This Is What Happens To Quantum Physics In Between Dimensions

 

Science is no stranger to weird, unintuitive results, but for factual discombobulating strangeness, you just can’t beat quantum mechanics. Considering physics on the subatomic scale, it sometimes seems more philosophy than science – and sometimes the questions seem even more baffling than the answers.

 

In a research published in Nature Physics, they studied the intriguing quantum behavior of subatomic particles when organized in geometric structures known as fractals.

 

Fractals are one of the most bonkers and stunning concepts in math. They are basically shapes that show something called “self-similarity”: you can zoom in on any part, as far as you can, and you will always see the same primary shape.

 

Even if you haven’t done mathematics since high school, you’ll still have come across them – fractals. We can witness them in the shape of galaxies and the orbits of planets, and in winter they fall from the sky in shape of snowflakes.

 

The Koch Snowflake. Open Source

Zooming in on the Koch snowflake reveals its self-similarity. 

One of the most mind-boggling properties of fractals is their dimension. We’re used to the dimension of an entity being very straightforward: we live in a three-dimensional world, whereas drawings on paper, with the citizens of Flatland, make do with two. But fractals do not play by the usual rules: they can have dimensions that aren’t whole numbers. The dimension of a Koch snowflake, for example, is 1.26186.

 

The Sierpinski triangle is one of the fractal. It is created by taking a triangle, splitting it into four equal parts, and taking out the central section. Then, for each smaller triangle, you do the exact same.

 

 

The evolution of the Sierpinski triangle. 

Using a little mathematical experience, it’s probable to prove that the Sierpinski triangle has a dimension of log23 – approximately 1.58.

 

Now, fractals are all pretty well in the world of math, where infinite limits and theoretical logic can replace the laws of physics, but in the physical world, there’s a limit to how small things can get. So the researchers looked at what would happen if they assembled a real-life Sierpinski triangle that was fractal all the way down to the level of singular electrons.

 

First, they built a frame made from carbon monoxide particles. Electrons were then positioned in this atomic “muffin tin” in the shape of the Sierpinski triangle.

 

 

Electrons in bonding (left) and non-bonding (right) Sierpinski triangles. Kempkes et al./Nature Physics, 2018

Electrons are present firmly within the world of quantum mechanics, and unlike objects directed by classical physics, they can only take on definite energy levels. So, by stating a particular energy level, researchers can fix an electron to a particular state. Using this method, scientists could image the wave functions related with the particles at different energy levels.

 

Once they had the wave functions of the triangle at these different states, they determined their dimensions – and they found something thrilling. The electrons had inherited the fractal dimension, acting as if they were living in 1.58 dimensions – just like the Sierpinski triangle.

 

"From a theoretical viewpoint, this is a very remarkable and revolutionary result," described study co-supervisor Cristiane de Morais Smith. “It opens a whole new line of study, raising questions such as: what does it actually mean for electrons to be limited in non-integer dimensions? Do they act more like in one dimension or in two dimensions? And what happens if a magnetic field is turned on vertically to the sample?

 

“Fractals have a very large number of applications, so these results may have a big influence on research at the quantum scale.”

References:

https://www.nature.com/articles/s41567-018-0328-0