WHEN was an undergraduate in the early 2000s, he avoided popular science accounts of string theory because he wanted to engage with it on a technical level, without preconceptions. It was a few years after the “second string theory revolution”, when theoretical physicists felt they might be about to crack open the deepest workings of reality, perhaps even deliver a theory of everything. As he explored the maths, Conlon was captivated.
String theory famously suggests that everything is made up of one-dimensional strings (see “String theory: A primer”, below), and also predicts a huge array of possible universes – some 10500, for those taking notes. Whatever you think about that, it is fair to say that string theory hasn’t generated the testable predictions that many were hoping for. Today, it has a reputation for being untestable, maybe even unscientific. One arch string theory critic dubbed it “not even wrong”.
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But for Conlon, now a physicist at the University of Oxford, the thrill never faded. String theory remains a potential route to uniting the incompatible ways we think about gravity and the quantum world, he argues, to create a unified theory of quantum gravity. He also claims that his field has been unfairly maligned, and that its detractors are applying double standards. He even insists that string theory does make predictions that we could conceivably probe with upcoming astronomical observations.
Here, Conlon tells żěè¶ĚĘÓƵ about the enduring joys of string theory, why it is too early to write it off, and why we might need to revise our conception of what makes a useful scientific idea.
Thomas Lewton: Why do you find string theory so compelling?
Joseph Conlon: When you start studying it, you realise it is an extremely rich set of ideas and the theory seems to know automatically about many of the incredible structures found in nature. As you construct the theory, you have to try hard to keep it consistent, in other words, to have no internal mathematical contradictions. You find that it keeps on almost failing – you’re forced to do things a certain way to avoid those contradictions – but, by a whisker, things work out. It is a Goldilocks calculation. There’s a phrase people use to describe this feeling: they call it “string magic”.
So, you have been forced towards a theory with a very particular structure. But then you find that the mathematics contains excitations that look very similar to the classes of particles that you find in the standard model of particle physics: “chiral fermions” that are analogous to the electron, or “vector bosons” that are analogous to W and Z bosons of the standard model, and so on. It’s like you squeezed through some narrow tunnel and then this enormous cavern opens up that is filled with diamonds.
That sounds very exciting! Where, then, has the idea come from that string theorists have taken a wrong turn?
It comes from a human desire to tell certain kinds of stories that have heroes and villains and an ending within quite short timescales. But it isn’t reasonable to expect a definitive answer to observational questions on quantum gravity any time soon. The energy scales where theories of quantum gravity, like string theory, are guaranteed to matter are much greater than those which we can access using current technology, such as CERN’s Large Hadron Collider. This means it’s very hard to say: “Yes, string theory is definitely right, or no, it is definitely wrong.”
There’s a lot of bad PR around the testing of string theory. There was no possible way to tell that atoms existed for most of human history – that didn’t mean that the idea of atoms was wrong. Theoretical physics is hard and things can take a long time.
One criticism levelled at string theory is that it describes every universe except our own. The space-time of our universe has a slight positive curvature, but string theory only describes universes with negative curvature. Isn’t this quite a problem?
The small, positive curvature of our universe comes about because of the small, positive energy contained in the vacuum of space. This is what is commonly known as dark energy. And, look, dark energy is the biggest open problem in physics. Attempts at theoretical calculations of this “vacuum energy” encounter quantum corrections, created by particles popping in and out of existence in the vacuum, that are vastly larger than the observed value. So, indeed, string theory does not get this right, but, currently, there are no good solutions to this problem outside of string theory either.
However, string theory has given strikingly precise and surprising descriptions of quantum gravity in spaces with negative vacuum energy. This happens through what is called the AdS/CFT correspondence. One insight that has emerged from this is that quantum gravity theory in, say, five dimensions can be identical to non-gravitational quantum theories in four dimensions. While negative vacuum energy is not something we see in our universe, to me, the depth of these results gives confidence in the underlying robustness of the theory.
What about the idea that string theory contains a near-infinite number of possible solutions and so is, again, detached from reality?
There are also an infinite number of solutions in general relativity and an infinite number of quantum field theories. The number of solutions is not a problem in itself, so long as the solutions that apply to our universe can be homed in on by comparing them to the world around us. The difficult thing with string theory – and other approaches to quantum gravity – is how to constrain potential solutions with observations. It is hard to make discriminating measurements, as the places where the theory becomes most relevant are at such incredibly high energies.
So how can we test string theory?
There are . For instance, there are things which would be wonderful if true, which are probably not true, but which you could get lucky on. Let me give you an example: cosmic strings are these hypothetical, extremely long threads of pure energy that travel close to the speed of light. One outside possibility is that these cosmic strings are really fundamental string theory strings. They could potentially be observed, because they would have the effect of warping space-time and deforming light coming to us from distant galaxies, so that we would see a kind of double image.
That sounds like a long shot…
There’s something else too. String theory is a 10-dimensional theory, which means, if it is true, there really are extra spatial dimensions compared to the three we know of. But if we can’t see them, where are they? An analogy that I find useful here is if you imagine trying to knit wearing boxing gloves. You can’t knit because the scale you’re trying to do stuff on is far smaller than what you’re sensitive to while wearing those huge gloves. But that doesn’t mean knitting is impossible.
