String theory is the best candidate we have for a theory of everything. Bend to its rule and the various tangled theories of conventional physics emerge as part of a sublime, higher-dimensional tapestry. It can unify all four of nature’s forces, including the most troublesome of all, gravity. With any luck, it can also tame big bangs and black holes without losing the thread.
There’s just one catch: string theory can’t explain a universe like ours. Its maths can describe gazillions of different possible universes, just not one expanding at an accelerating rate, which is precisely what we see ours doing. To be sure, no one knows what is driving this acceleration – a mysterious “dark energy” is the usual placeholder. According to theory, though, it probably shouldn’t be happening at all.
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For 25 years, this has been a big problem, but now we may have found a way past it. Superficially, the answer won’t shock anyone used to the extravagance of modern physics: we just have to rethink our universe as part of a much grander enterprise. Do this, and it can balloon to its heart’s content – indeed, accelerated expansion seems to come naturally. But this new scheme may be the wildest yet, one in which our familiar space is delicately poised between high-dimensional hyperspace and complete nothingness. “In our proposal, our existence is like a shadow – a projection onto a wall at the end of the world,” says , a physicist at the University of Nottingham in the UK.
For all its present-day grandeur, string theory has humble roots. It grew up in the late 1960s as a simple equation to make sense of collisions between protons, neutrons and other particles glued together by what is called the strong force. Back then, it wasn’t called string theory, but the name soon took after physicists realised that its collision probabilities could be interpreted as the different vibrations of quantum-mechanical strings. Tentatively, they began to wonder if the strings were more than mere tools to help understand particles – maybe they actually were the particles. In this picture, each fundamental particle – be it an electron, a quark, a Higgs boson or whatever – is actually the end of an infinitesimally tiny string, humming a particular tone.
As it happens, string theory initially stumbled in its efforts to properly calculate the strong force, though it quickly made headway elsewhere. There are three other known forces of nature: the weak force, which governs radioactivity; electromagnetism, which concerns light and the chemistry of everyday matter; and gravity, which is something of an oddball, making everything attract. String theory’s first major success was to achieve what previous quantum theories had never managed, and describe gravity. Later, the weak force, electromagnetism and the strong force, too, came under string theory’s umbrella. Suddenly, it was the front-runner as a viable theory of everything.
Its maths was bold, requiring 10 dimensions of space-time. We are familiar with just four dimensions – that is, three of space and one of time – but string theorists believe there are six more and that they are so minuscule as to be invisible to our senses or any current instruments. While the extra dimensions made the equations work and freed up space for the strings to curl up in, they also unleashed a host of other weird, higher-dimensional objects, somewhat misleadingly called membranes, or branes for short. Still, this was the 1980s. Anything was possible.
Unfortunately, it turned out that string theory was so flexible it could describe a truly vast array of fantastical universes. Something like 10500, in fact – a number so huge it belied any physical comparison and made a mockery of predictive science. Worse, astronomical observations in the late 1990s of distant supernovae revealed an amazing truth: that our universe is expanding faster and faster. Perplexing though this was for physicists in general, it was a disaster for string theorists. Very few of the universes in their immense selection had this accelerating property. “People began to wonder if our sort of universe is really just impossible in string theory,” says , a theorist at Uppsala University in Sweden. “Today, we still simply don’t know.”
String theory’s big problem
It might seem odd that string theory struggles with something so apparently mundane as an accelerating universe. The reason is that the rate of expansion comes from the very geometry of space-time, as defined by Albert Einstein’s general theory of relativity and later descibed in detail by cosmologist Willem de Sitter. In one solution to Einstein’s equations, space-time is spherical and expanding at an accelerating rate – what’s now known as a de Sitter (dS) space. In the alternative solution, space-time is saddle-shaped and cannot expand at all, called an anti-de Sitter (AdS) space. String theory strongly implies that only AdS space-times are stable and able to support themselves, even though a wealth of astronomical data, including from those distant supernovae, confirms that our present-day universe is dS.
