Physicists can now investigate not just on paper, but also experimentally the effects that phenomena
occurring in four (or even more) dimensions can have in our usual 3D world
Oded Zilberberg et al Zurich,2018
Ever since Albert Einstein developed the special theory of relativity in Zurich in 1905, by «4D» one usually means time.
But how can one visualize a fourth spatial dimension – in addition to top-bottom, right-left and front-back?
In the arts Salvador Dalí tried that: his crucifixion scene painted in 1954 shows as cross consisting
of the 3D unfolding of a hypercube in 4D (similarly to the unfolding of a cube into squares).
A completely different, but no less fascinating, look into the fourth spatial dimension was now obtained by two teams of scientists from
Switzerland, USA, Germany, Italy and Israel. The researcher Oded Zilberberg, professor at the Institute for Theoretical Physics,
played a pivotal role in both publications, which were recently published in the scientific journal Nature.
He provided the theoretical basis for the experiments in which a 4D physical phenomenon could be observed in 2D.
The quantum Hall effect
Both experiments dealt with the so-called quantum Hall effect. Commonly, that effect manifests in the boundary layer between two materials,
in which electrons can only move in two dimensions. A magnetic field perpendicular to the material initially leads to the classical Hall effect:
a current flowing through the material gives rise to a voltage in the perpendicular direction – the larger the magnetic field, the higher the voltage.
The reason for this is that the magnetic field generates a force acting at right angles to the direction of motion (the Lorentz force)
that deviates the electrons. At very low temperatures and very large magnetic fields, however, quantum mechanics starts playing a role,
which means that the voltage no longer increases continuously, but rather jumps in discrete steps.
Three Nobel Prizes in Physics have so far been awarded for experimental and theoretical work on the quantum Hall effect.
"At the time, however, that was more like science fiction”,
as actually observing something like that in an experiment seemed impossible
– after all, physical space only has three dimensions.” Zilberberg said
Zilberberg had a clever idea: using so-called topological pumps it should be possible to add a virtual dimension to both of the real dimensions
of the quantum Hall effect. A topological pump works by modulating a specific control parameter of the physical system, which causes its
quantum state to change in a characteristic way over time. The end result then looks as though the system had been moving in an
additional spatial dimension. In this way one can, theoretically, turn a 2D system into a 4D one.