Craig Frazier
We tend not to dwell on the fact that we exist in three dimensions. Forwards-back, left-right, up-down; these are the axes on which we navigate the world. When we try to imagine something else, it typically conjures images from the wildest science fiction – of portals in the fabric of space-time and parallel worlds.
Yet serious physicists have long been spellbound by the prospect of extra dimensions. For all their intangibility, they promise to resolve several big questions about the deepest workings of the universe. Besides, they can’t be ruled out simply because they are difficult to imagine and even harder to observe. “There’s no reason why it has to be three,” says at the University of Oxford. “It could have been two; it could have been four or 10.”
Advertisement
Still, there comes a point when any self-respecting physicist wants hard evidence. Which is why it is so exciting that, over the past few years, researchers have developed a handful of techniques that could finally snare proof of extra dimensions. We might yet spot gravity leaking into them, for instance. We may see their subtle imprint on black holes or find their traces in particle accelerators.
But now, in an unexpected twist, Obied and others are making the case for an extra dimension that is radically unlike any we have concocted previously. This “dark dimension” would conceal particles from the dawn of time that could solve the mystery of dark matter, whose gravitational pull is thought to have shaped the cosmos. Crucially, it should also be relatively easy to spot – and experiments are already underway that could reveal it or rule it out.
What is an extra dimension?
It isn’t difficult to define a dimension. “It basically refers to the directions you can move,” says Obied. You can thus think of the spatial dimensions as the x, y and z axes on a line drawing of a cube. Some see time as another dimension, giving us the concept of four-dimensional space-time.
To explain why we find it so hard to think beyond this, physicists often reference the 19th-century novel Flatland: A romance of many dimensions by Edwin Abbott. The story’s protagonist is a square who lives in a strictly two-dimensional world. One day, the square is visited by a sphere. He is unable to observe the sphere’s true form and only sees it in cross-sections, a series of circles of varying diameter. Gradually, the square begins to grapple with the realisation that his smooth world may not be the full extent of reality.
Physicists’ fascination with extra dimensions really picked up in the early 20th century. In 1915, Albert Einstein published his general theory of relativity, in which gravity arises from the warping of four-dimensional space-time by massive objects. A few years later, physicist Theodor Kaluza was playing with Einstein’s equations and introduced a fifth dimension. At first, there was little expectation behind this. It was more or less a case of adding extra mathematical terms to the equations – a w to go along with x, y and z.
Extra dimensions would be folded up in extremely complicated geometries PASIEKA/SCIENCE PHOTO LIBRARY
But astonishingly, Kaluza’s additions provided a way of accurately representing electromagnetic fields. In other words, this five-dimensional extension of general relativity seemed to elegantly unify two fundamental forces – gravity and electromagnetism – in a single framework. Kaluza’s contemporaries went further, speculating that gravity might somehow “leak” into this extra dimension, potentially explaining one of the major mysteries of physics: why gravity is so exceptionally weak compared with the other forces of nature.
In 1926, theoretical physicist Oskar Klein looked at Kaluza’s framework again, now from the perspective of newly discovered quantum theory. His analysis suggested that the extra dimension through which electromagnetism worked would have to be inestimably small – far smaller than an atom – with a radius of just 10-32 metres. Klein proposed that this diaphanous dimension would exist at every point in space, rolled up like an infinitesimal tape measure.
We now know that the Kaluza-Klein hypothesis, as it has come to be known, isn’t a true reflection of reality. Modern physics sees electromagnetism as operating through a quantum field in our familiar space-time. Nonetheless, the idea of invoking extra dimensions to explain away difficulties in physics endured. “Even though we now know that isn’t our universe, it did inspire some people to study ideas of higher dimensions from the mid-20th century,” says , a theorist at Harvard University.
Ultimately, that led to Vafa’s field of study, string theory. It says that everything is made of strings that vibrate in 10 dimensions, at least six of which are tiny and tightly coiled, like those that Klein envisaged. Fundamental particles – electrons, quarks, Higgs bosons – are nodes of the string that intersect the dimensions with which we are familiar.
