YOU are running through an open field with the wind in your hair. Or you are diving into the ocean, feeling the cool water surround you. At moments like these we feel free, liberated. Few of us stop to consider the truth – that we are trapped in an invisible prison.
Up-down, left-right, forward-back: these are the three dimensions in which we eat and breathe, make friends and grow old. As prisons go, it could be worse. Then again, we have never known anything else. Despite some imaginary claims to the contrary, no one has ever really experienced a higher dimension.
But now, in some of the world’s most sophisticated labs, we are building our own synthetic extra dimensions. The concept is so far removed from our experience that it is hard to imagine what they could be like. We have, however, already seen the ghostly effects of four-dimensional space touch on our own and wired up electric circuits with an extra dimension. It is unlikely to stop there. Now we have got the hang of it, there is talk of creating five, six or even more dimensions, and even suggestions that exotica such as new particles might lurk in the extra-dimensional wilderness.
This is a frontier that we are barred from exploring directly. We are forced instead to look for the subtle imprints that extra dimensions make on the three dimensions we are confined to. Even so, we could be about to extend the boundaries of reality in ways that come close to the limits of our descriptive powers.
What is the fourth dimension?
It depends on who you talk to—some people think it's the dimension of time, like in Donnie Darko. Others think it's another dimension of space, like the designer of the game Miegakure.
No one's quite sure—the fourth dimension mystifies even scientists like Micho Kaku, who said he felt like Alice in Wonderland after reading up on it. However, two new studies published in Nature have started to give a better picture of the fourth dimension.
Two teams of physicists created two separate experiments that simulated what the quantum Hall effect would look like in four dimensions by using only 3-D (and some nearly 2-D) materials. Essentially, the scientists figured out how to visualize fourth-dimensional phenomena in our lower, simpler third dimension.
The applications of this are still incredibly abstract, but there may be some sci-fi levels of payoff once we wrap our heads around the fourth dimension, according to Mikael Rechtsman, one the authors of the new papers: "Maybe we can come up with new physics in the higher dimension and then design devices that take advantage the higher-dimensional physics in lower dimensions."
If you're wondering what the quantum Hall effect is, you can watch this short video explaining it:
It's understandable if all this gets a little confusing—as we mentioned, even Michio Kaku was mystified by the fourth dimension.
When a two-dimensional (2D) electron gas is placed in a perpendicular magnetic field, its in-plane transverse conductance becomes quantized; this is known as the quantum Hall effect1. It arises from the non-trivial topology of the electronic band structure of the system, where an integer topological invariant (the first Chern number) leads to quantized Hall conductance.
Sometimes it's helpful to take a step back and try to think of the fourth dimension in terms that don't involve 2-D planes of electron gas. Here's Carl Sagan describing it:
