but the theory’s mathematical insights continue to have an alluring pull
by Brian Greene
In October 1984 I arrived at Oxford University, trailing a large steamer trunk containing a couple of changes of clothing and about five dozen textbooks. I had a freshly minted bachelor’s degree in physics from Harvard, and I was raring to launch into graduate study. But within a couple of weeks, the more advanced students had sucked the wind from my sails. Change fields now while you still can, many said. There’s nothing happening in fundamental physics.
Then, just a couple of months later, the prestigious (if tamely titled) journal Physics Letters B published an article that ignited the first superstring revolution, a sweeping movement that inspired thousands of physicists worldwide to drop their research in progress and chase Einstein’s long-sought dream of a unified theory. The field was young, the terrain fertile and the atmosphere electric. The only thing I needed to drop was a neophyte’s inhibition to run with the world’s leading physicists. I did. What followed proved to be the most exciting intellectual odyssey of my life.
That was 30 years ago this month, making the moment ripe for taking stock: Is string theory revealing reality’s deep laws? Or, as some detractors have claimed, is it a mathematical mirage that has sidetracked a generation of physicists?
Unification has become synonymous with Einstein, but the enterprise has been at the heart of modern physics for centuries. Isaac Newton united the heavens and Earth, revealing that the same laws governing the motion of the planets and the Moon described the trajectory of a spinning wheel and a rolling rock. About 200 years later, James Clerk Maxwell took the unification baton for the next leg, showing that electricity and magnetism are two aspects of a single force described by a single mathematical formalism.
The next two steps, big ones at that, were indeed vintage Einstein. In 1905, Einstein linked space and time, showing that motion through one affects passage through the other, the hallmark of his special theory of relativity. Ten years later, Einstein extended these insights with his general theory of relativity, providing the most refined description of gravity, the force governing the likes of stars and galaxies. With these achievements, Einstein envisioned that a grand synthesis of all of nature’s forces was within reach.
But by 1930, the landscape of physics had thoroughly shifted. Niels Bohr and a generation of intrepid explorers ventured deep into the microrealm, where they encountered quantum mechanics, an enigmatic theory formulated with radically new physical concepts and mathematical rules. While spectacularly successful at predicting the behavior of atoms and subatomic particles, the quantum laws looked askance at Einstein’s formulation of gravity. This set the stage for more than a half-century of despair as physicists valiantly struggled, but repeatedly failed, to meld general relativity and quantum mechanics, the laws of the large and small, into a single all-encompassing description.
Such was the case until December 1984, when John Schwarz, of the California Institute of Technology, and Michael Green, then at Queen Mary College, published a once-in-a-generation paper showing that string theory could overcome the mathematical antagonism between general relativity and quantum mechanics, clearing a path that seemed destined to reach the unified theory.
The idea underlying string unification is as simple as it is seductive. Since the early 20th century, nature’s fundamental constituents have been modeled as indivisible particles—the most familiar being electrons, quarks and neutrinos—that can be pictured as infinitesimal dots devoid of internal machinery. String theory challenges this by proposing that at the heart of every particle is a tiny, vibrating string-like filament. And, according to the theory, the differences between one particle and another—their masses, electric charges and, more esoterically, their spin and nuclear properties—all arise from differences in how their internal strings vibrate.
Much as the sonorous tones of a cello arise from the vibrations of the instrument’s strings, the collection of nature’s particles would arise from the vibrations of the tiny filaments described by string theory. The long list of disparate particles that had been revealed over a century of experiments would be recast as harmonious “notes” comprising nature’s score.
Most gratifying, the mathematics revealed that one of these notes had properties precisely matching those of the “graviton,” a hypothetical particle that, according to quantum physics, should carry the force of gravity from one location to another. With this, the worldwide community of theoretical physicists looked up from their calculations. For the first time, gravity and quantum mechanics were playing by the same rules. At least in theory.
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I began learning the mathematical underpinnings of string theory durin
But the simplest and most important question loomed large. Is string theory right? Does the math explain our universe? The description I’ve given suggests an experimental strategy. Examine particles and if you see little vibrating strings, you’re done. It’s a fine idea in principle, but string theory’s pioneers realized it was useless in practice. The math set the size of strings to be about a million billion times smaller than even the minute realms probed by the world’s most powerful accelerators. Save for building a collider the size of the galaxy, strings, if they’re real, would elude brute force detection.
