Let’s Learn Quantum Mechanics: Project Complete!

Yesterday morning, I finished my month-long project to get a good foundation in the basics of quantum mechanics.

I had picked this project for two reasons. First was because I knew it was going to be a challenging class and the idea of understanding the strange rules which govern all of reality has fascinated me for years. Second, because I wanted to try livestreaming an ultralearning project from start to finish.

How Did The Project Go?

I was happy with the outcome for the project in both counts—for learning quantum mechanics and for livestreaming.

I wrote a final exam for 8.04 – Quantum Physics I, the class I benchmarked for the project. The score on the exam was around 60-65%. This was complicated by the fact that about 10% of the marks were for material that hadn’t been covered in my session. Worse, I made a silly mistake (I read a question as u0 + u1, when it was u0 + u2), that made my answers wrong for multiple questions, losing around another 15%.

The class was difficult, and it took more time than I had initially expected. I had expected to put in around six hours per weekday on the project, but I ended up putting in more like seven. A lot of that difficulty came down to being rusty with a lot of the advanced calculus techniques I hadn’t practiced since the MIT Challenge, so getting caught up consumed more time than simply learning the class from scratch.

That being said, I do feel like I learned the material taught in 8.04 reasonably well. What was missing, however, was all the stuff taught in later quantum mechanics classes, such as 8.05, 8.06, and the theories which combine relativity and multiple particle interactions.

I didn’t think those things would be too important, but it turns out that a lot of the weirdness of quantum mechanics only appears once you start considering interacting particles and relativistic corrections.

I’d like to keep learning those extra classes, but as those classes don’t have any solutions to the assignments or exams, I may have more difficulties learning them the way I could with this class.

How Was Livestreaming?

I really enjoyed livestreaming the project, and I liked how it shifted the focus of the project in a new direction. The environment and passive constraints around any project often make subtle adjustments to how you approach things.

For instance, if you’re taking a class at school, the pressure to get a good grade and pass the class changes how you would learn than if you were learning to get a practical skill at work, or purely for curiosity.

My own projects in the past, too, have been influenced by those factors. Because my projects tended to culminate in some kind of bigger before-and-after write-up, I often designed projects that would work well in that format. That meant I often focused on learning things from scratch (to make the before picture clearer) and where there was an easy-to-recognize benchmark of success at the end.

Livestreaming, in contrast, is much more process oriented, so I could see it working well for tackling projects which have more ambiguous starting and end points. Some types of projects I’ve hesitated to turn into public challenges (because they don’t work well in the previous format I’ve used) might become viable, such as doing deliberate practice for skills I’m already decent at, or showing slices of learning efforts rather than complete projects.

What Did I Learn?

One downside of this project (especially for a livestream) is that if you don’t have enough math background, what I’m doing at any moment is often completely opaque. The language of quantum mechanics is written in complex valued differential equations, functional inner products and operator notation, so it’s not always clear exactly what I’m learning or doing at any moment if you haven’t followed from the beginning.

I wanted to try to mitigate that by, at the end, having a non-mathematical description of what I had learned. This is a bit foolhardy for two reasons. The first is that if a completely non-mathematical description of quantum mechanics were possible, there wouldn’t have been much need for me to learn this class in the first place.

A big part of my motivation for learning this class intensely was that I believe knowing the math is necessary, in some sense, to really understand how it actually works. Some ideas which seem disconnected are actually logical consequences of a simpler set of rules once you know the math.

The second difficulty is simply that, having only done 8.04, I’m still missing many pieces of the puzzle that would be needed to make the big picture. Trying to give a high-level summary while missing some pieces is risky, since I could give a misleading impression due to my own gaps of understanding.

Since quantum mechanics is so strange, it’s easy to grasp onto simpler, more intuitive understandings if you don’t know the reasons why those intuitions are actually incorrect. The world is full of bad quantum mechanics intuitions used as nonsense explanations for all sorts of pseudoscience, so I hesitate to add to that pile.

Therefore, if you want to really understand quantum mechanics, I recommend watching Richard Feynman’s (brief) lectures which introduce the subject far better than I could and do so without using any math harder than squaring a number:

I will try to summarize some of my intuitions about quantum mechanics, if only for the purposes of showing what I spent the last month trying to learn, rather than to pretend to have a complete understanding of all quantum phenomena, in a follow-on post.

I’ll also try to piece together some highlights/discussion from my actual recordings throughout the month-long learning efforts. This will take me awhile to process though, and I wanted to publish my thoughts on the project without too much delay after finishing it.

Overall it was a fun (and hard!) project, and I appreciate everyone who dropped by to follow along, offer encouragement of ask questions during the month. I’m excited to try new projects like this in the future, and to keep learning more about physics and quantum mechanics.