposes. It’s hard to imagine a more mind-stretching experience than learning, as we have over the last century, that the reality we experience is but a glimmer of the reality that is. But physics also has the equally important charge of explaining the elements of reality that we actually do experience. From our rapid march through the history of physics, it might seem as if this has already been achieved, as if ordinary experience is addressed by pre–twentieth-century advances in physics. To some extent, this is true. But even when it comes to the everyday, we are far from a full understanding. And among the features of common experience that have resisted complete explanation is one that taps into one of the deepest unresolved mysteries in modern physics—the mystery that the great British physicist Sir Arthur Eddington called the arrow of time.4
We take for granted that there is a direction to the way things unfold in time. Eggs break, but they don’t unbreak; candles melt, but they don’t unmelt; memories are of the past, never of the future; people age, but they don’t unage. These asymmetries govern our lives; the distinction between forward and backward in time is a prevailing element of experiential reality. If forward and backward in time exhibited the same symmetry we witness between left and right, or back and forth, the world would be unrecognizable. Eggs would unbreak as often as they broke; candles would unmelt as often as they melted; we’d remember as much about the future as we do about the past; people would unage as often as they aged. Certainly, such a time-symmetric reality is not our reality. But where does time’s asymmetry come from? What is responsible for this most basic of all time’s properties?
It turns out that the known and accepted laws of physics show no such asymmetry (Chapter 6): each direction in time, forward and backward, is treated by the laws without distinction. And that’s the origin of a huge puzzle.Nothing in the equations of fundamental physics shows any sign of treating one direction in time differently from the other, and that is totally at odds with everything we experience.5
Surprisingly, even though we are focusing on a familiar feature of everyday life, the most convincing resolution of this mismatch between fundamental physics and basic experience requires us to contemplate the most unfamiliar of events—the beginning of the universe. This realization has its roots in the work of the great nineteenth-century physicist Ludwig Boltzmann, and in the years since has been elaborated on by many researchers, most notably the British mathematician Roger Penrose. As we will see, special physical conditions at the universe’s inception (a highly ordered environment at or just after the big bang) may have imprinted a direction on time, rather as winding up a clock, twisting its spring into a highly ordered initial state, allows it to tick forward. Thus, in a sense we’ll make precise, the breaking—as opposed to the unbreaking— of an egg bears witness to conditions at the birth of the universe some 14 billion years ago.
This unexpected link between everyday experience and the early universe provides insight into why events unfold one way in time and never the reverse, but it does not fully solve the mystery of time’s arrow. Instead, it shifts the puzzle to the realm of cosmology—the study of the origin and evolution of the entire cosmos—and compels us to find out whether the universe actually had the highly ordered beginning that this explanation of time’s arrow requires.
Cosmology is among the oldest subjects to captivate our species. And it’s no wonder. We’re storytellers, and what story could be more grand than the story of creation? Over the last few millennia, religious and philosophical traditions worldwide have weighed in with a wealth of versions of how everything—the universe—got started. Science, too, over its long history, has tried its hand at cosmology. But it was Einstein’s discovery of general relativity that marked the birth of modern scientific cosmology.
Shortly after Einstein published his theory of general relativity, both he and others applied it to the universe as a whole. Within a few decades, their research led to the tentative framework for what is now called the big bang theory, an approach that successfully explained many features of astronomical observations (Chapter 8). In the mid-1960s, evidence in support of big bang cosmology mounted further, as observations revealed a nearly uniform haze of microwave radiation permeating space—invisible to the naked eye but readily measured by microwave detectors—that was predicted by the theory. And certainly by the 1970s, after a decade of closer scrutiny and substantial progress in determining how basic ingredients in the cosmos respond to extreme changes in heat and temperature, the big bang theory secured its place as the leading cosmological theory (Chapter 9).
