Some familiarity with linear algebra and the notion of quantum states as objects in Hilbert spaces is necessary if you want to follow the logic as it's presented. That's a question of obtaining competence with a mathematical toolkit, which isn't going to be everyone's cup of tea, but it's available to anyone who takes it on.
It's easier, of course, to keep it mysterious by not fully taking that step, and there's nothing wrong with that. But keep a beady eye out for those who assert that quantum mechanics is fundamentally mystical or paradoxical or incoherent, and perhaps aren't sufficiently imaginative to recognise that there are subjects for which far more clarity exists than they may experience themselves. Especially those who make a living by doing so.
There are a lot of them about.
So here we have a public lecture on quantum mechanics by Sidney Coleman of Harvard University, given in 1994. In it, he explains how quantum mechanics is not at all reliant on:
- anything special about the measurement process
- the collapse of the wavefunction
- anything inherently probabilistic or random
- non-locality or spooky action at a distance
It's fashionable to go all out to get people excited about the weirdness of quantum mechanics. And that's great... to start with. Hopefully the people who are truly excited by it will, at some stage, want to know what's going on, rather than just holding on to the idea of it being weird.
Bursting the mystical bubble of something doesn't make the wonder of it go away. It opens it right up, and opens up new worlds with it. As Feynman put it, "It only adds. I can't understand how it subtracts."
If you prefer to get your insights from the greats while watching the wonders of nature and listening to music rather than attending lectures, then I don't blame you. Watch this video instead. It's nice :)Tip of the hat to Matt Strassler.