On 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.
I began learning the mathematical underpinnings of string theory during an intense period in the spring and summer of 1985. I wasn’t alone. Graduate students and seasoned faculty alike got swept up in the potential of string theory to be what some were calling the “final theory” or the “theory of everything.” In crowded seminar rooms and flyby corridor conversations, physicists anticipated the crowning of a new order.
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.
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