Its successes notwithstanding, the theory suffered significant shortcomings. It had trouble explaining why space has the overall shape revealed by detailed astronomical observations, and it offered no explanation for why the temperature of the microwave radiation, intently studied ever since its discovery, appears thoroughly uniform across the sky. Moreover, what is of primary concern to the story we’re telling, the big bang theory provided no compelling reason why the universe might have been highly ordered near the very beginning, as required by the explanation for time’s arrow.
These and other open issues inspired a major breakthrough in the late 1970s and early 1980s, known as inflationary cosmology (Chapter 10). Inflationary cosmology modifies the big bang theory by inserting an extremely brief burst of astoundingly rapid expansion during the universe’s earliest moments (in this approach, the size of the universe increased by a factor larger than a million trillion trillion in less than a millionth of a trillionth of a trillionth of a second). As will become clear, this stupendous growth of the young universe goes a long way toward filling in the gaps left by the big bang model—of explaining the shape of space and the uniformity of the microwave radiation, and also of suggesting why the early universe might have been highly ordered—thus providing significant progress toward explaining both astronomical observations and the arrow of time we all experience (Chapter 11).
Yet, despite these mounting successes, for two decades inflationary cosmology has been harboring its own embarrassing secret. Like the standard big bang theory it modified, inflationary cosmology rests on the equations Einstein discovered with his general theory of relativity. Although volumes of research articles attest to the power of Einstein’s equations to accurately describe large and massive objects, physicists have long known that an accurate theoretical analysis of small objects—such as the observable universe when it was a mere fraction of a second old— requires the use of quantum mechanics. The problem, though, is that when the equations of general relativity commingle with those of quantum mechanics, the result is disastrous. The equations break down entirely, and this prevents us from determining how the universe was born and whether at its birth it realized the conditions necessary to explain time’s arrow.
It’s not an overstatement to describe this situation as a theoretician’s nightmare: the absence of mathematical tools with which to analyze a vital realm that lies beyond experimental accessibility. And since space and time are so thoroughly entwined with this particular inaccessible realm—the origin of the universe—understanding space and time fully requires us to find equations that can cope with the extreme conditions of huge density, energy, and temperature characteristic of the universe’s earliest moments. This is an absolutely essential goal, and one that many physicists believe requires developing a so-called unified theory.
Over the past few centuries, physicists have sought to consolidate our understanding of the natural world by showing that diverse and apparently distinct phenomena are actually governed by a single set of physical laws. To Einstein, this goal of unification—of explaining the widest array of phenomena with the fewest physical principles—became a lifelong passion. With his two theories of relativity, Einstein united space, time, and gravity. But this success only encouraged him to think bigger. He dreamed of finding a single, all-encompassing framework capable of embracing all of nature’s laws; he called that framework a unified theory. Although now and then rumors spread that Einstein had found a unified theory, all such claims turned out to be baseless; Einstein’s dream went unfulfilled.
Einstein’s focus on a unified theory during the last thirty years of his life distanced him from mainstream physics. Many younger scientists viewed his single-minded search for the grandest of all theories as the ravings of a great man who, in his later years, had turned down the wrong path. But in the decades since Einstein’s passing, a growing number of physicists have taken up his unfinished quest. Today, developing a unified theory ranks among the most important problems in theoretical physics.
For many years, physicists found that the central obstacle to realizing a unified theory was the fundamental conflict between the two major breakthroughs of twentieth-century physics: general relativity and quantum mechanics. Although these two frameworks are typically applied in vastly different realms—general relativity to big things like stars and galaxies, quantum mechanics to small things like molecules and atoms—each theory claims to be universal, to work in all realms. However, as mentioned above, whenever the theories are used in conjunction, their combined equations produce nonsensical answers. For instance, when quantum mechanics is used with general relativity to calculate the probability that some process or other involving gravity will take place, the answer that’s often found is not something like a probability of 24 percent or 63 percent or 91 percent; instead, out of the combined mathematics pops an infinite probability. That doesn’t mean a probability so high that you should put all your money on it because it’s a shoo-in. Probabilities bigger than 100 percent are meaningless. Calculations that produce an infinite probability simply show that the combined equations of general relativity and quantum mechanics have gone haywire.
