What are the Strings in String Theory? - Script (Patreon)

You may have heard the usual pop-sci description of string theory. There are these tiny vibrating strings … and that’s where all particles and forces come from. Including gravity.

This raises many more questions than it answers. Why strings? What are they made of?

How did physicists even come up with this bizarre idea?  And what’s all this nonsense of extra dimensions?

In physics we like to reduce down our description of the mechanics of reality to the simplest possible form. We expect the most fundamental machinery to have the fewest possible moving parts – or free parameters. This is why the standard model of particle physics is considered incomplete. Its equations predict many things with stunning accuracy, but they first require us to tune many mathematical knobs and dials. We need to use physical measurement to fix 19 free parameters like the masses of particles.  And then there’s gravity, which doesn’t fit into the standard model at all. So surely there exists a deeper set of cogs and wheels – a theory that brings all observable phenomena into the same mechanical framework. That would be a theory of everything, and this is the great hope of string theory.

In following episodes we’re going to explore the gory details of string theory, but today is string theory 101. Where did this crazy idea come from? I mean, why tiny vibrating strings versus literally any other tiny vibrating anything? What exactly are the strings of string theory?

OK, first let’s do a quick primer on the origins of string theory. The idea started in the 60s with efforts to understand the behavior of hadrons – collections of quarks bound by the the gluons of the strong nuclear force. That includes protons and neutrons, as well as mesons, which are combinations of a quark and an antiquark. Peculiarities in the interactions between pairs of mesons, as well as an odd relationship between their angular momenta and masses – suggested that the quarks in mesons are connected by – you guessed it – strings. In this case the strings are stretched-out tubes of strong nuclear force - vibrating elastic bands made of gluons. A lot of work went into figuring out a quantum theory for the strong interaction based on the physics of strings. The theory had some success, but kind of got stuck and was ultimately replaced by quantum chromodynamics.

One of the reasons this strong force version of string theory got stuck is that it predicted the existence of unexpected and unwanted vibrational modes in the gluon field of these strings. What’s a vibrational mode in a quantum field? A particle. And one of those modes appeared to be a massless, spin-2 particle. But the only hypothetical massless spin-2 particle is the graviton – the conjectured quantum particle of the gravitational field. If the gravitational field is made up of quantum particles. Which it might be. We really don’t know. But if it is, then the quanta of gravity should have an uncanny resemblance to the type of particle predicted by this little investigation into hadronic strings. Except that there’s no way anything like the graviton should appear in that sort of string.

This realization came in the early 70s. A bold new proposal emerged: forget mesons; what if the math of this theory could be used in a theory of quantum gravity? In fact, what if ALL force-carrying particles result from oscillations in tiny strings? All we needed to do was make the strings a bit smaller. Like, 20 orders of magnitude smaller, shrinking from the size of a proton to the Planck scale. Roughly the scale difference between the Milky Way galaxy and your living room. Oh, and we needed to add 22 dimensions to the familiar 4. No biggie. This was so-called bosonic string theory. If it worked would be a candidate for a grand unified theory – combining all known forces.

But why stop there? If wiggly strings can explain force-carrying bosons, why not the fermions that comprise matter? Though the 70s and 80s several proposals introduced the idea of supersymmetry to bring fermions and bosons into the same framework. The resulting superstring theory sought to become an all-encompassing mechanism to explain the underlying workings of our entire reality – a theory of everything. As an added bonus, this ambition also shaved off a bunch of dimensions – only 10 were needed once fermions where added! Then in 1995, Ed Witten brought the many forms of superstring theory together into the single framework of M-theory. All for the low price of adding one more spatial dimension, for an 11-dimensional theory.

OK, enough with the history lesson. Let’s talk strings. So, wiggly strings could explain the whole universe. That’s a hell of a claim. To understand quantum strings first we need to look at regular strings. They’re cooler than you think. The key is that strings can carry waves, and if the string has ends or is tied in a loop then a wave will end up overlapping with itself. In that case you can get a standing wave. Roughly speaking, when these traveling waves overlap each other they can end stack up or cancel out – constructive or destructive interference. Constructive interference only happens if the wavelength of the wave fits a neat number of times along the length of the string. Then the phases of the overlapping waves match in the right way, and that wavelength-slash-frequency of wave is enhanced. All others frequencies tend to die out.

