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 (here and here) 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."

The waveguide set-up used to test the 4D quantum Hall effect. Rechtsman laboratory, Penn State University

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.

The effect cannot be observed in three dimensions. It was first observed in two dimensions when electrical charges were sandwiched between two surfaces. Once the surface cools to almost absolute zero and is subjected to a strong magnetic field, the amount of charge that it can transmit is quantized, fixed by the fundamental quantities of nature.

"Quantization is striking because even if the material is 'messy' – that is, it has a lot of defects – this 'Hall conductance' remains exceedingly stable," said Rechtsman. "This robustness of electron flow – the quantum Hall effect – is universal and can be observed in many different materials under very different conditions."

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.