Tuesday, January 9, 2018

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.


  1. Somewhere down about the level of an atom or maybe just below neutrons, protons, and electrons, "normal" no longer exists. Personally and with only minimal experience and education (sub-PhD level) in sub-atomic physics, I feel there's a "new" theory on Unified Fields relating these events waiting to be discovered.

    A fascinating world - one my path and time only touched upon the outliers. Maybe different if I were 18 today.

    Today's version of quantum theory may be only the door and perhaps we've only stuck our heads into the darkness to see what's there - but when the light turns on, I think that "name" will do to Einstein's world what Einstein did to Newton's world.

    I also think this ties in with my no-more-than-a-hunch that we don't understand what we call time, the speed of light is constant only because we've declared it so (like GND is 0V only because we've defined it so), and the universe is far, far weirder at both micro and macro scales than the most imaginative SF writer - or theoretical quantum physicist - has even a hint of.

    But that's just me.

    Per snow in FL: I was at UF in Gainesville. It's colder in Florida when in the mid-20s than the same temp up around the Great Lakes ... perhaps due to it being expected weather and better preparation up there. I got >cold< - no insulation in the place I was living ... and I didn't have winter gear with me. But it was fun (in a joyful sense) watching adults experience snow for the first time.


    1. We took a vacation to Brian Head, Utah, long enough ago that I don't remember the year. We got talking with the guy running the ski shop and when he found out where were from he said he had been near here and felt colder in Florida than he ever did in Utah. His take was that humidity makes it soak in worse.

      I've seen that said elsewhere.

      As for quantum weirdness, I understand that what you're saying is strictly opinion and can't be based on data, but I think you're more likely right than not. There's a tremendous tendency for people to think "we know so much more now!", but I just think of the way that has turned out historically. Like how a little over a hundred years ago, there was talk that physics was Done. Everything nicely tied away, with just a few little oddities to settle - the oddities that gave us the 20th century, quantum theory, relativity, and a few "little jots and tittles" like that.

  2. Just draw a line that intersects our three dimensions, and is also simultaneously perpendicular to all three, and there's your fourth spatial dimension. Piece of cake.

  3. The potential for additional dimensions that abut Hall Space (call it the fifth dimension but plz don't sing "Age of Aquarius") is considerable and the math exists to describe it. Finding a way to "observe" it and test the math and the theoretical physics is a challenge. That it's not one of those 6 dimensions of 'curved space' that exist at Planck Length makes it more interesting, and potentially more understandable.

  4. Everything is geometry, is you look closely enough. Quantum field theory has been held back for decades by the Copenhagen interpretation problem, and the purely mathematical approach of many physicists. They can do the math, but, fundamentally, they really don't understand what is going on.

    The same applies for many electronics engineers, of course. The math works, and that's all most of them need to understand. It's a shame that so many people can't see the beauty of the geometry - it's there in the oscilloscope and the spectrum analyzer.

  5. What I took from that reading was not a 4th spatial dimension, but a 4th-dimensional analysis technique for the existing 3 spatial dimensions.

  6. I dunno, they flash a laser, something goes 'bloop' and all of a sudden its " Oh, here's the fourth dimension, here's warp drive, here's teleportation!" No, here's something going 'bloop' when you shine a laser at it!
    Of course, the most common use of the Hall effect is electronic ignition systems IIRC.

  7. Trying to visualize thing that can't be visualized is a waste of time and effort. (In mathematics, we constantly deal with many more than 4 dimensions.) Just stick to the math. It will tell you things if you try to understand it on its own. (Which it sounds like what they did to win the Nobel.)

  8. Quantum physics spends a lot of time doing math in a higher number of dimensions (10 springs to mind for some reason) and then spend a lot of time and effort to renormalize to 4 dimensions - maybe now 5) but it begs the question of why limit ourselves to 3 (or 4) spatial dimensions.

    1. In math, people spend a lot of time doing problems in much higher dimensions. Occasionally something like a Rubix cube will come along and illustrate a particular example (That is an 8 dimensional space modded by a 12 dimensional space - very limited in terms of excepted values), but mostly you learn to just pay attention to what the math is trying to say without trying to visualize things that can't be visualized.

      Why do we remember the past and not the future?

    2. ...it begs the question of why limit ourselves to 3 (or 4) spatial dimensions. I think there's a human tendency to try figure out what it means in terms of things we have in our experience base. I think there's an Einstein quote along the lines of "common sense is the deposit of our prejudices laid down before the age of 10". Some of what we learn in science and engineering doesn't seem to gel with common sense, but we try to visualize it nonetheless.

      Certainly in math we can do any number of dimensions, but this stuff has to be experimentally verified or else it isn't really telling you anything about the universe. It's just math for math's sake. Not that there's anything wrong with doing math for math's sake, but if you're trying to understand the physical world it distracts you from it.