Extra dimensions are string theoryâ€™s most outlandish prediction. String theory demands that our cosy 4D view of the world is wrong. In fact the universe of strings must have ten dimensions! This is immediately at odds with our perception of reality, but we can resolve the paradox by requiring the six unseen dimensions to be incredibly small.
So what makes aÂ dimension? Intuitively each dimension is an independent direction in which we can move. We live in three dimensions of space, â€śforward-backwardâ€ť, â€śleft-rightâ€ť and â€śup-downâ€ť. Thereâ€™s also a single time dimension, â€śpast-futureâ€ť, making 4 dimensions in total. But our perception of dimension is greatly affected by scale.
Imagine watching a faraway ship approaching port. It starts out looking like a zero-dimensional dot on the horizon. Soon you realise it has a mast pointing high into the sky: it now appears to be a one-dimensional line. Next, its sails come into view making it seem two-dimensional. As it nears the dock you finally notice that it has a long deck, the third dimension.
Thereâ€™s nothing strange here. Itâ€™s just that at large distances we canâ€™t resolve dimensions. So perhaps there could be extra dimensions, so small that we donâ€™t perceive them. The process of curling up space to produce these tiny invisible dimensions is known asÂ compactification.
Suppose you’re a squirrel living on an infinitely long tree trunk. The trunk is (more or less) a cylinder. You can move in two independent directions, â€śalongâ€ť and â€śaroundâ€ť. Â One day you get bored and move to a thinner tree – the circumference of the trunk is greatly reduced.
Now your â€śaroundâ€ť dimension is much smaller than it used to be. It only takes a few steps to go all the way round the trunk. Any meaningful movement has to be done in the â€śalongâ€ť dimension. You jump to a yet finer trunk. Now a single step takes you round the tree a hundred times! The â€śaroundâ€ť dimension has become far too small for you to detect.
As the tree trunks get narrower, the dimensions of your world reduce from two to one. In string theory this must happen for all six extra dimensions. We wrap them up so they are inconceivably tiny. Every time you move your hand through space you circle the six hidden dimensions a vast number of times.
The size of these compactified dimensions is similar to the length of a string, the Planck scale. This has two important consequences. Firstly itâ€™s unlikely that weâ€™ll be able to detect them by direct experiment. NeverthelessÂ several possible testsÂ have been suggested, though generally they rely on having a healthy slice of luck. Secondly the extra dimensions form a surface which strings can become caught up in.
The shape and size of strings is vital to modelling theirÂ vibrations and interactions. Therefore itâ€™s important to understand how they wrap themselves around the six curled-up dimensions. The precise structure of the surface formed by compactification changes the physics arising from the strings.
It turns out there are many different ways of mushing up the extra dimensions into a tiny space. Which method gives rise to conventional physics? Nobody knows!Â Current researchÂ focuses onÂ Calabi-Yau manifolds, a promising group of compactifications. Â But as of yet there is no definitive answer.