Scientists Simulate Fourth Spatial Dimension In New Quantum Hall Experiments

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More than a century has passed since Albert Einstein proposed his theory of relativity in 1905. In the years since then, time has often been considered as the fourth dimension of space, with three spatial dimensions where one can go up or down, left or right, or forward or backward. But two new papers published in the journal Nature suggest that there might be a fourth spatial dimension, one that could possibly suggest previously undiscovered directions of motion.

As detailed in a report from Gizmodo, two separate teams of researchers created their own two-dimensional setups, with one team using ultra-cold atoms and the other one working with waves of light. While the studies produced varying results, the findings complemented each other, as they both exhibited examples of the so-called “quantum Hall effect” in four-dimensional form.

“Physically, we don’t have a 4D spatial system, but we can access 4D quantum Hall physics using this lower-dimensional system because the higher-dimensional system is coded in the complexity of the structure,” explained Penn State University professor Mikael Rechtsman, lead author of one of the new studies, in an interview with Gizmodo.

“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.”

According to the International Business Times, the quantum Hall effect was first observed about two decades ago and takes place when an electron’s motions within a material are confined to only two dimensions. Once magnetic fields pass through the material in a perpendicular motion, this limits some electrical properties in the system to multiples of exact numbers, as voltage doesn’t increase continuously as it normally would, but rather in specific intervals. Scientists had previously theorized that this effect represents something similar to what takes place when particles are in the fourth dimension, but as Gizmodo pointed out, the lack of an actual fourth spatial dimension made it hard to determine the other outcomes of the quantum Hall effect.

In order to work around this limitation, a team of European researchers led by Michael Lohse of the Ludwig-Maximilians University in Germany made use of rubidium atoms, trapping them with lasers in two dimensions, much like trapping atoms in an egg crate with the boundaries dictated by the lasers. This resulted in a two-dimensional quantum “charge pump,” which then allowed the researchers to mimic the process of transporting electric charges. For the two additional spatial dimensions, the researchers coded an extra variable based on how the atoms behaved. With all that in place, the European team was able to find signs of a fourth spatial dimension, using their novel system to measure the “second Chern number.”

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Meanwhile, Penn State researcher Rechtsman and his colleagues used a special type of glass box to manipulate the shape of laser-generated light waves, allowing them to mimic how electric fields behave on charged particles. As the researchers wiggled the glass box’s furthest edge, light would jump and ripple from one end of the device to another, representing a physical effect linked to the four-dimensional quantum Hall effect.

Although both teams came up with complementary results, with the European team looking at how the fourth spatial dimension manifests in a physical system and the U.S. team studying how 4D effects appear on said system’s edges, Gizmodo stressed that neither study featured actual four-dimensional systems, but rather simulations of 4D effects. Still, both lead authors told the publication that they are interested in further research on these effects, specifically what would happen if the atoms and photons in the systems interacted with each other.

At the moment, both quantum Hall experiments do not have any practical use, according to Oded Zilberberg, a professor at ETH Zurich who oversaw both studies. However, the International Business Times noted that papers could give scientists a better idea of where to start when researching the fourth spatial dimension. The studies could also offer more clarity with regards to the string theory, which, in part, suggests that there might be more than just four dimensions of spacetime.