A friend of mine recently convinced me to take a class on quantum computing. The class just started, but I'm already learning interesting things.

For example, one student linked to a lecture on quantum physics which explains it as a generalization of probability theory which allows for complex numbers (although they're "amplitudes", not "probabilities"):

Quantum mechanics is what you would inevitably come up with if you started from probability theory, and then said, let's try to generalize it so that the numbers we used to call "probabilities" can be negative numbers. As such, the theory could have been invented by mathematicians in the 19th century without any input from experiment. It wasn't, but it could have been.

The class also takes a similar approach, starting with amplitudes and explaining what they are, instead of the standard historical approach, showing the problems with classical physics and explaining how quantum physics solves them. I'm a big fan of this approach, because I think it makes things easier to understand, and I also tend to find history more interesting after I know what "the point" is. I've taken several classes in the past that left the most important information for last (or in the case of Algebra-Based Physics, left the most important information out entirely).

Working with amplitudes is strange, but not as confusing as people make it out to be (probably because I'm looking at this from a mathemetical perspective, and I just accept that there's no way to picture a fundamental particle).

What I did find confusing actually wasn't the wave nature of particles, but how they can also be discrete, or asked another way, "Why does the wave function collapse at all?" Apparently, I need to study quantum decoherence, which is a common explanation, and is initially satisfying to me because it states that the wave function doesn't actually collapse, it just appears to:

Decoherence does not generate actual wave function collapse. It only provides an explanation for the appearance of the wavefunction collapse, as the quantum nature of the system "leaks" into the environment. That is, components of the wavefunction are decoupled from a coherent system, and acquire phases from their immediate surroundings. A total superposition of the global or universal wavefunction still exists (and remains coherent at the global level), but its ultimate fate remains an interpretational issue.

Of course, just because it's satisfying doesn't mean it's real, but right now any explanation would help me to understand this.

Anyway, more updates to come as I understand more of this stuff.