Scientists have been aware of the tension between general relativity and quantum mechanics for more than half a century, but for a long time relatively few felt compelled to search for a resolution. Instead, most researchers used general relativity solely for analyzing large and massive objects, while reserving quantum mechanics solely for analyzing small and light objects, carefully keeping each theory a safe distance from the other so their mutual hostility would be held in check. Over the years, this approach to détente has allowed for stunning advances in our understanding of each domain, but it does not yield a lasting peace.
A very few realms—extreme physical situations that are both massive and tiny—fall squarely in the demilitarized zone, requiring that general relativity and quantum mechanics simultaneously be brought to bear. The center of a black hole, in which an entire star has been crushed by its own weight to a minuscule point, and the big bang, in which the entire observable universe is imagined to have been compressed to a nugget far smaller than a single atom, provide the two most familiar examples. Without a successful union between general relativity and quantum mechanics, the end of collapsing stars and the origin of the universe would remain forever mysterious. Many scientists were willing to set aside these realms, or at least defer thinking about them until other, more tractable problems had been overcome.
But a few researchers couldn’t wait. A conflict in the known laws of physics means a failure to grasp a deep truth and that was enough to keep these scientists from resting easy. Those who plunged in, though, found the waters deep and the currents rough. For long stretches of time, research made little progress; things looked bleak. Even so, the tenacity of those who had the determination to stay the course and keep alive the dream of uniting general relativity and quantum mechanics is being rewarded. Scientists are now charging down paths blazed by those explorers and are closing in on a harmonious merger of the laws of the large and small. The approach that many agree is a leading contender is superstring theory (Chapter 12).
As we will see, superstring theory starts off by proposing a new answer to an old question: what are the smallest, indivisible constituents of matter? For many decades, the conventional answer has been that matter is composed of particles—electrons and quarks—that can be modeled as dots that are indivisible and that have no size and no internal structure. Conventional theory claims, and experiments confirm, that these particles combine in various ways to produce protons, neutrons, and the wide variety of atoms and molecules making up everything we’ve ever encountered. Superstring theory tells a different story. It does not deny the key role played by electrons, quarks, and the other particle species revealed by experiment, but it does claim that these particles are not dots. Instead, according to superstring theory, every particle is composed of a tiny filament of energy, some hundred billion billion times smaller than a single atomic nucleus (much smaller than we can currently probe), which is shaped like a little string. And just as a violin string can vibrate in different patterns, each of which produces a different musical tone, the filaments of superstring theory can also vibrate in different patterns. These vibrations, though, don’t produce different musical notes; remarkably, the theory claims that they produce different particle properties. A tiny string vibrating in one pattern would have the mass and the electric charge of an electron; according to the theory, such a vibrating string would be what we have traditionally called an electron. A tiny string vibrating in a different pattern would have the requisite properties to identify it as a quark, a neutrino, or any other kind of particle. All species of particles are unified in superstring theory since each arises from a different vibrational pattern executed by the same underlying entity.
Going from dots to strings-so-small-they-look-like-dots might not seem like a terribly significant change in perspective. But it is. From such humble beginnings, superstring theory combines general relativity and quantum mechanics into a single, consistent theory, banishing the perniciously infinite probabilities afflicting previously attempted unions. And as if that weren’t enough, superstring theory has revealed the breadth necessary to stitch all of nature’s forces and all of matter into the same theoretical tapestry. In short, superstring theory is a prime candidate for Einstein’s unified theory.
These are grand claims and, if correct, represent a monumental step forward. But the most stunning feature of superstring theory, one that I have little doubt would have set Einstein’s heart aflutter, is its profound impact on our understanding of the fabric of the cosmos. As we will see, superstring theory’s proposed fusion of general relativity and quantum mechanics is mathematically sensible only if we subject our conception of spacetime to yet another upheaval. Instead of the three spatial dimensions and one time dimension of common experience, superstring theory requires nine spatial dimensions and one time dimension. And, in a more robust incarnation of superstring theory known as M-theory, unification requires ten space dimensions and one time dimension—a cosmic substrate composed of a total of eleven spacetime dimensions. As we don’t see these extra dimensions, superstring theory is telling us that we’ve so far glimpsed but a meager slice of reality.
