New Results in Physics Imply A Fourth Spatial Dimension

I'm going to go out on a limb and guess that many of you have heard of something called the "Hall effect" exists.  Hall actually discovered this in 1879, before the electron was discovered, but he found an effect on electrical current caused by a magnetic field perpendicular to the direction of the current.  Today, you can buy Hall effect devices off the shelf from a number of electronic semiconductor makers, such as Texas Instruments.

Although the "everyday Hall effect" is something a lot of Makers and hobbyists play with, there's also a quantum hall effect in which the conductance becomes quantized in discrete levels.

Thanks to some rather advanced calculations – which won the Nobel Prize for Physics in 2016 – we know that the quantum Hall effect points to the existence of a fourth spatial dimension.

Fourth spatial dimension?   By now, most people have heard of considering time as the fourth dimension: we have one dimension for movement left/right, one dimension for forward/backward, one dimension for up/down and the fourth dimension is time.  But time isn't a spatial dimension.  We know two things can't be in the same place at the same time.  They can occupy the same place at different times, but time isn't spatial, it's like a separator flowing (in some sense) independent of the XYZ space.  You may have heard something like the quip, "time keeps everything from happening at once".  It's another property of what we call spacetime. 

So what's a fourth spatial dimension?  It's trivially easy to introduce a fourth dimension in math, but we can't really see it.  While we can't see it, we can see effects that using the fourth dimension predicts would happen.  I turn here to Gizmodo which posted this review of the evidence for it.

This isn’t a fourth dimension that you can disappear into or anything like that. Instead, two teams of physicists engineered special two-dimensional setups, one with ultra-cold atoms and another with light particles. Both cases demonstrated different but complementary outcomes that looked the same as something called the “quantum Hall effect” occurring in four dimensions. These experiments could have important implications to fundamental science, or even allow engineers to access higher-dimension physics in our lower-dimension world.

“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,” Mikael Rechtsman, professor at Penn State University behind one of the papers, told 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.”

To borrow a concept from the classic book Flatland (which isn't about my home state) imagine how beings living in a 2-dimensional world might experience a three dimensional object.  They couldn't understand a cube; if they encountered it,  they would see its projection, its "shadow" in 2D.  They would see a line and when they tried to go around it, they'd encounter another line to get past.  A sphere could be anything from a point to progressively bigger lines, depending on where the sphere intersects flatland, and would look like a line as a 2D being tries to get around it.

In other words, just as a 3D object casts a 2D shadow, scientists have managed to observe a 3D shadow potentially cast by a 4D object – even if we can't actually see the 4D object itself. That could unlock some new findings in the very fundamentals of science.

In the same way, the physicists are seeing the projection into our three dimensional world of things happening in the fourth dimension.

Confused?  Me, too.  Well, I understand the concepts, but I can't understand what it looks like any better.  Both Gizomodo and Science Alert embed this explanation from a video game.



Gizmodo points out the drawback of these two precisely-engineered systems that display the expected result:

The major limitation of both is that, well, this is not a real four-dimensional system, but two highly engineered systems demonstrating what some effect would look like if it were happening in four dimensions. Both teams have more work they’d like to do in order to study this effect, though. Lohse and Rechtsman told Gizmodo that the atoms and photons in their systems don’t interact with one another. They’d like to see how the effect manifests itself with interacting systems. 

As for implications, Lohse hopes his system could support the study of even wilder physics, like quantum gravity and Weyl semimetals. Rechtsman thought his system could lead to other photonic devices that take advantage of higher dimensional system, or that perhaps they could find other similar effects in other materials.

“There’s another question of whether real solid-state materials with complex unit cells have these hidden dimensions, and if their physics can be understood in higher dimensional physics that wasn’t accessible before,” said Rechtsman. “Could it give us new understanding of phases of matter with complex geometry?”

If you watch that video on YouTube, you'll get links to a few more videos on trying to visualize a fourth dimension.  I liked this one.