There’s hardly a problem that physicists haven’t tried to solve by adding extra dimensions to our everyday three of space and one of time: whether with scrunched up dimensions too small to see, or the idea that our 4D world exists on a “brane” floating in an inaccessible higher dimensional world.
How to envisage such things? Physicist of the University of Marseilles, France, doesn’t personally have much truck with more than three spatial dimensions – “I do not think they exist,” he says – but he finds extra dimensions easy enough to picture. “It is just a space where you can go up-down, left-right, ahead-back, but also in one other dimension, something like leftB-rightB,” he says. “It is a bit like having many arms, like an Indian god.”
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Others are more circumspect. “Visualising higher dimensions is certainly harder,” says of the University of California, Santa Barbara (UCSB). One standard trick is to start at the bottom and work your way up, extrapolating your understanding of lower dimensions to higher ones. The principle is illustrated in Edwin Abbott’s 1884 classic novella Flatland. When the 3D Sphere passes through 2D Flatland, the inhabitants of the 2D plane perceive the sphere as a sudden dot that grows into a big circle before diminishing back into a dot again.
Even if this process of slicing a higher-dimensional object into a series of projections becomes impossible to envisage in more dimensions than three, it will always work in this way: simply add extra dimensions to your equations, supplementing the standard x, y, z and t with extra coordinates, say w or s. “In the end there is always mathematics,” says , also at UCSB.
Polchinski’s speciality is string theory, still the most favoured route to unifying quantum theory and general relativity, the two irreconcilable underpinnings of modern physics. Depending on what variant you choose, it requires 10 or 11 dimensions. The mathematics works fine. As to whether these dimensions actually exist – well, that’s anyone’s guess.
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This article appeared in print under the headline “How to think about higher dimensions”
