Chaos: The real problem with quantum mechanics

You have probably heard people saying that the problem with quantum mechanics is that it's non-local or that it's impossible to understand or that it defies common sense. But the problem is much simpler, it's that quantum mechanics is a linear theory and therefore doesn't correctly reproduce chaos. Physicists have known this for a long time but it's rarely discussed. In this video I explain what the problem is, what physicists have done to try and solve it, and why that solution doesn't work.

And you can find a brief summary on Sean Carroll's blog

0:00 Intro
0:27 The trouble with Hyperion
4:04 The alleged solution
6:02 The trouble with the solution
7:46 What a real solution requires
10:31 Sponsor message

[BigZebraCom]

I was going to solve the problem of Quantum Mechanics--but then things got really busy at work.

[georgH]

"poor thing" barely 10 seconds in and I'm already laughing out lout :D
I love your physics videos, your style, and how well you explain your point! Best science channel!

[DallasMay]

Sabine: "Quantum mechanics has been falsified."

Me: "IS NOTHING SACRED WITH YOU!"

[rickkearn]

I can't thank Sabine enough for the excellent service she provides to her viewers and subscribers. No other science channel like this. I watch every post, mesmerized. Cheers.

[GamingDemiurge]

This video is brilliant. This is something it is not talked about in any classroom I'm aware off. Thanks Sabine for bringing this up, I had no idea.

[quantumbrick]

Dear Sabine,

I enjoy your videos a lot, but quantum chaos is my field of expertise and I have some comments:

2:50 The statement that linear equations don't allow for classical chaos is correct, but classical mechanics can be formulated in terms of classical probability densities. The corresponding Liouville equation for the whole probability density is linear, even though each point that composes it follows a chaotic trajectory. In the end the main distinction from classical and quantum mechanics regarding this point is that the latter does not allow for a local description, i.e. one cannot formulate a quantum theory for just a piece of the wavefunction, while in classical mechanics this is precisely the whole point.

3:25 Your definition of Ehrenfest time assumes that classical and quantum mechanics start to disagree due to classical chaos. This is incorrect. Disagreement is due to the onset of quantum interference in quantum mechanics that cannot be reproduced classically. The distinction between chaotic and integrable systems is only in the Ehrenfest time itself: for the latter, it scales linearly with the characteristic action of the system, while for the former the expression involves Lyapunov exponents. Only for completely hyperbolic systems the Ehrenfest time is zero, but these systems are essentially impossible to find in nature... Generally, phase space is a mix between integrable and chaotic regions, and depending on where you "drop" your initial state, the Ehrenfest time can be very long (near a stable equilibrium) or very short (near a homoclinic tangle).

In my opinion, your transition between quantum chaos and open systems / the measurement problem is very hard to follow. At least for me, those are separate matters that don't necessarily need to be considered together.

Last but not least: The first person to inquire about the quantization of chaotic systems, believe it or not, was Albert Einstein. In 1917, before the Schroedinger equation, Komolgoroff-Arnol'd-Moser theory and a proper definition of chaos, Einstein wrote a paper where he stated that quantizing things that were not regular was a big problem. He forgot about this, the paper was ignored, and only 60 years later it was rediscovered by Moser. The problem of quantum chaos, therefore, is 105 years old. For an excellent and accessible story check Douglas Stone's review "Einstein’s Unknown Insight and the Problem of Quantizing Chaos" in Physics Today (2005).

[danieljones]

I never heard about this even though I have read a lot of layman material on QM. I love your channel it is so interesting.

[sjzara]

This is a rare video that actually shocked me. If quantum mechanics has a problem with a moon, how can some physicists talk of the “the wave function of the universe”?

[MaryAnnNytowl]

The way you explain things is so helpful, even when I just barely understand the hard stuff, and my brain melts out of my ears on the most complicated stuff. 😄 Still, I do learn things here, and that's what I'm here for - aside from you, the amazing Sabine, that is! 🖖🏽 ❤️❤️ 👍🏼

[Gismho]

Excellent series of videos. This lady really makes science extremely interesting. The descriptions are concise and highly intelligible/comprehensible.

[robertperry]

Sabine, you do an awesome job at explaining concepts that I've always struggled to understand. I always enjoy your videos. Thanks for the great content!

[Ambienfinity]

Mind-boggling, well explained by Sabine, who always casts light on these shadowy problems.

[halleuz]

I took Quantum Mechanics I & II at the University of Heidelberg. Nobody said anything about this problem. Thank you, Sabine!

[davidhand]

I've always been fascinated with the idea that the uncertainty principle and some undiscovered chaotic component modifying the Schrodinger equation could account for the apparent randomness of QM. As I've studied, though, I've been steadily dissuaded. I can't believe it took this long for someone to tell me about this neat wrinkle. It gives me a new way to approach the problem. Thanks for spilling the beans, Sabine!

[blinkingmanchannel]

Dude! This is awesome!

Congrats on reaching a million subscribers, by the way!

I think you should START any explanation of ‘quantum mechanical stuff’ with this video. For me, this generated that big “click” sound in the back of my mind!

I once wrote you that each time I reach a phase of formulating reasonable questions, I find another of your videos that takes me forward. This is yet another such example!!! Well done!

I can see that I’m not asking the questions in the right order, so I know I’m not really understanding as I should, but this one gets me “over the hump” of doubting myself in questioning the magical-ness of entanglement. This is the “back up and take a breath” moment I needed! Phew! (Heuristics wins, over math, if there’s a conflict.)

So for me, this video means I can now sleep soundly in the knowledge that we have a few hundred years of playing around with batteries in the lab before we can reach another plateau from which to leap for the next big insight. In the mean time, I’m okay with using probabilities to make predictions in a range… And when we have an application for better predictions, we will be in a position to make more useful observations too. Peace.😅

Keep going! You’re awesome!

[juanrobles]

Sabine Hossenfelder is doing a good job of questioning many theories that many accept as a law, the reality is that much remains to be learned and we have no answer from the cosmos or the microcosm.

[fez]

if it wasn't for you how would we know these kinds of things?! Keep up the good work👏
essential content/information indeed!

[CAThompson]

Like Hyperion, my own orientation is somewhat chaotic. 😀
This is a fascinating way to approach the problem.

[jimmyzhao]

What a great way to start my Saturday morning. Coffee & Quantum Weirdness.

[Animatthias]

Dear Sabine, I'm sure I'm not the only one who would pay for a private Q&A about Physics with you. You could record those and turn the BestOfs into great videos again. Maybe that would further bridge some gap between professional and public understanding. Thanks so much for all your insights and your clear communication!