What we see and feel would be just a projection of a greater reality, beyond our senses
The seed of an idea to get around this impasse was planted even before physicists had fully got to grips with dark energy and the accelerating universe. In 1999, in an attempt to solve an entirely different problem in string theory, theorists and toyed with the concept of high-dimensional branes, albeit in a less extravagant, easier-to-describe, five-dimensional (5D) setting.
In geometry, the surface of an object always requires one dimension fewer than the object itself – for instance, each face of a 3D cube is a 2D square. Likewise, Randall and Sundrum discovered that it was possible to have a pair of 5D AdS space-times separated by a brane that was merely 4D, just like our universe. Moreover, Randall’s later work with theorist showed that this brane would have an accelerating, dS geometry – again, just like our universe. Did we live on a brane? The possibility was tantalising.
Alas, despite its superficial promise, the Randall-Karch brane never much helped to ease string theory’s woes. The reason was that, sandwiched between two mammoth AdS space-times, it wasn’t much more stable than the few pure dS universes that could be wrenched out of string theory. About five years ago, however, Danielsson and his colleagues at Uppsala University had an epiphany. “We thought, what if instability wasn’t a problem?” he says. “What if we could turn it to our advantage?”
Every space-time model has a certain level of energy woven into its fabric, governing the types and behaviours of the particles, strings, branes and other entities that may be contained within it. If a space-time doesn’t reside at the lowest possible energy, quantum mechanics says it is inherently unstable and has the risk of “decaying”, suddenly transforming into a new universe in which the energy is lower. Danielsson’s group a 5D AdS space-time that begins high on this energy ladder, and found that if even a tiny part of it decays, this fragment quickly forms a “dark bubble” of lower-energy 5D AdS space-time. As in the Randall-Karch scenario, this bubble is enclosed by a 4D dS space-time like our own – yet crucially, it arises out of instability, rather than being at the mercy of it.
In this new scenario, the bubble membrane on which our cosmos is poised still wouldn’t be perfectly stable. But that just means another dark bubble would occasionally pop up, or nucleate, within its inner 5D space-time, which we can’t see. In fact, new dark bubbles would continually nucleate within each other, each enclosed by a dS brane – in effect, a new universe. In this grand multiverse, what we refer to as “the” big bang would be just the moment our parent bubble gave birth to ours.
Danielsson argues that this idea is actually more intuitive than accepted big-bang cosmology. “A favourite picture of the big bang is that it’s like a balloon expanding into space,” he says. “Usually someone tells you that’s wrong: the balloon isn’t expanding into space, because that extra space – the beyond – simply doesn’t exist. But with the dark bubble, actually it does.”
Leaking gravity
However, there is a fear that, on closer inspection, the bubble may burst. The issue has to do with that most pesky of nature’s forces, gravity, and, in particular, why it is so weak. A common illustration of gravity’s weakness is the comparative strength of a fridge magnet, which is able to exert enough electromagnetic force to stick to a metal door and, in so doing, counteract the gravitational pull of the entire planet. String theory offers a generic, hand-waving answer to gravity’s feebleness: with 10 dimensions to act in, gravity is somehow diluted more than the others. But if gravity is leaking away, theorists still have to explain why it isn’t so weak as to let planets escape their orbits and spinning galaxies fly apart.
The trick is to somehow confine gravity so that only a little – just the right amount – seeps away into the extra dimensions. Padilla argues that dark bubbles don’t successfully do this. After all, the dark bubble multiverse is infinite, so gravity can potentially leak anywhere. As a result, Danielsson’s group has had to introduce additional strings in their fifth dimension to tether gravity to the bubble membranes.
“To us, it looked like you have to jump through hoops to get gravity to look 4D,” says Padilla. For this reason, he and his colleagues and at the University of Nottingham began to toy with : get rid of the multiverse and have just one bubble. With no infinite space-time, gravity’s leakage is stemmed, allowing it to be weak, but not too weak. And while our world is still the 4D brane surrounding a 5D bubble, it is now also the barrier between a 5D cosmos and pure nothingness. In other words, it is literally the edge of the universe, an “end of the world” brane. “Of course, this also presents a problem,” says Padilla. “What’s nothing, and how can something come out of it?”