That may sound far out. But physicists find it compelling partly because the maths of string theory is so elegant. “We can very easily extend our mathematics to more dimensions, and indeed, some of mathematics works better or gives kind of the right answer in higher dimensions,” says cosmologist at the University of Portsmouth, UK. String theory has also led to all sorts of insights in other, unrelated fields, which, to some theorists, gives it the ring of truth.
The principle reason why extra dimensions are so fiendishly difficult to detect is their size. “Imagine you’re trying to knit something using boxing gloves,” says Joseph Conlon at the University of Oxford. “You just cannot possibly feel it because the boxing gloves are big and crude, and the yarn is very fine and small.”
There is a workaround. Physicists believe that fundamental particles are generally banned from moving in extra dimensions. “Our objects don’t really exist in that extra dimension,” says Kris Pardo at the University of Southern California. But there may be exceptions. Extra dimensions are essentially gossamer filaments of space-time, which implies they have a gravitational field. By extension, hypothetical particles called gravitons, thought to carry the force of gravity, ought to be able to traverse these extra dimensions. That raises the possibility of spotting an extra dimension by watching gravity, in the form of gravitons, vanish into it.
Vanishing gravitons
We now have the opportunity to do just that, thanks to gravitational waves, or ripples in space-time. These waves are caused by the epic collisions of black holes or neutron stars in the distant cosmos. If we could watch the waves diminish in power as they swish towards us, that would be a sign that gravity is leaking into an extra dimension.
A chance presented itself in 2017, when astronomers spotted the cataclysmic merger of two neutron stars. In this rare case, they saw both the gravitational waves that emanated from it and the explosion of visible light, called a kilonova, it produced. Pardo and his colleagues jumped into action. “We were looking to see how far away the light told us this merger was, compared to the distance the gravitational waves told us it was,” says Pardo. If the gravitational waves seemed to come from a much greater distance, that would have been a sign of the gravitational power slipping away.
They found no evidence of such an effect, though Pardo says that may just be due to the constraints of our technology. At the moment, we can only detect fairly low frequencies of gravitational waves. Higher frequencies are more likely to be affected by putative extra dimensions because their wavelengths would be a closer match for the size of these dimensions, but we won’t see them until we have more advanced detectors. Pardo says the , currently under construction at the California Institute of Technology, may offer us hope.
We navigate the world in three dimensions, but there may be others hidden from us Colton Stiffler/Getty Images
Extra dimension hunters have other methods at their disposal too, such as looking at the large-scale structure of the universe. The arrangement of galaxies is especially sensitive to the laws of gravity, says Baker. If we tweak our accepted models of how gravity works – by postulating that it escapes into higher dimensions, for example – then the way that galaxies cluster would also change. Baker and others are therefore running simulations of how extra dimensions would affect this pattern. They can then compare their simulated patterns with observations, which are getting more precise and comprehensive all the time. “We’re up to billions of galaxies now,” says Baker. Any differences, which of course would be slight, could be evidence of higher dimensions.
Perhaps the strangest observational implication of extra dimensions involves the appearance of lookalike particles. An extra dimension is essentially a bonus direction in which a graviton can travel. And some physicists think that other force-carrying particles, like the W and Z bosons, the carriers of the weak nuclear force, could also traverse extra dimensions. It follows that these particles must have momentum in each additional dimension, says Obied. And in our three-dimensional space, that would appear as extra mass. In practice, then, we would expect to see some signature of gravitons or other force-carrying particles with the exact same properties, except two, three or more times their usual mass, depending on the number of extra dimensions out there.
It must be said that we have never seen a graviton, and if they do exist, they must be extremely light or even massless. But, in principle, gravitons could be produced in particle collisions at the Large Hadron Collider near Geneva and . Or we might perhaps spot a particle that looks just like a W boson but 10 times heavier. Physicists have searched for these signs and come up empty.