Making the situation seemingly more dire, researchers had come upon a remarkable but puzzling mathematical fact. String theory’s equations require that the universe has extra dimensions beyond the three of everyday experience—left/right, back/forth and up/down. Taking the math to heart, researchers realized that their backs were to the wall. Make sense of extra dimensions—a prediction that’s grossly at odds with what we perceive—or discard the theory.
String theorists pounced on an idea first developed in the early years of the 20th century. Back then, theorists realized that there might be two kinds of spatial dimensions: those that are large and extended, which we directly experience, and others that are tiny and tightly wound, too small for even our most refined equipment to reveal. Much as the spatial extent of an enormous carpet is manifest, but you have to get down on your hands and knees to see the circular loops making up its pile, the universe might have three big dimensions that we all navigate freely, but it might also have additional dimensions so minuscule that they’re beyond our observational reach.
In a paper submitted for publication a day after New Year’s 1985, a quartet of physicists—Philip Candelas, Gary Horowitz, Andrew Strominger and Edward Witten—pushed this proposal one step further, turning vice to virtue. Positing that the extra dimensions were minuscule, they argued, would not only explain why we haven’t seen them, but could also provide the missing bridge to experimental verification.
Strings are so small that when they vibrate they undulate not just in the three large dimensions, but also in the additional tiny ones. And much as the vibrational patterns of air streaming through a French horn are determined by the twists and turns of the instrument, the vibrational patterns of strings would be determined by the shape of the extra dimensions. Since these vibrational patterns determine particle properties like mass, electric charge and so on—properties that can be detected experimentally—the quartet had established that if you know the precise geometry of the extra dimensions, you can make predictions about the results that certain experiments would observe.
For me, deciphering the paper’s equations was one of those rare mathematical forays bordering on spiritual enlightenment. That the geometry of hidden spatial dimensions might be the universe’s Rosetta stone, embodying the secret code of nature’s fundamental constituents—well, it was one of the most beautiful ideas I’d ever encountered. It also played to my strength. As a mathematically oriented physics student, I’d already expended great effort studying topology and differential geometry, the very tools needed to analyze the mathematical form of extra-dimensional spaces.
And so, in the mid-1980s, with a small group of researchers at Oxford, we set our sights on extracting string theory’s predictions. The quartet’s paper had delineated the category of extra-dimensional spaces allowed by the mathematics of string theory and, remarkably, only a handful of candidate shapes were known. We selected one that seemed most promising, and embarked on grueling days and sleepless nights, filled with arduous calculations in higher dimensional geometry and fueled by grandiose thoughts of revealing nature’s deepest workings.
The final results that we found successfully incorporated various established features of particle physics and so were worthy of attention (and, for me, a doctoral dissertation), but were far from providing evidence for string theory. Naturally, our group and many others turned back to the list of allowed shapes to consider other possibilities. But the list was no longer short. Over the months and years, researchers had discovered ever larger collections of shapes that passed mathematical muster, driving the number of candidates into the thousands, millions, billions and then, with insights spearheaded in the mid-1990s by Joe Polchinski, into numbers so large that they’ve never been named.
Against this embarrassment of riches, string theory offered no directive regarding which shape to pick. And as each shape would affect string vibrations in different ways, each would yield different observable consequences. The dream of extracting unique predictions from string theory rapidly faded.
From a public relations standpoint, string theorists had not prepared for this development. Like the Olympic athlete who promises eight gold medals but wins “only” five, theorists had consistently set the bar as high as it could go. That string theory unites general relativity and quantum mechanics is a profound success. That it does so in a framework with the capacity to embrace the known particles and forces makes the success more than theoretically relevant. Seeking to go even further and uniquely explain the detailed properties of the particles and forces is surely a noble goal, but one that lies well beyond the line dividing success from failure.
Nevertheless, critics who had bristled at string theory’s meteoric rise to dominance used the opportunity to trumpet the theory’s demise, blurring researchers’ honest disappointment of not reaching hallowed ground with an unfounded assertion that the approach had crashed. The cacophony grew louder still with a controversial turn articulated most forcefully by one of the founding fathers of string theory, the Stanford University theoretical physicist Leonard Susskind.
