# Leaving Flatland: looking into a fourth dimension in the lab

In our experience, the world has three dimensions of space, along which we move left/right, forward/backward and up/down, as well as one dimension of time. But scientists have long wondered how physics would be different in a hypothetical world with four or even more spatial dimensions. Now, experiments have developed techniques to artificially simulate extra spatial dimensions, allowing us to start exploring these fundamental questions in the laboratory.

To count the number of spatial dimensions in which an object moves, we can ask how few co-ordinates are needed to specify its location at a given time. For example, to find a sailing ship, we only require two numbers, its longitude and latitude, as the ocean surface can be effectively mapped onto a two-dimensional sheet. Instead, to locate a flying plane, we need a third co-ordinate, its altitude, as the plane manoeuvres in all three spatial dimensions as it flies. In a simple sense then, we can think of four spatial dimensions as requiring an extra fourth co-ordinate to label where an object is.

Visualising such a higher-dimensional world, however, can still be tremendously challenging, as vividly pointed out over a century ago in Edwin A. Abbott’s Flatland: A Romance of Many Dimensions. This satirical novella tells the story of a two-dimensional world, populated by geometric shapes such as triangles and squares. Confined to Flatland, the close-minded inhabitants have no concept of a third dimension, until they are visited one day by a sphere. In vain, the sphere tries to explain three dimensions to a Flatlander, showing that as it moves along the third dimension, it passes through the two-dimensional world. But, stuck in two dimensions, the unconvinced Flatlander only sees a circle (a slice through the sphere), which first grows and then shrinks as the sphere passes through.

Scientists trying to understand four spatial dimensions face a similar problem, as we are stuck in a spatially three-dimensional laboratory. Nevertheless, theoretical physicists have predicted that fascinating phenomena would emerge in a four-dimensional world, such as new types of the so-called ‘topological’ physics that was recognised by the 2016 Physics Nobel Prize, awarded partly for research at Birmingham.

Very recently, we have verified one of these predictions by taking a first look into four-dimensional physics in the laboratory. In these experiments, a set-up of cold atoms or particles of light was carefully designed to look like a slice of a hypothetical system with four spatial dimensions. As the set-up was tuned, it scanned over different slices, reconstructing how the whole four-dimensional system would behave – a bit like a Flatlander could reconstruct the sphere by piling up the growing and then shrinking circles that it sees.

Soon, experiments may even leave ‘Flatland’ altogether by using a recently demonstrated technique to make particles behave like they move in extra artificial dimensions. In addition to the usual three spatial co-ordinates, these particles have an extra label, specifying their internal state, which can act like a co-ordinate along a synthetic spatial direction. By tracking all four co-ordinates together, experimentalists would map out in real time how a particle moves in four dimensions. And there is no need to stop there; by adding more labels, we could investigate the physics of five, six or even more spatial dimensions.

Together, these advances open up exciting directions, made possible by theoretical research into fundamental science and improvements in the experimental control of quantum systems. By looking into a fourth spatial dimension in the laboratory, we are just at the start of our exploration of higher dimensions and of our discovery of the new physics awaiting us there.