Graduate Student Proves a Quantum Uncertainty Principle for Fractals

Quanta Magazine ^ | 08/12/2026 | Shalma Wegsman

[BenLurkin]

At the quantum scale, tiny particles behave in bizarre ways. One reason for this is the uncertainty principle, which says that the more you know about where a quantum particle is, the less you can know about how fast it’s moving, and vice versa.

The new uncertainty principle relates to fractals, shapes that remain equally complex no matter how much you zoom in on them.

Around a decade ago, Semyon Dyatlov was studying whether quantum particles behave differently than ordinary particles when put into the same chaotic situations. Sometimes, an object moving chaotically can become trapped into following a fractal-like path forever. Could quantum particles do the same?

Quantum particles tend to spread out like waves, which blurs their exact location. To figure out whether quantum particles blur too much to take on these intricate trapped paths, Dyatlov needed a new uncertainty principle — one that could tackle fractals.

In 2016, with key ideas from Jean Bourgain — a renowned mathematician — Dyatlov proved the fractal uncertainty principle for one-dimensional fractals, which look like jagged lines. These lines can represent the paths taken by objects moving in two dimensions, like balls traveling around a billiard table. That fall, Dyatlov and Bourgain gathered mathematicians from ar1ound the world in New Jersey for a workshop, hoping to extend the proof to higher dimensions. An extended proof could be used to study the three-dimensional world and would become a universal mathematical tool in its own right.

But the task proved too difficult.

It wasn’t until years later that Alex Cohen, while a doctoral student at MIT, finally made a breakthrough. In a paper published in 2025 in the Annals of Mathematics, widely considered to be the field’s top journal, he extended the fractal uncertainty principle to all higher dimensions.

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TOPICS: Astronomy; Science
KEYWORDS: astronomy; physics; science; stringtheory

[BenLurkin]

[Dr. Sivana]

Heisenberg!

[dfwgator]

[SMARTY]

So there is a real university with real scholars ???

[Nateman]

I can still remember when the Mandelbrot set was discovered. Amazing that this infinite complexity can arise from a simple repeated equation.

[SunkenCiv]

Thanks!

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[tired&retired]

I love to view the videos created with the mathematical models.

I attended a presentation by a math professor from the UK on this topic at a conference in Italy a few years ago. Absolutely amazing.

There are lots of YouTube videos on this subject.

[Teflonic]

I can see it being perfect for AI brain mapping - infinite categories and subcategories to index data storage for faster recall.

[Honorary Serb]

Three cheers for my undergraduate alma mater, MIT!

I am a mere biologist, and understand none of this stuff! I did well enough in calculus and differential equations to get a hard-won B in MIT physical chemistry (when many were getting Ds and Fs), and to make a certain mathematical determination of molecular weights as part of my Harvard PhD thesis. But I’ve forgotten most of my mathematics because of disuse, and could never tackle fractals!

Perhaps this researcher deserves a Fields Medal. We’ll just have to wait and see!