What this means is that string theory’s extra dimensions must be what we call “compactified”, in other words, screwed up so small that we can’t detect them. Here’s where we get to the core of the matter. When you do this mathematically, you find that a legacy is the existence of particles called moduli, which have properties that are characteristic of the size and shape of the extra dimensions. Moduli are particularly interesting in the context of cosmology because they live a very long time and so tend to hang around, and so potentially can give observable signatures.
Are you saying we could search for moduli?
Yes, they are an example of something we could, in principle and with some luck, find. It seems that moduli would have been produced in the very first fraction of a second after the big bang, and because they only interact through gravity, they would have survived in larger numbers for a short while compared to other kinds of particles. For a fraction of a second, the energy of the universe would primarily be in the form of moduli, which are characteristically stringy in origin. This is one area where we can have a conversation about stringy ideas of the early universe and how they relate to observations.
Can we see back far enough in time to look for these telltale particles?
Not yet, but there is hope. The context here is that we know very little about what the universe was like immediately after the big bang up until the point when the first nuclei were made, not even how much of the universe was composed of matter and how much was radiation. However, string models of cosmology strongly suggest something different at this time compared to standard cosmology, as the two frameworks predict different “equations of state”. With my colleagues, I recently published a paper where we would be.
In principle, gravitational waves offer a chance of mapping this period. They pass through everything and so can emanate from a sliver of a fraction of a second after the big bang. These very ancient beasts are called primordial gravitational waves and they are one explanation for the recently discovered background hum of gravitational waves. The way in which the size of this background changes according to the length of gravitational waves observed can tell you about what the equation of state of the universe is. With future observations, we might be able to look at the gravitational wave spectrum and tell if there was a long, matter-dominated spectrum early in the universe which then transitioned into radiation. Technology for detecting gravitational waves is rapidly advancing: for example, the recent observations using pulsar timing arrays by the North American Nanohertz Observatory for Gravitational Waves.
If you saw this signature, would it be solid proof of string theory?
All you could strictly say is that you have domination by matter particles that behave like moduli. That doesn’t tell you, for certain, that these particles are originating in extra-dimensional string compactification. I prefer to think of it as string theory motivating certain scenarios which can be tested in the way that you do ordinary science. But even if moduli particles are found to exist, that wouldn’t establish string theory as the one true theory of the universe.
By the way, the same is true of another type of particle that often arises in string theory called the axion. Even if we established that multiple kinds of axions exist, that would not prove string theory is true.
What if you had many different kinds of observations – cosmic strings, moduli, axions – all pointing towards string theory from different directions?
If it starts going “quack, quack, quack”, and it walks on land, and it floats in water, then you start to think, well, it might be a duck.
Is there anything that would make you give up on string theory?
Not while it remains a wonderful motivator of ideas which you might not otherwise think about. String theory has given so much to all the areas around the particular question of how you combine quantum mechanics and gravity. For example, if you care about understanding quantum field theories or mathematics or cosmology or particle physics – far removed from the realm of quantum gravity – string theory has answers for you. A lot of the rivals to string theory do not have that much engagement with other areas of theoretical physics beyond quantum gravity.
Do you believe there is a single unifying structure underneath all those areas of theoretical physics?
The standard model of particle physics is clearly structured. For example, the particles come in these sets of three that we call generations. There’s something underlying this; the standard model is not the final story. And I think if you’re serious about where the good ideas are for finding out what the final story is, then the route passes through string theory.
String theory: A primer
String theory is a leading candidate for a "theory of everything", because it promises to unite quantum mechanics and general relativity, the two main pillars of modern physics, into a unified theory of quantum gravity. It says that everything is made of tiny strings, whose vibrations produce effects that we interpret as particles. For that to work, string theory also posits that we live in a universe with 10 dimensions or more, most of them curled up so tightly that we don't notice them.
The idea had its genesis in the late 1960s, when Gabriele Veneziano, at the time a visiting theorist at the CERN particle physics laboratory near Geneva, Switzerland, realised this mathematical framework may describe the strong nuclear force, one of the four forces of nature. Troublesome anomalies thwarted his work initially, but over the following decades, many theorists became convinced that string theory depicts physical reality.
During the "first string theory revolution" in the mid-1980s, those troublesome anomalies were eliminated and it became clear that the theory contains all you need to describe the fundamental particles. Plus, physicists alighted on a nifty way to spool up string theory's many dimensions so that it resembled our four-dimensional reality.
Then, as part of the "second string theory revolution" in the mid-1990s, Juan Maldacena at the Institute for Advanced Study in Princeton, New Jersey, discovered a kind of Rosetta Stone within string theory. It allowed lower-dimensional quantum descriptions of reality to be projected into higher-dimensional models of quantum gravity. It is highly technical stuff, but it provided a long-sought link between the ostensibly separate theories of gravity and the quantum world. The AdS/CFT correspondence, as Maldacena's discovery is called, created shock waves among physicists – and it suggested that our universe was a giant hologram.
The only trouble is that the "AdS" part, which stands for anti-de Sitter space, means that string theory only works for universes with a special kind of curvature, which is different to the one we observe around us. String theorists see this as a minor wrinkle to be ironed out. But the problem has persisted for two decades, leading some physicists to feel the whole string theory project has got itself into an unpickable knot. TL
