Wouldn’t it be great to reach your arm into a fourth dimension of space? You could then liberate yourself from the shackles of ordinary geometry. Hopelessly tangled extension cords would slip apart with ease. A left-handed glove could be flipped over to replace the right-handed one your dog ate. Dentists could do root canals without drilling or even asking you to open your mouth.
As fantastic as extra dimensions of space sound, they might really exist. From the relative weakness of gravity to the deep affinity among seemingly distinct particles and forces, various mysteries of the world around us give the impression that the known universe is but the shadow of a higher-dimensional reality. If so, the Large Hadron Collider (LHC) near Geneva could smash particles together and release enough energy to break the shackles that keep particles in three dimensions and let us reach into that mind-blowing realm.
Proof of extra dimensions “would alter our whole notion of what reality is,” says cosmologist Max Tegmark of the Massachusetts Institute of Technology, who in 1990 wrote a four-dimensional version of the video game Tetris to get a taste of what extra dimensions might be like. (You keep track of the falling blocks using multiple 3-D slices of the full 4-D space.)
In modern physics theories, the main rationale for extra dimensions is the concept of supersymmetry, which aims to unite all the different types of particles into one big happy family. Supersymmetry can fulfill that promise only if space has a total of 10 dimensions. The dimensions could have gone unnoticed either because they are too small to enter or because we are, by our very nature, stuck to a 3-D membrane like a caterpillar clutching onto a leaf.
To be sure, not every proposed unified theory involves extra dimensions. So their discovery or nondiscovery would be a helpful data point. “It would focus what we do,” says physicist Lisa Randall of Harvard University, who made her name studying the caterpillar-and-leaf option.
One way to get at those dimensions is to crank up the energy of a particle accelerator. By the laws of quantum mechanics, the more energy a particle has, the more tightly confined it is; an energy of one tera-electron-volt (TeV) corresponds to a size of 1019 meter. If an extra dimension is that big, the particle would literally fall into it and begin to vibrate.
In 1998 physicist Gordon Kane of the University of Michigan at Ann Arbor imagined that the LHC smashed together two protons and created electrons and other particles that not only had the energy of 1 TeV but also integer multiples thereof, such as 2 or 3 TeV. Such multiples would represent the harmonics of the vibrations in extra dimensions set off by the collision. Neither standard particle processes nor exotica such as dark matter particles could account for these events.
Extra dimensions might betray themselves in other ways. If the LHC produced subatomic black holes, they would be immediate proof of extra dimensions, because gravity in ordinary 3-D space is simply too weak to create holes of this size. For geometric reasons, higher dimensions would strengthen gravity on small scales. They would likewise change the small-scale behavior of other forces, such as electromagnetism. And by dictating how supersymmetry operates, they might lead to distinctive patterns among the masses and other properties of particles. Besides the LHC, scientists might find hints of extra dimensions in measurements of the strength of gravity and in observations of the orbits of black holes or of exploding stars.
The discovery would transform not only physics but also its allied disciplines. Extra dimensions might explain mysteries such as cosmic acceleration and might even be a prelude to reworking the entire notion of dimensionality—adding to a growing sense that space and time emerge from physical principles that play out in a spaceless, timeless realm.
“So while extra dimensions would be a terrific discovery,” says physicist Nima Arkani-Hamed of the Institute for Advanced Study in Princeton, N.J., “at a deeper level, conceptually they aren’t particularly fundamental.”
Whatever the charms of extra dimensions for physicists, we will never be able to visit them for ourselves. If they were open to the particles that make up our bodies, the added liberty of motion would destabilize complex structures, including life. Alas, the frustration of tangled cords and the pain of dental work are necessary trade-offs to allow us to exist at all.