String theory began over 50 years ago as a way to understand the strong nuclear force. Since then, it’s grown to become a theory of everything, capable of explaining the nature of every particle, every force, every fundamental constant, and the existence of the Universe itself. But despite decades of work, it has failed to deliver on its promise.
What went wrong, and where do we go from here?
Beginning threads
Like most revolutions, string theory had humble origins. It started in the 1960s as an attempt to understand the workings of the strong nuclear force, which had only recently been discovered. Quantum field theory, which had been used successfully to explain electromagnetism and the weak nuclear force, wasn’t cutting it, so physicists were eager for something new.
A group of physicists took a mathematical technique developed (and later abandoned) by quantum godfather Werner Heisenberg and expanded it. In that expansion, they found the first strings—mathematical structures that repeated themselves in spacetime. Unfortunately, this proto-string theory made incorrect predictions about the nature of the strong force and also had a variety of troublesome artifacts (like the existence of tachyons, particles that only traveled faster than light). Once another theory was developed to explain the strong force—the one we use today, based on quarks and gluons—string theory faded from the scene.
But again, like most revolutions, whispers remained through the years, keeping hopes alive. In the 1970s, physicists uncovered several remarkable properties of string theory. One, the theory could support more forces than just the strong nuclear force. The strings in string theory had enormous tension, forcing them to curl up on themselves into the smallest possible volume, something around the Planck scale. Once in place, the strings could support various vibrations, just like a taut guitar string. The different vibrations led to different manifestations of forces: one note for strong nuclear, another for electromagnetism, and so on.
One of the possible vibrations of the string acted like a massless spin-2 particle. This is a very special particle because that would be the quantum force carrier of the gravitational force, the holy grail of a quantized theory of gravity. The theorists at the time couldn’t believe their chalkboards: String theory naturally, elegantly included quantum gravity, and they weren’t even trying!
The second big deal to come out in the 1970s was the introduction of supersymmetry, which claimed that all the particles that carry forces (called bosons, a category that includes photons and gluons) were linked to a supersymmetric partner from the collection of particles that build stuff (called fermions, like electrons and quarks), and vice versa.
This symmetry doesn’t appear in everyday settings; it only manifests at extremely high energies. So if you were to go back in time to the earliest moments of the Big Bang or had enough funding to build a particle collider along the orbit of Jupiter, you wouldn’t just see the normal zoo of particles we’re familiar with; you'd see all their supersymmetric partners, too. These were given suitably stupid names, like selectrons, sneutrinos, squarks, photinos, and my personal (least) favorite, the wino boson.
By making this connection, string theory could build a bridge from the bosons to the fermions, allowing it to leap from just a theory of forces to a theory of every single particle in existence. The introduction of supersymmetry also solved the nasty problem of tachyons by replacing those troublesome particles with supersymmetric partners, which was a nice flourish.
At the end of the 1970s, string theory could potentially explain all the particles and all the interactions among them and provide a quantum solution to gravity.
One theory to rule them all, one theory to find them, one theory to bring them all, and in the stringiness bind them.
A string perturbed
It’s been almost half a century since physicists first realized that string theory could potentially provide a theory of everything. Despite decades of work involving hundreds of scientists over several (academic) generations and countless papers, conferences, and workshops, string theory hasn't quite lived up to that potential.
One of the biggest issues involves the way that strings interact with each other. A major pain in the asymptote when it comes to quantum theory is the infinite variety of ways that particles can interact. It’s easy enough to write down the fundamental governing equations that describe an interaction, but the math tends to blow up when we actually try to use it. In string theory, fundamental particles aren’t particles at all; they’re tiny loops of vibrating… well, strings. When we see two particles bouncing off each other, for example, it’s really two strings briefly merging and then separating. That sounds super cool, but there are still an infinite number of ways that process can unfold.
