If there are two words dear to every sci-fi nerd’s heart, they are quantum and fractal. How many sci-fi tropes have been created over the past thirty years just by adding one of these words to the front of some other, more pedestrian word? “Quantum drive.” “Quantum torpedo.” “Fractal encryption.” “Fractal-verse.”
So, when I stumbled up this article, “Graduate Student Proves a Quantum Uncertainty Principle for Fractals,” whose title has both “quantum” and “fractal” in it, I clicked immediately. And, after reading the first few paragraphs, I realized two things. First, this must be a truly momentous discovery. Second, it’s really, really cutting-edge, so much so that it doesn’t have many YouTube videos devoted to it, nor even a Wikipedia page.
The article describes how a young physicist, Alex Cohen, who was a grad student at the time, published a paper last year which proves “the fractal uncertainty principle to all higher dimensions.” To break that down a bit, the fractal uncertainty principle is an application of Werner Heisenberg’s famous Quantum Uncertainty Principle—which states that certain combinations of quantum properties such as momentum and position cannot be accurately measured at the same time—to fractals, those mesmerizing, infinitely-repeating mathematical structures that look the same no matter how far you zoom in or out on them.
Of course, at first glance, the two concepts seem completely opposite to each other. The uncertainty principle illuminates the limitations of measurement and predictability, while fractals describe completely pre-determined, unchanging patterns that continue into infinity. What gives?
It seems that ten years ago, another young nerd named Semyon Dyatlov studied how chaotically moving particles (like the molecules in a gas) can sometimes—if they are occupying a one-dimensional fractal geometric plane—get trapped in a fractal-shaped rabbit-hole, following a fractal path forever. Dyatlov wondered if quantum-based particles (such as electrons or photons) could also become trapped in such a rabbit-hole. As it turns out, they cannot. He proved this mathematically while, at the same time, creating a brand-new concept in physics: the Fractal Quantum Uncertainty Principle, orFUP. (A rare, math-heavy video on the subject is pasted at the end of this post. Watch it if you dare.)
Dyatlov’s brilliant work put paid to the question of quantum particles in a one-dimensional plane. But what about worlds with, you know, more than one dimension? Like ours, for instance?
Turns out, the math to handle this question is extremely friggin hard—even for guys and girls who understand one-dimensional fractal manifolds. As a practical matter, the problem might even be impossible.
Well, you know the old saying about what happens whenever a person (usually a very learned, respected old man) says something is impossible; some young whippersnapper comes along and does it. That’s what occurred last year when an MIT doctoral student wrote a paper proving the FUP in all dimensions. Pretty cool, huh?
Of course, I have no idea how Mr. Cohen actually proved this. I doubt he could explain it to me, even if I gave him a year or two of my full attention and an infinite supply of crayons. But I suspect that his proof will turn out to be a huge, consequential discovery, one that will eventually have real-world, practical applications. After all, I don’t believe there is such a thing as pure science. Every time a branch of intellectual study is labelled as “useless,” someone finds a way to use it—and often with world-altering consequences.
Even if Mr. Dyatlov’s and Mr. Cohen’s discoveries fail to bear practical fruit in my lifetime, I’m sure that all the new science and mathematics that springs from it will be beautiful to behold. If you’re smart enough to understand them.
Which, alas, I am not.
Ash Clifton, Writer 