Of course, the lack of observational evidence for extra dimensions might also mean they don’t exist and that superstring theory is wrong. However, drawing that conclusion would be extremely hasty. Even decades before superstring theory’s discovery, visionary scientists, including Einstein, pondered the idea of spatial dimensions beyond the ones we see, and suggested possibilities for where they might be hiding. String theorists have substantially refined these ideas and have found that extra dimensions might be so tightly crumpled that they’re too small for us or any of our existing equipment to see (Chapter 12), or they might be large but invisible to the ways we probe the universe (Chapter 13). Either scenario comes with profound implications. Through their impact on string vibrations, the geometrical shapes of tiny crumpled dimensions might hold answers to some of the most basic questions, like why our universe has stars and planets. And the room provided by large extra space dimensions might allow for something even more remarkable: other, nearby worlds—not nearby in ordinary space, but nearby in the extra dimensions—of which we’ve so far been completely unaware.
Although a bold idea, the existence of extra dimensions is not just theoretical pie in the sky. It may shortly be testable. If they exist, extra dimensions may lead to spectacular results with the next generation of atom smashers, like the first human synthesis of a microscopic black hole, or the production of a huge variety of new, never before discovered species of particles (Chapter 13). These and other exotic results may provide the first evidence for dimensions beyond those directly visible, taking us one step closer to establishing superstring theory as the long-sought unified theory.
If superstring theory is proven correct, we will be forced to accept that the reality we have known is but a delicate chiffon draped over a thick and richly textured cosmic fabric. Camus’ declaration notwithstanding, determining the number of space dimensions—and, in particular, finding that there aren’t just three—would provide far more than a scientifically interesting but ultimately inconsequential detail. The discovery of extra dimensions would show that the entirety of human experience had left us completely unaware of a basic and essential aspect of the universe. It would forcefully argue that even those features of the cosmos that we have thought to be readily accessible to human senses need not be.
Past and Future Reality
With the development of superstring theory, researchers are optimistic that we finally have a framework that will not break down under any conditions, no matter how extreme, allowing us one day to peer back with our equations and learn what things were like at the very moment when the universe as we know it got started. To date, no one has gained sufficient dexterity with the theory to apply it unequivocally to the big bang, but understanding cosmology according to superstring theory has become one of the highest priorities of current research. Over the past few years, vigorous worldwide research programs in superstring cosmology have yielded novel cosmological frameworks (Chapter 13), suggested new ways to test superstring theory using astrophysical observations (Chapter 14), and provided some of the first insights into the role the theory may play in explaining time’s arrow.
The arrow of time, through the defining role it plays in everyday life and its intimate link with the origin of the universe, lies at a singular threshold between the reality we experience and the more refined reality cutting-edge science seeks to uncover. As such, the question of time’s arrow provides a common thread that runs through many of the developments we’ll discuss, and it will surface repeatedly in the chapters that follow. This is fitting. Of the many factors that shape the lives we lead, time is among the most dominant. As we continue to gain facility with superstring theory and its extension, M-theory, our cosmological insights will deepen, bringing both time’s origin and its arrow into ever-sharper focus. If we let our imaginations run wild, we can even envision that the depth of our understanding will one day allow us to navigate spacetime and hence explore realms that, to this point in our experience, remain well beyond our ability to access (Chapter 15).
Of course, it is extremely unlikely that we will ever achieve such power. But even if we never gain the ability to control space and time, deep understanding yields its own empowerment. Our grasp of the true nature of space and time would be a testament to the capacity of the human intellect. We would finally come to know space and time—the silent, ever-present markers delineating the outermost boundaries of human experience.
