This Is What Happens To Quantum Physics In Between Dimensions

Alex Moe/Shutterstock, IFLScience

Katie Spalding 13 Nov 2018, 17:47

Science is no stranger to bizarre, unintuitive results, but for true discombobulating weirdness, you just can’t beat quantum mechanics. Dealing with physics on the subatomic scale, it sometimes appears more philosophy than science – and occasionally the questions seem even more confusing than the answers.

One such question was answered this week by Utrecht University physicists. In a study published in Nature Physics, they investigated the intriguing quantum behavior of subatomic particles when arranged in geometric structures known as fractals.

Fractals are one of the most bonkers and beautiful concepts in math. They’re essentially shapes that exhibit something called “self-similarity”: you can zoom in on any part, as far as you like, and you'll always see the same original shape.

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

The Koch Snowflake. Open Source
Zooming in on the Koch snowflake reveals its self-similarity. Open Source

One of the most mind-bending properties fractals have is their dimension. We’re used to the dimension of an object being pretty straightforward: we live in a three-dimensional world, while drawings on paper, along with the citizens of Flatland, make do with two. But fractals don’t play by the normal rules: they can have dimensions that aren’t whole numbers. The dimension of a Koch snowflake, for instance, is 1.26186.

The Sierpinski triangle is one such fractal. It is constructed by taking (surprise!) a triangle, splitting it into four equal parts, and removing the central section. Then, for each smaller triangle, you do the same.

The evolution of the Sierpinski triangle. Open source

Using a bit of mathematical know-how, it’s possible to prove that the Sierpinski triangle has a dimension of log23 – roughly 1.58.

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

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