Click to access maths_qm_v3.pdf
This is the third version of my short paper that tries to act as an alternative introduction to Quantum Mechanics (QM).
I’ve changed the title to the more provocative “Why Quantum Mechanics is (mostly) Obvious” in the hope of actually getting someone to read it. I’m keen to get it out there now in case I catch the covid-19 virus. (I have several high risk comorbidities and don’t fancy my chances if I do catch it).
I consider this paper to be, by far, the most important thing I’ve ever written. That may seem odd, since I also claim that there’s nothing actually new in it. All it does is set out the argument for QM in a different order from normal.
Almost without exception, QM is taught in something like the following order.
1. The failures of classical physics are introduced.
2. Some hand wavy justifications for QM are suggested.
3. The full mathematical structure of QM is then introduced as a series of assumptions.
4. It’s interpretation as a theory of probability is justified.
5. QM is applied to a wide range of problems.
This paper completely turns this on its head. It starts out with examples of simple random variables, such as the roll of a die or the spin of a coin, and shows how the mathematical structure of QM inevitably flows from them. The actual physical content that distinguishes quantum mechanics from classical mechanics is actually very small. Most of what I think most people regard as unique to QM is really just the mathematical model that surrounds this.
I’ve tried to make the paper accessible to final year school students or first year university students. In other words, to the very people who might be just about to embark on a first course on QM.
Comments are, of course, very welcome.
Platitude of the Day 