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In August 2003, I was sitting with Susskind at a conference in Sigtuna, Sweden, discussing whether he really believed the new perspective he’d been expounding or was just trying to shake things up. “I do like to stir the pot,” he told me in hushed tones, feigning confidence, “but I do think this is what string theory’s been telling us.”
Susskind was arguing that if the mathematics does not identify one particular shape as the right one for the extra dimensions, perhaps there isn’t a single right shape. That is, maybe all of the shapes are right shapes in the sense that there are many universes, each with a different shape for the extra dimensions.
Our universe would then be just one of a vast collection, each with detailed features determined by the shape of their extra dimensions. Why, then, are we in this universe instead of any other? Because the shape of the hidden dimensions yields the spectrum of physical features that allow us to exist. In another universe, for example, the different shape might make the electron a little heavier or the nuclear force a little weaker, shifts that would cause the quantum processes that power stars, including our sun, to halt, interrupting the relentless march toward life on Earth.
Radical though this proposal may be, it was supported by parallel developments in cosmological thinking that suggested that the Big Bang may not have been a unique event, but was instead one of innumerable bangs spawning innumerable expanding universes, called the multiverse. Susskind was suggesting that string theory augments this grand cosmological unfolding by adorning each of the universes in the multiverse with a different shape for the extra dimensions.
With or without string theory, the multiverse is a highly controversial schema, and deservedly so. It not only recasts the landscape of reality, but shifts the scientific goal posts. Questions once deemed profoundly puzzling—why do nature’s numbers, from particle masses to force strengths to the energy suffusing space, have the particular values they do?—would be answered with a shrug. The detailed features we observe would no longer be universal truths; instead, they’d be local bylaws dictated by the particular shape of the extra dimensions in our corner of the multiverse.
Most physicists, string theorists among them, agree that the multiverse is an option of last resort. Yet, the history of science has also convinced us to not dismiss ideas merely because they run counter to expectation. If we had, our most successful theory, quantum mechanics, which describes a reality governed by wholly peculiar waves of probability, would be buried in the trash bin of physics. As Nobel laureate Steven Weinberg has said, the universe doesn’t care about what makes theoretical physicists happy.
Many researchers have pinned their hopes on finding a new class of so-called “supersymmetric” particles that emerge from string theory’s highly ordered mathematical equations. Other collider signals could show hints of extra-spatial dimensions, or even evidence of microscopic black holes, a possibility that arises from string theory’s exotic treatment of gravity on tiny distance scales.
While none of these predictions can properly be called a smoking gun—various non-stringy theories have incorporated them too—a positive identification would be on par with the discovery of the Higgs particle, and would, to put it mildly, set the world of physics on fire. The scales would tilt toward string theory.
But what happens in the event—likely, according to some—that the collider yields no remotely stringy signatures?
Experimental evidence is the final arbiter of right and wrong, but a theory’s value is also assessed by the depth of influence it has on allied fields. By this measure, string theory is off the charts. Decades of analysis filling thousands of articles have had a dramatic impact on a broad swath of research cutting across physics and mathematics. Take black holes, for example. String theory has resolved a vexing puzzle by identifying the microscopic carriers of their internal disorder, a feature discovered in the 1970s by Stephen Hawking.
Looking back, I’m gratified at how far we’ve come but disappointed that a connection to experiment continues to elude us. While my own research has migrated from highly mathematical forays into extra-dimensional arcana to more applied studies of string theory’s cosmological insights, I now hold only modest hope that the theory will confront data during my lifetime.
Even so, string theory’s pull remains strong. Its ability to seamlessly meld general relativity and quantum mechanics remains a primary achievement, but the allure goes deeper still. Within its majestic mathematical structure, a diligent researcher would find all of the best ideas physicists have carefully developed over the past few hundred years. It’s hard to believe such depth of insight is accidental.
I like to think that Einstein would look at string theory’s journey and smile, enjoying the theory’s remarkable geometrical features while feeling kinship with fellow travelers on the long and winding road toward unification. All the same, science is powerfully self-correcting. Should decades drift by without experimental support, I imagine that string theory will be absorbed by other areas of science and mathematics, and slowly shed a unique identity. In the interim, vigorous research and a large dose of patience are surely warranted. If experimental confirmation of string theory is in the offing, future generations will look back on our era as transformative, a time when science had the fortitude to nurture a remarkable and challenging theory, resulting in one of the most profound steps toward understanding reality.