Michael Nielsen has a nice essay up explaining Why the world needs quantum mechanics:

Conventional wisdom holds that quantum mechanics is hard to learn. This is more or less correct, although often overstated. However, the necessity of abandoning conventional ways of thinking about the world, and finding a radically new way – quantum mechanics – can be understood by any intelligent person willing to spend some time concentrating hard. Conveying that understanding is the purpose of this essay.

For a good explanation of Bell inequalities, jump to Michael’s essay.

At the end of the article, Michael compares his essay, explaining Bell inequality violations, with the traditional manner in which quantum theory is taught:

The standard explanation is based on the historical development of quantum mechanics between 1900 and 1930. During that time there were a series of crises in physics. The pattern was that each time some experimental fact would be noticed that seemed hard to explain with the old “classical” way of viewing the world. Each time, physicists would bandage over the old classical thinking with an ad hoc bandaid. This happened over and over again until, in the mid-1920s, the sick patient of classical physics finally keeled over completely, and was replaced with the new framework of quantum mechanics.The problem with this style of explanation, and what makes it confusing, is that none of those early crises was entirely clearcut. In each case, there were physicists who argued that the new experimental results could be explained pretty well with a conventional classical picture. And, in fact, with hindsight, we can now see that some of these crises have pretty good explanations that are essentially classical.

Which made me think: what if we take this idea seriously and tried to teach Bell inequalities *first* (before we tell the students lies about Planck and the Raleigh Jean’s Law)? This is a bit akin to the idea of teaching the basics of quantum computing before teaching the basics of quantum mechanics (i.e. separating the basics of quantum theory from the physics which you put on top of quantum mechanics) but not quite the same. One interesting point about this is that one can’t really explain *why* quantum theory violates Bell inequalities without building up quantum theory. One can, however explain very early on, in line with Michael’s essay, what a Bell inequality is, and that quantum mechanics *does* appear to violate the inequality. Thus the course could very nicely form a circle, as later in the course you could do the quantum mechanical calculation.

More speculatively, the way quantum theory appears to be taught, is very close to the 1950s published textbook of David Bohm. At least in my mind, most of the textbooks of quantum theory follow a similar tact to Bohm’s. Now suppose that we build a large scale quantum computer, such that everyone had easy access to these strange machines. Would this change how we would teach quantum theory?