Two independent groups of scientists have been able to reproduce four-dimensional properties of a quantum mechanical effect using a two-dimensional analog. The two studies were published in Nature and focus on the quantum Hall effect. This effect describes how the conductance (how well something transmits electricity) of a two-dimensional electron system acts at a low temperature and in a strong magnetic field. It has been known for a long time that this effect could also exist in a four-dimensional system, but this has not been possible to prove until now...
"When it was theorized that the quantum Hall effect could be observed in four-dimensional space, it was considered to be of purely theoretical interest because the real world consists of only three spatial dimensions; it was more or less a curiosity, " Mikael Rechtsman, assistant professor of physics and author of one of the papers, said in a statement. "But, we have now shown that four-dimensional quantum Hall physics can be emulated using photons – particles of light – flowing through an intricately structured piece of glass – a waveguide array." Thanks to a new technique, glass waveguides can be etched in a way that makes them sport synthetic dimensions, allowing photons going through the waveguides to act like they are in a true four-dimensional system. This breakthrough allowed researchers to finally test if the quantum Hall effect truly exists in four dimensions. And it does.
While there are no direct applications of four-dimensional physics, the scientists think that a better understanding of the four-dimensional quantum Hall effect could be used to develop new optical systems, and maybe the use of higher dimensional waveguides could help explain bizarre solids like quasicrystals.
Kemo D. 7