By Richard E. Bleil, Ph.D.
Last night, I was helping a young student with quantum mechanics. The rules of electronic configuration feel like they are arbitrary. They are actually solutions of a mathematical model. This model is largely accepted as accurate because of its ability to make predictions on systems that are experimentally verifiable. However, the mathematical solutions (numbers) are often given letters and words as symbols, which leads to the feeling of arbitrary rules.
One of the predictions of this model is called, unfortunately, “spin”. As I’ve said, the rules are a mathematical solution to a model, so every aspect of electronic configuration is numerical in nature. For example, one of the final components of the mathematical model came up to have values of either +1/2, or -1/2. To discuss this solution, somebody coined the phrase “spin”, and called +1/2 “spin up”, and -1/2 “spin down”, but they had no concept of with what physical property this corresponds, and we still do not today.
Modern textbooks, including at the university level, will draw a picture of an electron as a sphere with an axis through it, and will state, quite confidently, that “spin up” is the electron spinning clockwise, and “spin down” is the electron spinning counterclockwise. Let me state, for the record, that this is wrong. Just wrong. The principle on which all quantum mechanics is based, which is always taught in any textbook or lecture in quantum mechanics, is the Heisenberg Uncertainty Principle, which states categorically that we are not allowed to know enough about electron behavior to be able to predict if it’s spinning at all, let alone the direction of spin. Reverse the direction of the arbitrarily defined axis, in fact, and the spin is opposite. What’s more, earlier experiments that even predate Heisenberg proves that the electron is behaving as much as a wave than as a particle, so the audacity to draw it as a sphere in and of itself is beyond comprehension.
Okay, by now you are wondering why you are reading an article on quantum theory, but, in fact, you are reading an article lamenting the dumbing down of the American educational system. These college level textbooks are written by university professors, presumably experts in the field, and yet they run through Heisenberg telling us we’re not allowed to know the behavior of electron, and in the same chapter going on to explain the behavior right down to the shape and direction it is moving on its axis.
So why should you care about electron spin? Honestly, unless you have a passion for it as I do, you probably should not. Having a working knowledge with such detail of quantum theory probably will have no impact on your life. But, to live in a society at a time when experts are so arrogant as to be unable to accept that they do not know something, and publishers with such ill-informed editors to allow such enormous mistake through, should very much concern you.
In recent studies, there have been a multitude of errors found in K-12 science textbooks throughout the nation. In one such study, the authors looked at twelve popular K-12 science textbooks and cataloged over five hundred pages of errors. Five hundred pages of errors in just twelve science textbooks. This is unacceptable. Is it any wonder that in international ranking, the US slipped to the 27th place worldwide. This means that there are 26 nations with higher quality K-12 education than the US. “We’re number one?” Really?
This is simply unacceptable. We can do better. It’s one thing to oversimplify science to get concepts across to students who have yet to reach a level to be able to understand the details, but today there are too many authors that clearly do not understand the subjects themselves. At the college level, there is no excuse for an author to fail to understand the difference between heat capacity and specific heat, yet too many advanced chemistry textbooks conflagrate these terms into the meaningless phrase “specific heat capacity”. This shows not only a lack of understanding of the difference, but a distinct lack of attention to detail and lazy attitude to be unwilling to discover the difference before passing their lack of knowledge on to the students. Publishing companies fail to take responsibility for their textbooks by showing a lack of editorial skills to permit these mistakes to be passed along.
And it’s the students who pay the price.