How About That Fourth Dimension?

Dimensions is a fairly complex and often misunderstood topic in everyday life. Usually, different people have different ideas about what the word means, sci-fi and comic books being involved in the confusion as well. Let’s talk about it this way:

In this universe, in this reality, we perceive three spatial dimensions (plus one dimension of time, but that is not spatial); those dimensions being height, width, and depth. In mathematics, we often use lower dimensions in our calculations, but let us start from the beginning.

Dimension 0 is a point of no width, no depth, and no height; it has no dimensions and it cannot be measured.

The first dimension, is simply a line. That line only has one attribute, whichever it is (for example, length).

From lines, we get a plane, which contains the dimensions of length and width, but no height. The edges of the 2-Dimensional plane are 1-Dimensional lines.

From 2-Dimensional planes, we get our 3D structure, which contains all the attributes that we find in our perceived reality. Even the seemingly flattest object (like a sheet of paper), has those three dimensions. The perfect example of a structure like that would be a regular cube, the edges of which are 2-Dimensional planes.

Now, you’re going to have to use your imagination a little bit. I am now going to ask you to think of an extra attribute we can add, basically an extra dimension. Think of yourself floating in an empty space, able to move around in any and every direction. Up down (height), left right (width), forward backward (length). Every movement you make, is a combination of these three. Try to imagine yourself moving through a line, that is neither of those, a new dimension. You probably find it tricky, but there’s nothing to worry about. It’s simply because our 3D wired brains have not evolved to think in higher dimensions than the one we are accustomed to.

But then, how do we picture the 4th spatial dimension? Notice how we went up to scale step by step, from a point to a line, to a plane, and finally a cube. The edges of a 2D plane are 1D lines, and the edges of a 3D cube are 2D planes. Starting from there, we know that the edges of a 4D hypercube must be 3D cubes. Now, don’t leave yet! I promise it’s not that difficult once you grasp the basics.

Pictured above, is a structure known as a hypercube or a tesseract. A regular cube can spin and move alongside the X, Y, and Z axis. A hypercube does so in one extra. Admittedly, that’s only the shadow of it, since we can’t exactly see into the fourth dimension, or even visualize it. But, in order to grasp the idea behind it, it does its job pretty well. Just like a 3D object leaves a 2D shadow, so we expect a 4D object to leave a 3D shadow; and it’s that shadow that is studied.

Now that we’re done with the basics, let’s get on with the complicated stuff.

Any experimenting involved in trying to show the fourth dimension are partly theoretical and really complex, and rely on Quantum Mechanics.

From Science Alert:

By placing together two specially designed 2D setups, two separate teams of researchers – one in Europe and one in the US – were able to catch a glimpse of this fourth spatial dimension through what’s known as the quantum Hall effect, a certain way of restricting and measuring electrons.

“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,” a researcher with the US-based team, Mikael Rechtsman from Penn State University, told Ryan F. Mandelbaum at Gizmodo.

Even though we cannot see the 4D object itself, we can study its shadow, which could potentially unlock new fundamentals in science.

From Gizmodo:

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.
What is the Hall Effect?
What is the Quantum Hall Effect?

Thanks to these calculations that won the 2016 Nobel Prize in physics, we are aware that the quantum hall effect points to a possible fourth dimension. What these new experiments do, is give light to the possible effects that this fourth spatial dimension might have.

The European’s team setup, involved atoms cooled down to near absolute zero and placed on a 2D lattice, through the use of lasers.

With extra “lasers”, they were able to excite the atoms and get them moving. The slight variations on their movement matched the ripples that would be caused by a 4D quantum hall effect, getting us closer to the possibility that a higher dimension can somehow be accessed.

The US experiment, although different, also put in use lasers. But this time, they were controlling the movement of light through a block of glass. The light was manipulated to stimulate an electric field on charged particles, and gave similar results to the European findings; the consequences of 4D quantum hall effect were observed.

We can’t exactly travel to this fourth dimension (yet), but at least we can get a picture of it, by means of quantum physics, and widen exponentially our limited view of the universe. The researchers want to build on these studies, to take a closer look, and maybe explore even more advanced physics along the way (as if this wasn’t complex enough). And maybe, just maybe, some day in the future, we can at least catch a glimpse on this dimension, and be able to explain to near perfection how it works.

For a better understanding of the fourth dimension, click here.

To read the findings of both the US and European researchers, click here, and here.

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