Hacker News

"In 2017, Dyatlov and Long Jin from Tsinghua University in Beijing used the one-dimensional fractal uncertainty principle to prove that you can never trap a wave on a hyperbolic surface; it will always spread out until it touches every corner. To do so, they imagined a region on the surface that a wave never enters, even after having infinite time to spread out. When they removed all the trajectories that entered that region, what remained was the same sort of fractal dust that appeared in the pinball example. Since the fractal uncertainty principle forbids a wave from being trapped on a fractal, no such region can exist — the wave must spread everywhere."

As a non-mathematician this is a wonderfully evocative summary. I'm curious if mathematicians find it a reasonable characterization of the proof.

For those that aren't aware, the uncertainty principle goes pretty deep. You can actually define the uncertainty principle as an inequality involving the integral of a function vs the function's Fourier transform: https://en.wikipedia.org/wiki/Uncertainty_principle#Harmonic... . And in a quantum system you can construct the momentum of a particle as the Fourier transform of the position (up to a constant) and the uncertainty principle falls out because of this. This article doesn't state that super explicitly. So the real interesting thing being done here is getting a Fourier transform that works on fractal spaces.

I'm not very good at math, and I read quantum physics in lay-books, but I would like to say that whoever wrote the article did a good job leading to where it was going (even if maybe not clear to me), I ended up thinking "Square root of -1" and then a few paragraphs later, there it was...

This could have just been a lucky guess, but I feel like the way they presented it my intuition understood what was happening though I can't mentally see/grok it. I think making music and messing with waveforms in synths also helps to understand this intuitively more than the actual math.

I would like to credit "The Theory of Almost Everything" by Robert Oerter for explaining it in a way I could understand 15 years ago https://www.goodreads.com/book/show/183207.The_Theory_of_Alm...

Great book with the history and explanation of a lot of quantum stuff, without being huge like Brian Greene's books (which I also love).

As a physics layman I find it fascinating how quantum mechanics are tied to information theory.

For example, take quantum decoherence (which, IMHO, is the most logical explanation for the collapse of the wave-function - by saying it does not actually collapse). Quantum decoherence is almost like a giant constraint resolution system - once a particle randomly interacts with another they become entangled and both now have fewer degrees of freedom. When it interacts with many particles, like any macro-effect it has essentially no degrees of freedom anymore. It's all about who knew about what and when. The experiments around this fascinating. (Note that there are other theories, like the many-worlds interpretation, that also explain the collapse of the wave function)

This seems to be another example of this. Anyway, as I said, just a layman.