Unlike its quantum cousins, when it comes to string theory, we have no fundamental theory—we have only a set of approximation and perturbation methods. We’re not exactly sure if our approximations are good ones or if we’re way off the mark. We have perturbation techniques, but we’re not sure what we’re perturbing from. In other words, there’s no such thing as string theory, just approximations of what we hope string theory could be.
The second major difficulty involves the vibrations of the strings themselves. Early on, physicists realized that the strings had to vibrate in more than three dimensions of space if they were to explain the full variety of forces and particles in the Universe. 3D was just too limiting; it constricted the number of potential vibrations so severely that it was no longer a theory of everything, just a theory of some things, which isn’t nearly as exciting.
The earliest versions of string theory needed 26 spatial dimensions, but after supersymmetry and some dimensional layoffs, theorists were able to slim that number down to “only” 10.
Now, the Universe doesn’t have 10 spatial dimensions, at least on large scales, because we would have noticed them by now. So all the extra dimensions have to be tiny and curled up on themselves. When you wave your arm in front of you, you’re traversing these tiny dimensions countless times, but they’re so small (typically at the Planck scale) that you don’t notice them.
The extra dimensions give the strings enough vibrational options to explain all of physics. And the variety of shapes those dimensions can take as they curl up on themselves are known as Calabi-Yau manifolds. If you curl a piece of paper up on itself, you have a few choices: you can connect just one pair of edges (a cylinder) or both pairs (a delicious doughnut), you can introduce one flip (a Mobius strip) or two (a Klein bottle), and so on. That’s only two dimensions. With six, you have somewhere between 10500 and 1010,000 possible options.
We care about all these possible shapes because the way the extra spatial dimensions curl up determines the possible set of vibrations of the strings—each shape produces a different set of string vibrations, like different musical instruments. A tuba sounds different from a saxophone because of the way it’s structured and the kind of vibrations it can support. But our Universe is only a single instrument (an oboe, perhaps) with a single set of “notes” that correspond to our suite forces and particles.
So which one of the zillions of potential Calabi-Yau structures corresponds to our reality? We don’t know. Because we don’t have a full accounting of string theory, only approximations, we don’t know how the shape of the curled-up dimensions affects the string vibrations. We have no reliable machinery that goes from a given Calabi-Yau manifold to the physics that appears in that universe, so we can’t run the reverse operation and use our unique experience of physics to discover the shape of the curled-up dimensions.
Supersymmetry super-headaches
It gets worse. By the early 1990s, string theorists had developed not one, not two, but five different versions of string theory. The variations were based on how a fundamental string was treated. In some versions, all strings had to form closed loops; in others, they could be open. In some, the vibrations could only travel in one direction; in others, they could travel both, and so on. For the curious (and those eager for edgy names for your kids) the five string theories are Type 1, Type IIA, Type IIB, SO(32) heterotic, and E8xE8 heterotic.
So now we have a slight embarrassment of riches. Five potential theories, all claiming to be the best approximation of the true string theory. That’s pretty awkward, but in the 1990s, physicist Edward Witten declared a winner: all of them.
He discovered dualities, which are mathematical relationships between theories that allow you to transform one to the other. In this case, Witten tied the five string theories into a single knot. This idea has yet to be mathematically proven, but it indicates that the five string theories are really manifestations of a single, unified-for-real-this-time string theory, which Witten called M-theory. We don’t know what M-theory is—or even what the “M” stands for (my vote is “Manchego”)—but it should be the actual string theory.
That’s potentially very useful since once we determine whether our approximation schemes are valid, all the five versions of string theory should converge on it, and our Universe should pop out of the math.
But that was almost 30 years ago, and we still don’t know what M-theory is. We still haven’t figured out a solution for string theory.
To be clear, our inability to understand string theory isn’t limited by experiment. Even if we could build a super-duper-collider experiment that achieved the energies necessary to unlock quantum gravity, we still wouldn’t be able to test string theory because we have no string theory. We have no mathematical model that can make reliable predictions, only approximations that we hope accurately represent the true physics. We can test those approximations, I guess, but it won’t help us determine the inner workings of the true model.