These lookalike particles would also affect the properties of black holes. When black holes bump into each other or neutron stars, they release energy in the form of gravitational waves – much like during neutron star mergers. Towards the end of this process, the black hole goes through a fleeting stage called ringdown, where – for a fraction of a second – the waves “ring” like a wine glass tapped with a knife.
During this brief resonant hum, the waves’ amplitude naturally decreases. But if the lookalike particles do exist, they would . Physicists are currently from these events in the hope of hearing such a signal. You won’t be surprised to hear that there has been no joy so far. No one said finding a hidden dimension was going to be easy.
But there is new hope, at least, with the recent invention of a so-called dark dimension. This one wouldn’t be a cinch to detect either, and yet it has two big attractions. First, it could explain the nature of dark matter, the stuff we know is out there influencing the shape of galaxies through its gravitational pull but that we have failed to identify despite decades of attempts. Second, its proponents insist that simple experiments could soon reveal the presence of the dark dimension, or rule it out.
Into the swampland
The origins of this idea lie in string theory. One of the niggles with the theory is that it predicts a vast array of possible universes, known as the landscape, depending on precisely how its extra dimensions are curled up. To combat this, Vafa initiated a programme of research a few years ago to work out which areas of the landscape – that is, which versions of string theory – can be ruled out because they don’t align with our observations of the universe. Vafa dubbed these untenable parts of the landscape the “swampland”.
Vafa’s ongoing swampland research programme has led him to several mathematical hypotheses, one of which is the distance conjecture. This says that when a physical parameter has an extreme value, there are particular mathematical repercussions. “If some parameter in the theory is extreme, there must be another description where the physical description is simpler,” says Vafa. One such parameter is the strength of dark energy, the unknown force that is pushing the universe apart. Despite operating over cosmic scales, dark energy is almost preposterously weak. Starting in 2022, Vafa applied the distance conjecture to the strength of dark energy and found something surprising: it predicted that and would hold a suite of particles.
Working through the details, Vafa found that, in this scenario, graviton particles with a range of masses would have been produced soon after the big bang and most would have leaked into the dark dimension, the width of which would be about a micrometre, or a thousandth of a millimetre – making it a giant among dimensions. We couldn’t detect these particles directly, but we would feel their effect. As Vafa wrote in published this year, this dimension could explain dark matter. “This extra dimension pieces together all the properties we want dark matter to have,” he says. “We don’t have to postulate a new particle for dark matter, gravity itself is that particle.”
Vafa’s idea is based on an unproven conjecture, so it could easily be wrong. But it has the advantage of being relatively easy to check. In four-dimensional space-time, the force of gravity between two masses is inversely proportional to the square of the distance between them – this is Isaac Newton’s inverse square law. When another dimension is added, however, gravity should be proportional to the cube of the separation. This effect would only show up at scales similar to the width of the dark dimension. So, to test for it, physicists would need to hold two feather-light masses about 1 micrometre apart and check if gravity adheres to the inverse square law or not.
Experiments from a group of researchers at the University of Washington have already shown that the inverse square law still holds . But ongoing experiments from a group in Austria, which includes at the Austrian Academy of Science, hope to whittle that distance down. Their work involves swinging particles from a tiny pendulum set alongside another tiny mass. Changes in the force of gravity can be inferred from the swing of the pendulum. “If future experiments find that the inverse-square law is violated at extremely small distances, it will have profound implications for our understanding of the universe,” says Shayeghi. Vafa reckons we could be attempting these experiments at the scale of 1 micrometre within years. “We’re not too far away,” he says.
Should physicists actually find hard evidence of this dark dimension, it would be an earthshaking revelation, akin to the square in Flatland encountering the sphere. Admittedly, it is rather hard to imagine. But scientifically, says Baker, “the confirmation that extra dimensions actually exist could solve a lot of problems.”
Chen Ly is a freelance science journalist based in London
91av audio
You can listen to many articles – look for the headphones icon in our app
Topics:
