How is 4D space affected by time?

Quantum effect in the fourth dimension

Double breakthrough: For the first time, physicists have succeeded in an experiment that has long been considered impossible. They succeeded in demonstrating a four-dimensional variant of the exotic quantum Hall effect. This quantum mechanical phenomenon has so far been postulated theoretically, but has long been considered to be undetectable experimentally. Now two research groups have made the leap from two to four dimensions.

We live in a world with three spatial dimensions - at least only these can be grasped in everyday life. But in search of a theory that combines gravity with quantum mechanics, physicists have been discussing since Albert Einstein whether there might be other dimensions in the universe. Proponents of string theory even assume ten or eleven dimensions.

Quantized voltage

The problem with this is that such additional dimensions and the processes that take place in them are not visible or tangible for us - actually. Now, however, two research teams have succeeded in producing a physical phenomenon that normally only occurs in four dimensions in a two-dimensional experimental setup.

Both experiments dealt with the so-called quantum Hall effect. It occurs when electrically charged particles move in a two-dimensional plane that is exposed to a magnetic field. Due to the Lorentz force, an electrical voltage is generated perpendicular to the direction of the current. The special thing about it: At ultra-cold temperatures and strong magnetic fields, this voltage does not rise continuously, but quantized - in discrete steps.

A question of topology

This surprising effect is related to the topology of the quantum mechanical wave functions that describe the behavior of the ultracold electrons. For certain strengths of the magnetic field, they can only flow on very specific paths. This quantum Hall effect could only be observed, however, if the electrons can only move in two dimensions - at least that's what people thought.

But the theoretical physicist Oded Zilberberg from ETH Zurich saw it differently: 20 years ago he predicted that the two-dimensional quantum Hall effect could be given additional virtual dimensions under special conditions. Theoretically, there should therefore also be a 4D quantum Hall effect.

“Back then it was more like science fiction,” explains Zilberberg. “Because actually observing something like this in experiments seemed impossible - physical space just has three dimensions.

Couplings in the light guide

But the supposedly impossible experiment has now been successfully carried out by two research teams. For this purpose, Zilberberg and his colleagues first burned a two-dimensional grid of serpentine waveguides in a glass block with laser beams. Depending on the distance, light that has passed through this grating can more or less easily jump into an adjacent waveguide.

The highlight: the constantly changing couplings between the waveguides influence the behavior of the particles as if they were moving in four dimensions. As the researchers observed, this makes the edge states characteristic of the four-dimensional quantum Hall effect, in which light only emerges from the waveguides at the edge of the grating, directly visible.

Two superimposed laser grids form a kind of light crystal in which atoms sit. Their reaction to shifts proves the 4D quantum Hall effect. © LMU / MPQ

Atoms in the laser lattice

In the second experiment, Immanuel Bloch from the Max Planck Institute for Quantum Optics and his team used ultra-cold atoms to demonstrate the quantum Hall effect in 4D. To do this, they caught a cloud of ultra-cold atoms in a two-dimensional optical lattice made of laser beams. The researchers then radiated further laser beams of a different wavelength in both directions and shifted the two grids against each other in a special way.

By measuring the two-dimensional movement of the atoms in the lattice, the physicists were able to confirm that they behaved according to the quantum Hall effect in four dimensions: the atoms moved both in the direction of the modulation and transversely to it - and both movements were quantized.

Exciting for basic research

The practical use of it all? “At the moment, these experiments are still miles away from useful applications,” admits Zilberberg. But they represent an important step forward for basic research. Physicists can now investigate not only on paper but also experimentally what effects phenomena from four - or even more - dimensions can have in our everyday three-dimensional world.

An example of this are quasicrystals in metal alloys. In three spatial dimensions these do not have a periodic structure, but if you look at them in virtual higher dimensions, they again show regular patterns. And finally there is the string theory, according to which higher spatial dimensions should be “compactified” in such a way that in the end our normal three-dimensional world emerges. (Nature, 2018; doi: 10.1038 / nature25011, doi: 10.1038 / nature25000)

(Swiss Federal Institute of Technology Zurich, Max Planck Institute for Quantum Optics, January 5, 2018 - NPO)

5th January 2018