Even so, the experiments we do have aren’t exactly helping. When supersymmetry was developed by the string theory community in the 1970s, it proved to be such a popular idea that many particle physicists took it as their own, using those techniques to develop models of high-energy physics beyond the Standard Model.
Supersymmetry isn’t a single theory; it's a family of theories. They all share the same core principle: that bosons and fermions are partners of each other at high enough energies. But the details of the interactions are left as a homework exercise for each individual theorist. Some supersymmetric theories are relatively (and that’s putting a lot of work on the word) straightforward, while others are more complex. Either way, in the 1990s, physicists became so convinced the supersymmetry was super-terrific that they devised a super-powerful collider to test it out: the Large Hadron Collider.
The beams of the LHC began their first test operations in 2008 with two main science goals in mind: finding the elusive Higgs boson and finding evidence of supersymmetry.
Four years later, the Higgs was found. Supersymmetry was not. It’s now 15 years later, and there are still no signs of supersymmetry.
In fact, all the “easy” versions of supersymmetry have been ruled out, and many of the more complicated ones, too. The dearth of evidence has slaughtered so many members of the supersymmetric family that the whole idea is on very shaky ground, with physicists beginning to have conferences with titles like “Beyond Supersymmetry” and “Oh My God, I Think I Wasted My Career.”
Where does that leave string theory? Well, since (and I’ll never stop reminding you of this) there is no string theory, only approximations, it’s not quite pining-for-the-fjords dead yet. It’s possible to build a version of string theory without using supersymmetry… maybe. The math gets even thornier and the approximations even sketchier, though. Without supersymmetry, string theory isn’t gone, but it’s certainly on life support.
Duality of the fates
After 50 years of work on a theory of everything, we’re left with approximate theories that seem so tantalizingly close to explaining all of physics… and yet always out of reach. Work continues on finding the underlying dualities that link the different versions of string theory, trying to suss out the mysterious M-theory that might underlie them all. Improvements to perturbation theory and approximation schemes provide some hope for making a breakthrough to link the dimensional structure of the extra dimensions to predictable physics. Routes around the damage caused by the LHC’s lack of evidence for supersymmetry continue to be laid.
In response to our inability to choose which Calabi-Yau manifold corresponds to our Universe—and more importantly, why our Universe has that manifold rather than any of the other ones—some string theorists appeal to what you might call the landscape. They argue that all possible configurations of compact dimensions are realized, each one with its own unique universe and set of physical laws, and we happen to live in this one because life would be impossible in most or all of the others. That’s not the strongest argument to come out of physics, but I’ll save a dissection of the idea for another day.
We don’t have a string theory, so we can’t test it. But it might be possible to perform experiments on string theory-adjacent ideas, and there’s been some progress on that front. Perhaps the event of inflation, which occurred immediately after the Big Bang, can teach us about string theory (or the formation of Universe-spanning cosmic strings). And perhaps there’s more to the dualities than we initially thought.
Recently, theorists have proposed another duality, the AdS/CFT correspondence. It’s not exactly string theory, but the idea is certainly sponsored by it. This correspondence proposes that you can write down a string theory in a special three-dimensional setting and connect it to a special kind of quantum theory on its two-dimensional boundary. In principle, the correspondence should allow you to transform your impossible-to-solve string theory problem into a merely really-difficult-to-solve quantum problem (or vice versa, allowing you to use some of the mathematical tools developed in string theory to solve your thorny quantum problem).
The AdS/CFT correspondence has found some limited applications, but its full utility remains unclear. And while the AdS/CFT correspondence has yet to be proven, theorists claim it should be possible soon (although they said the same thing about string theory itself during the Reagan administration).
Most string theorists of the modern era don’t work on string theory directly but instead mostly on the AdS/CFT correspondence and its implications, hoping that continuing to probe that mathematical relationship will unlock some hidden insight into the workings of a theory of everything.
I wish them luck.