Coming of Age in Space and Time
When I turned the last page of The Myth of Sisyphus many years ago, I was surprised by the text’s having achieved an overarching feeling of optimism. After all, a man condemned to pushing a rock up a hill with full knowledge that it will roll back down, requiring him to start pushing anew, is not the sort of story that you’d expect to have a happy ending. Yet Camus found much hope in the ability of Sisyphus to exert free will, to press on against insurmountable obstacles, and to assert his choice to survive even when condemned to an absurd task within an indifferent universe. By relinquishing everything beyond immediate experience, and ceasing to search for any kind of deeper understanding or deeper meaning, Sisyphus, Camus argued, triumphs.
I was struck by Camus’ ability to discern hope where most others would see only despair. But as a teenager, and only more so in the decades since, I found that I couldn’t embrace Camus’ assertion that a deeper understanding of the universe would fail to make life more rich or worthwhile. Whereas Sisyphus was Camus’ hero, the greatest of scientists— Newton, Einstein, Niels Bohr, and Richard Feynman—became mine. And when I read Feynman’s description of a rose—in which he explained how he could experience the fragrance and beauty of the flower as fully as anyone, but how his knowledge of physics enriched the experience enormously because he could also take in the wonder and magnificence of the underlying molecular, atomic, and subatomic processes—I was hooked for good. I wanted what Feynman described: to assess life and to experience the universe on all possible levels, not just those that happened to be accessible to our frail human senses. The search for the deepest understanding of the cosmos became my lifeblood.
As a professional physicist, I have long since realized that there was much naïveté in my high school infatuation with physics. Physicists generally do not spend their working days contemplating flowers in a state of cosmic awe. Instead, we devote much of our time to grappling with complex mathematical equations scrawled across well-scored chalkboards. Progress can be slow. Promising ideas, more often than not, lead nowhere. That’s the nature of scientific research. Yet, even during periods of minimal progress, I’ve found that the effort spent puzzling and calculating has only made me feel a closer connection to the cosmos. I’ve found that you can come to know the universe not only by resolving its mysteries, but also by immersing yourself within them. Answers are great. Answers confirmed by experiment are greater still. But even answers that are ultimately proven wrong represent the result of a deep engagement with the cosmos—an engagement that sheds intense illumination on the questions, and hence on the universe itself. Even when the rock associated with a particular scientific exploration happens to roll back to square one, we nevertheless learn something and our experience of the cosmos is enriched.
Of course, the history of science reveals that the rock of our collective scientific inquiry—with contributions from innumerable scientists across the continents and through the centuries—does not roll down the mountain. Unlike Sisyphus, we don’t begin from scratch. Each generation takes over from the previous, pays homage to its predecessors’ hard work, insight, and creativity, and pushes up a little further. New theories and more refined measurements are the mark of scientific progress, and such progress builds on what came before, almost never wiping the slate clean. Because this is the case, our task is far from absurd or pointless. In pushing the rock up the mountain, we undertake the most exquisite and noble of tasks: to unveil this place we call home, to revel in the wonders we discover, and to hand off our knowledge to those who follow.
For a species that, by cosmic time scales, has only just learned to walk upright, the challenges are staggering. Yet, over the last three hundred years, as we’ve progressed from classical to relativistic and then to quantum reality, and have now moved on to explorations of unified reality, our minds and instruments have swept across the grand expanse of space and time, bringing us closer than ever to a world that has proved a deft master of disguise. And as we’ve continued to slowly unmask the cosmos, we’ve gained the intimacy that comes only from closing in on the clarity of truth. The explorations have far to go, but to many it feels as though our species is finally reaching childhood’s end.
To be sure, our coming of age here on the outskirts of the Milky Way6 has been a long time in the making. In one way or another, we’ve been exploring our world and contemplating the cosmos for thousands of years. But for most of that time we made only brief forays into the unknown, each time returning home somewhat wiser but largely unchanged. It took the brashness of a Newton to plant the flag of modern scientific inquiry and never turn back. We’ve been heading higher ever since. And all our travels began with a simple question.
What is space?