How to get something from nothing is a vexed question, to say the least. From the dawn of philosophical thought, people have wondered how space, time, substance – even the rules governing those things – can arise if there is nothing there to begin with. As physics deals with relationships between entities, there seems little hope that it can ever fully answer this mystery.
And yet, as theorists and , when they were both at Princeton University, it can get surprisingly close. Drawing on earlier work by their then Princeton colleague and string theory heavyweight , they posited the case of an AdS space-time geometry that curves infinitely in on itself. Such a geometry is like a piece of paper that has been crunched up more and more, each scrunch adding curvature, until it is infinitesimally small. This, said Brown and Dahlen, is pretty much the best “nothing” you can define within the framework of physics.
A space-time with this geometry is an inhospitable place indeed. At infinite curvature, all lengths shrink to zero, so there simply wouldn’t be any space for anything to exist. On the other hand, quantum mechanics would still reign supreme, and quantum mechanics doesn’t allow any such definitive statements. Where there is nothing, it says, there is still the fleeting chance of a little something – the teeniest of spaces for a bubble space-time to nucleate.
The Nottingham group wanted to exploit this possibility but faced another problem. If the parent space-time is infinitely curved, how can a bubble formed within it have a benign geometry? Fortunately, physicists are used to grappling with this kind of issue. In quantum field theory, which underlies our current standard model of fundamental particles, physicists routinely have to cancel out high-energy terms in their equations, lest their answers turn infinite. Although it can sound arbitrary, this “renormalisation” process works: witness the amazing precision with which physicists predict the rates of collisions at particle smashers such as the Large Hadron Collider.
Last year, Padilla and his colleagues employed a similar procedure, known as holographic renormalisation, when calculating the nucleation of a finitely curved bubble within an infinitely curved AdS space-time. It was a success. “The result is exactly described by an end-of-the-world brane, with nothing outside,” says Padilla.
Superficially, it seems that the universe we think we know could really be this brane, with nothingness on the outside and a 5D bubble on the inside. If that is the case, Padilla points out that the strings making up our everyday existence would really be living in the 5D space inside the bubble, with only their ends, which we perceive as the fundamental particles, stuck to our 4D braneworld. In that case, these particles – what we see and feel – would really be a shadow or projection of a much greater reality beyond our senses.
Still, it should be noted that neither the Nottingham nor the Uppsala group’s ideas are fully fledged string theories. Because the researchers’ proposals have only five dimensions, they need to demonstrate that the rest of string theory’s 10 dimensions can successfully be compacted into their worlds. “The full string theory embedding of this scenario will likely come with new obstacles,” says , a string theorist at the Max Planck Institute for Physics in Garching, Germany.
Although the Uppsala group has claimed some progress towards this goal, significant challenges remain as those obstacles begin to reveal themselves – and a path through isn’t clear. “This may be just a technical difficulty or it may be a reflection of a more fundamental obstruction,” says at the Institute of Theoretical Physics in Madrid, Spain.
But even if they are successful theoretically, it is tempting to ask: are the ideas simply a little too out-there? Physicists can test for gravity leaking into extra dimensions by looking for deviations in the laws of gravity as we know them, either in the behaviour of balances and cantilevers in tabletop experiments or, as has only recently become possible, in the sizes of black holes in astronomical imagery. They can also use particle colliders to search for the energy signatures of gravitons, the particles thought to carry the force of gravity, operating in higher dimensions. Unfortunately, the precision of these tests isn’t yet sufficient to rule out or provide evidence for the braneworld scenarios, although it is improving all the time.
Meanwhile, the ideas have injected new optimism into string theory – a glimmer of hope that, despite all its difficulties and excesses, it might be able to describe our humble expanding universe after all. “It’s definitely too early for a final verdict,” says Blumenhagen. But the possibility that we live on a brane may mean that the acceleration of our cosmos isn’t truly the end of the world for string theory.
Spend a weekend with some of the brightest minds in science, as you explore the mysteries of the universe in an exciting programme that includes an excursion to see the iconic Lovell Telescope.
Mysteries of the universe: Cheshire, England
