I don’t think the subject is inherently difficult. For example quantum computing and quantum cryptography can be explained to anyone with basic clue and basic math skills.
That’s because quantum computing and quantum cryptography only use a subset of quantum theory. Your link says, for example, that the basics of quantum computing only require knowing how to handle ‘discrete (2-state) systems and discrete (unitary) transformations,’ but a full treatment of QT has to handle ‘continuously infinite systems (position eigenstates) and continuous families of transformations (time development) that act on them.’ The full QT that can deal with these systems uses a lot more math.
I wonder if there’s a general trend for people who are interested in quantum computing and not all of QT to play down the prerequisites you need to learn QT. Your post reminded me of a Scott Aaronson lecture, where he says
The second way to teach quantum mechanics leaves a blow-by-blow account of its discovery to the historians, and instead starts directly from the conceptual core—namely, a certain generalization of probability theory to allow minus signs. Once you know what the theory is actually about, you can then sprinkle in physics to taste, and calculate the spectrum of whatever atom you want.
Which is technically true, but if you want to know about quark colors or spin or exactly how uncertainty works, pushing around |1>s and |2>s and talking about complexity classes is not going to tell you what you want to know.
To answer your question more directly, I think the best way to understand quantum physics is to get an undergrad degree in physics from a good university, and work as hard as you can while you’re getting it. Getting a degree means you have the physics-leaning math background needed to understand explanations of QT that don’t dumb it down.
I might be overestimating the amount of math that’s necessary—I’m basing this on sitting in on undergrad QT lectures—but I’ve yet to find a comprehensive QT text that doesn’t use calculus, complex numbers, and linear algebra.
That’s because quantum computing and quantum cryptography only use a subset of quantum theory. Your link says, for example, that the basics of quantum computing only require knowing how to handle ‘discrete (2-state) systems and discrete (unitary) transformations,’ but a full treatment of QT has to handle ‘continuously infinite systems (position eigenstates) and continuous families of transformations (time development) that act on them.’ The full QT that can deal with these systems uses a lot more math.
I wonder if there’s a general trend for people who are interested in quantum computing and not all of QT to play down the prerequisites you need to learn QT. Your post reminded me of a Scott Aaronson lecture, where he says
Which is technically true, but if you want to know about quark colors or spin or exactly how uncertainty works, pushing around |1>s and |2>s and talking about complexity classes is not going to tell you what you want to know.
To answer your question more directly, I think the best way to understand quantum physics is to get an undergrad degree in physics from a good university, and work as hard as you can while you’re getting it. Getting a degree means you have the physics-leaning math background needed to understand explanations of QT that don’t dumb it down.
I might be overestimating the amount of math that’s necessary—I’m basing this on sitting in on undergrad QT lectures—but I’ve yet to find a comprehensive QT text that doesn’t use calculus, complex numbers, and linear algebra.