The result is that, for a given string, only certain frequencies, corresponding to certain energies are possible. These resonant frequencies depend on the length of the string. Also its tension, which defines wave velocity, and so relates frequency to wavelength. For example, this leads to the specific frequencies of vibration of a guitar string. But this sort of behavior, where only specific, discrete energy modes are allowed, also sounds very quantum-like. String theorists weren’t the first to notice this. Neils Bohr came up with the first quantum model for electron orbits by thinking of them as ring-like standing waves around the hydrogen atom. But quantum strings are much more ambitious than “Bohr-ing” electron orbits.

The hope is that, tweaked just right, those discrete vibrational modes can be made to match the properties of known particles. Particle mass just comes from the length of the string and its tension. Tension is, after all, just energy per unit length. String length defines mass, but also defines which complex vibrational modes are possible. And those modes in turn define particle properties, like electric charge and spin. So this is the great promise of string theory – by defining a single parameter, string tension – or, equivalently, string length scale, all of the possible particles should be automatically defined. Compare that 1 parameter to the 19 free parameters of the standard model. It sure sounds closer to a fundamental theory.

OK, recap: we have these Planck-scale, 1-dimensional structures that can be in loops or extended. They have vibrational modes that define particle properties. By the way, those vibrations – the standing waves – aren’t some abstract internal wave. The strings are real, physical strands and the waves are wiggles in actual space. But physical strands of what? Common answers include pure mass-energy; fundamental, irreducible existence; topological irregularities in the fabric of reality; or the most common answer – it’s a meaningless question, a material also known as “shut-up-and-calculate-onium”.

Most string theorists are more interested in what strings do, not what they’re made of. So what to they do? Well, vibrate obviously. They can hold energy, they can stretch, and also merge with each other and split apart. These last properties are important because it gives a mechanism for the particles of string theory to interact and to decay into other particles.

The picture of strings coming together, joining, and splitting apart again is a huge strength of the theory. It solves one of the main problems with quantizing gravity. Maybe you remember from our episode on quantum gravity; if you try to describe gravitational interactions on the smallest scales, the energies required to interact at that scale produce black holes. There’s no way to even think about the shape of the gravitational field at the Planck scale that doesn’t produce a hopeless conflict. String theory fixes this because the graviton is a loop, not a point particle. Its interactions are smeared around that string, handily avoiding the explosion of mathematical infinities you get below the Planck length.

All of this stuff sounds great, and just doesn’t work with any other geometrical structure other than a 1-D string. So vibrating guitar strings yes, drum skins no. Unfortunately it’s not going to be this easy. Yeah the strings themselves are 1-D, but to even start to produce the properties of known particles, they need to vibrate in more than just 3 dimensions of space. In fact the theory only works in precisely 9 spatial dimensions – plus one for time. Plus one for M-theory – don’t worry about that for now. We’ll to the details in another episode, but in short: without exactly this number of dimensions you don’t get gravitons or any other massless particle. This is awkward to say the least. It’s a theory that works in a universe that is clearly not our own, with its measly 3 dimensions of space.

But this sort of thing doesn’t deter string theorists. There’s a way to add extra spatial dimensions that is still consistent with our perceived 3-D universe. To get our heads around this, imagine we lived in a 2-D flatland universe. We only perceive the giant x and y directions. But what if flatland isn’t truly flat? What if the z direction has a tiny, tiny width. This is a Pac Man dimension. Travel the tiny width of this dimension and you’d find yourself back where you started. Very tiny objects like quantum strings could explore that extra dimension, and, importantly, oscillate in it. But we giant, lumbering flatlanders would have no clue it existed. OK, now scale this up. 3 large dimensions of space and 6 tiny, Pac Man dimensions that only strings experience. Voila, string theory is saved.

Modern M-theory proposes an additional large spatial dimension. Our universe of 3-D space and 1-D time is like a flatland on this 5-D object called a 5-brane. M-theory unites different string theories because it demonstrates some philosophically fascinating dualities between different ways of thinking about the dimensions. Ultimately, it also leads to the ultimate duality that is the holographic principle. Patience, grasshoppers. We’ll get there.

The exact behavior of strings depends on the shape of the compact dimensions. In fact the single free parameter in string theory becomes the configuration of the extra dimensions. Find the right location in this string landscape and you perfectly describe the universe. The only issue is that there are an estimated 10^500 possible choices, and almost no way to figure out which one is ours.

Right now string theory appears to be at an impasse. It has produced no confirmed predictions. Some would say it’s made no testable predictions. Tuning the string landscape to match our universe is daunting and perhaps impossible. Yet despite this impasse, its promise and its elegance has convinced many that it must be right – or at least the right path. In upcoming episodes we’ll look deeper into both the successes, the failures, and the profound weirdnesses of string theory. Then you can decide for yourself whether you accept the fundamentally stringy nature of space time.