Quantum theory based on real numbers can be experimentally falsified

So GHZ is just a name for a specific arrangement that is maximally entangled.

John Preskill has some lectures on quantum computing for the University of Waterloo I believe, also a Hans Bethe lecture at Cornell. If you are just looking for an hour's commitment to understand a little better, I would go with one of those.

If you wanted an actual textbook, Nielsen and Chuang is very popular... The other place I would look would be OpenCourseWare, you might be able to find some good problems to work on there. Sometimes video lectures can be good if you can pause the video right after a problem was introduced and try to solve it yourself before you get the answer from the professor.

The difficulty in being an autodidact is, listening to stories around a campfire is deep in our bones, it makes us feel good. But it's not a very efficient way to learn. So there is a mismatch where watching a TED talk feels like you have just changed everything, but then if I come to you a month later probably nothing has changed.

Text is a lot faster, as a medium. Way slower to write but seekable, skimmable, can contain links to previous sections... I'm pretty sure we also retain more of it. But that's not the main problem with videos/TED talks. Like, the text form of TED talks is someone telling you how monads are burritos and that makes it all better.

It's too clean?

Good learning is messy. A good abstraction allows you to clean up a mess of confusion in your head. This confused mess can only exist if you have created it. So you have to do lots of examples, exercises, memorize strange times when you have been wrong about things and your expectations don't align with the problem domain... If you think about learning a language, there is that phase where you don't know which thing to use when and your words are all out of order in the sentence... Per Ira Glass the only way to improve is to do lots of work, put yourself on a schedule, grind through mediocrity. The TED talk/monad tutorial fallacy is that we can give our children an easier time than we had it. It's BS. We can't. “I made so many mistakes, I will help you so that you don't have to deal with that pain” blithely unaware that the pain was how you learned it, that learning is pain.

Sorry, didn't mean to rant and now it seems awkward to delete it.

What you are proposing is essentially using a different number basis, and the simplest applicable one would be a basis which expresses numbers using whole numbers{...,-1,0,1,2...} times pi. This allows you to exactly express pi as just 1, and all such using only whole numbers which is nice. It also unfortunately means that simple things like y= 1_{decimal} x would have to be expressed using the relative to basis transcendental number pi i.e with precision problems. And every basis you could chose behave like this.

Different basis have different advantages, same as different function basis. The classic example would be that in a standard basis, its easy to add and subtract, but more costly to multiply, divide or factorize, while in the prime basis the former is expensive as hell, but the latter is trivial.

As a result, rationals and pi in a sense disjunct domains. You cannot express either using less less than an infinite number of the other, and the same holds for combinations of a rational and pi. Numbers which behave this way relative to each other are more common than the rationals, and pi is just the most common example.

It does lead to a rather neat requirement for the fundamental physical constants though.

The reasoning goes like this, imagine that a model K2 of physics could be described using two constants, a, b. gravity and the speed of light say. Now lets say we managed to prove that a = 2b and therefore that everything predicted by model K2 can also be predicted by model K1, which just uses the coefficient b. K2 is equivalent to K1, sure, but only one constant would then be fundamentally required, and if K2 is sufficient to describe all of physics, physics would only have one fundamental constant. The same reasoning would hold if a=b^2, and so on. But, if the function required to express a as a function of b requires infinite information, this does not meaningfully apply, as this will always apply to every pair of numbers. Meaning that we know that if the fundamental constants of a model of physics does not lie in disjunct domains in the sense above, there is a simpler version which has fewer constants. For example, since pi has infinite information, if a=pi b, then the simplification cannot be meaningfully made without introducing pi as a fundamental. More generally this also fundamentally means that true physics cannot be expressed using finite precision if ideal grand unified theory as more than one fundamental constant.

The complex numbers are the closure regardless of dimension. When I was writing that I was thinking of the Quaternions, which are the 4 dimensional analog of the complex numbers, in 2^N dimensions this is the Cayley Dickson construction.

The fluke is this: Euclidean space of dimension N has N(N-1)/2 rotational dimensions. If you plug 2 into that you get 2x1/2 which is 1 dimension. i.e. the rotations in 2D space look like a circle. If you add an extra dimension (the radius) you get the polar form of complex numbers.

In other dimensions this doesn't always work. In 3 dimensions we have 3x2/2 = 3 rotational dimensions, so we need a space with dimension 4 (the quaternions). In 4 dimensions we need a 6 dimensional rotation space. We just established that Cayley Dickson algebras only come in powers of 2, so it doesn't fit at all.